Quality of Service in Multiservice IP Networks: Second International Workshop, QoS-IP 2003, Milano, Italy, February 24-26, 2003, Proceedings (Lecture Notes in Computer Science, 2601) 3540006044, 9783540006046

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Lecture Notes in Computer Science Edited by G. Goos, J. Hartmanis, and J. van Leeuwen

2601

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Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo

Marco Ajmone Marsan Giorgio Corazza Marco Listanti Aldo Roveri (Eds.)

Quality of Service in Multiservice IP Networks Second International Workshop, QoS-IP 2003 Milano, Italy, February 24-26, 2003 Proceedings

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Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Marco Ajmone Marsan Politecnico di Torino, Dipartimento di Elettronica Corso Duca degli Abruzzi 24, 10129 Torino, Italy E-mail: [email protected] Giorgio Corazza Universit`a di Bologna, DEIS Viale Risorgimento 2, 40136 Bologna, Italy E-mail: [email protected] Marco Listanti Aldo Roveri Universit`a di Roma "La Sapienza", Dipartimento di INFOCOM Via Eudossiana, 18, 00184 Roma, Italy E-mail: {marco/roveri}@infocom.ing.uniroma1.it Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .

CR Subject Classification (1998): C.2, D.2, H.4.3, K.6 ISSN 0302-9743 ISBN 3-540-00604-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Printed in Germany Typesetting: Camera-ready by author, data conversion by Boller Mediendesign Printed on acid-free paper SPIN 10872718 06/3142 543210

Preface

IP has become the dominant paradigm for all sorts of networking environments, from traditional wired networks to innovative networks exploiting WDM links and/or wireless accesses. Key to the success of IP is its flexibility that allows the integration within one network of a number of systems which at lower layers may have different characteristics, as well as the transport over a common infrastructure of the traffic flows generated by a variety of applications (web browsing, email, telephony, audio and video distribution, multimedia multicasting, financial transactions, etc.) whose performance requirements may be extremely different. This situation has generated a great interest in the development of techniques for the provision of quality-of-service guarantees in IP networks offering a variety of services through a range of different user interfaces (wired and wireless, of different nature). In 2001 and 2002, the Italian Ministry of Education, Universities and Research funded four research programmes on these topics, named IPPO (IP packet optical networks), NEBULA IP (techniques for end-to-end quality-of-service control in multidomain IP networks), PLANET-IP (planning IP networks), and RAMON (reconfigurable access module for mobile computing applications). At the end of their activity, these four programmes organized in Milan, Italy in February 2003 the (QoS-IP 2003), for the presentation of high-quality recent research results on QoS in IP networks, and for the dissemination of the most relevant research results obtained within the four programmes. This volume of the LNCS series contains the proceedings of QoS-IP 2003, including 1 invited paper as well as 53 papers selected from an open call. These very high quality papers provide a clear view of the state of the art of the research in the field of quality-of-service provisioning in multiservice IP networks, and we hope that these proceedings will be a valuable reference for years to come. This volume benefitted from the hard work of many people: the researchers of IPPO, NEBULA, PLANET-IP, and RAMON, the paper authors, the reviewers, and the LNCS staff, Alfred Hofmann in particular. We wish to thank all of them for their cooperation. Special thanks are due to Luigi Fratta and Gian Paolo Rossi for taking care of the conference organization in Milan, and to Michela Meo, Claudio Casetti, and Maurizio Munaf` o for their help in the preparation of the technical program of QoS-IP 2003.

December 2002

Marco Ajmone Marsan Giorgio Corazza Marco Listanti Aldo Roveri

Organization

Program Committee Program Committee Cochairs Marco Ajmone Marsan (Politecnico di Torino) Giorgio Corazza (Universit`a di Bologna) Marco Listanti (Universit`a di Roma, La Sapienza) Aldo Roveri (Universit` a di Roma, La Sapienza) Program Committee Members Anthony Acampora Ian F. Akyildiz Mohammed Atiquzzaman Tulin Atmaca Andrea Baiocchi Mario Baldi Albert Banchs Roberto Battiti Giuseppe Bianchi Nicola Blefari-Melazzi Chris Blondia Franco Callegati Pietro Camarda Andrew T. Campbell Augusto Casaca Olga Casals Claudio Casetti Carla-Fabiana Chiasserini Franco Davoli Edmundo A. de Souza e Silva Christophe Diot Lars Dittman Jos`e Enr`ıquez-Gabeiras Serge Fdida Enrica Filippi Viktoria Fodor Andrea Fumagalli Rossano Gaeta Richard Gail Giorgio Gallassi

Stefano Giordano Weibo Gong Enrico Gregori Ibrahim Habib Mounir Hamdi Boudewijn Haverkort Sundar Iyer Bijan Jabbari Laszlo Jereb Denis A. Khotimsky Daniel Kofman Udo Krieger Santosh Krishnan Anurag Kumar T.V. Lakshman Jean-Yves Le Boudec Luciano Lenzini Emilio Leonardi Christoph Lindemann Alfio Lombardo Saverio Mascolo Marco Mellia Michela Meo Sandor Molnar Masayuki Murata Michele Pagano Sergio Palazzo Krzysztof Pawlikowski George C. Polyzos Ramon Puigjaner

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Organization

Carla Raffaelli Roberto Sabella Stefano Salsano Fausto Saluta Andreas Schrader Matteo Sereno Dimitris Serpanos Rajeev Shorey Aleksandra Smiljanic Josep Sol`e-Pareta

Organizing Committee Organizing Committee Cochairs Luigi Fratta (Politecnico di Milano) Gian Paolo Rossi (Universit` a di Milano) Organizing Committee Members Antonio Capone (Politecnico di Milano) Fiorella Moneta (Politecnico di Milano) Elena Pagani (Universit` a di Milano)

Sponsoring Institution Ericsson Lab Italy

Tatsuya Suda Guillaume Urvoy-Keller Yutaka Takahashi Tetsuya Takine Asser Tantawi Phuoc Tran-Gia Sergio Treves Adam Wolisz

Table of Contents

Analytical Models I On Evaluating Loss Performance Deviation: A Simple Tool and Its Practical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Extending the Network Calculus Pay Bursts Only Once Principle to Aggregate Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Modelling the Arrival Process for Packet Audio . . . . . . . . . . . . . . . . . . . . . . .

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On Packet Delays and Segmentation Methods in IP Based UMTS Radio Access Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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QoS Routing On Performance Objective Functions for Optimising Routed Networks for Best QoS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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An Adaptive QoS-routing Algorithm for IP Networks Using Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A QoS Routing Mechanism for Reducing the Routing Inaccuracy Effects .

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Stability and Scalability Issues in Hop-by-Hop Class-Based Routing . . . . . 103

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Table of Contents

Measurements and Experimental Results Network Independent Available Bandwidth Sampling and Measurement . . 117

Less than Best Effort: Application Scenarios and Experimental Results . . 131

TStat: TCP STatistic and Analysis Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

End-to-End QoS Supported on a Bandwidth Broker . . . . . . . . . . . . . . . . . . . 158 Multidomain End to End IP QoS and SLA . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

QoS Below IP Dimensioning Models of Shared Resources in Optical Packet Switching Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Efficient Usage of Capacity Resources in Survivable MPλS Networks . . . . 204

Performance Evaluation of a Distributed Scheme for Protection against Single and Double Faults for MPLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

Edge Distributed Admission Control for Performance Improvement in Traffic Engineered Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

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End-to-End QoS in IP Networks Bandwidth Estimation for TCP Sources and Its Application . . . . . . . . . . . . 247

Best-Effort and Guaranteed Performance Services in Telecommunications Networks: Pricing and Call Admission Control Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

TCP Smart Framing: A Segmentation Algorithm to Improve TCP Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Live Admission Control for Video Streaming . . . . . . . . . . . . . . . . . . . . . . . . . 292

QoS Multicast : An Overlay Scheme for Quality of Service Differentiation in Source Specific Multicast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

Directed Trees in Multicast Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

A Proposal for a Multicast Protocol for Live Media . . . . . . . . . . . . . . . . . . . 334

On the Use of Sender Adaptation to Improve Stability and Fairness for Layered Video Multicast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

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Analytical Models II A New Fluid-Based Methodology to Model AQM Techniques with Markov Arrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

Stochastic Petri Nets Models for the Performance Analysis of TCP Connections Supporting Finite Data Transfer . . . . . . . . . . . . . . . . . . . . . . . . 372

A Queueing Network Model of Short-Lived TCP Flows with Mixed Wired and Wireless Access Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

TCP-SACK Analysis and Improvement through OMQN Models . . . . . . . . 405

Optical Networks QoS Provision in Optical Networks by Shared Protection: An Exact Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Design of WDM Networks Exploiting OTDM and Light-Splitters . . . . . . . 433

DWDM for QoS Management in Optical Packet Switches . . . . . . . . . . . . . . 447

Space Division Architectures for Crosstalk Reduction in Optical Interconnection Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

Table of Contents

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Reconfigurable Protocols and Networks The RAMON Module: Architecture Framework and Performance Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

Reconfigurable Packet Scheduling for Radio Access Jointly Adaptive to Traffic and Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

Mobility Management in a Reconfigurable Environment: The RAMON Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

Improving End-to-End Performance in Reconfigurable Networks through Dynamic Setting of TCP Parameters . . . . . . . . . . . . . . . . . . . . . . . . 513

Provision of Multimedia Services Adaptive MPEG-4 Video Streaming with Bandwidth Estimation . . . . . . . . 525

Dynamic Quality Adaptation Mechanisms for TCP-friendly MPEG-4 Video Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

Traffic Sensitive Active Queue Management for Improved Multimedia Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

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Table of Contents

A QoS Providing Multimedia Ad Hoc Wireless LAN with Granular OFDM-CDMA Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

QoS in Multidomain Networks SIP Originated Dynamic Resource Configuration in Diffserv Networks: SIP / COPS / Traffic Control Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 581

Virtual Flow Deviation: Dynamic Routing of Bandwidth Guaranteed Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592

Design and Implementation of a Test Bed for QoS Trials . . . . . . . . . . . . . . . 606

A Linux-Based Testbed for Multicast Sessions Set-Up in Diff-Serv Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

Invited Paper Light-Trails: A Solution to IP Centric Communication in the Optical Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634

Congestion and Admission Control End-to-End Bandwidth Estimation for Congestion Control in Packet Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645

Table of Contents

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Priority-Based Internet Access Control for Fairness Improvement and Abuse Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

A Probing Approach for Effective Distributed Resource Reservation . . . . . 672

Dynamic Adaptation of Virtual Network Capacity for Deterministic Service Guarantees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

Architectures and Protocols for QoS Provision Towards RSVP Version 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704

Analysis of SIP, RSVP, and COPS Interoperability . . . . . . . . . . . . . . . . . . . . 717

Simulation Study of Aggregate Flow Control to Improve QoS in a Differentiated Services Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729

Quality of Service Multicasting over Differentiated Services Networks . . . 742

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757

On Evaluating Loss Performance Deviation: A Simple Tool and Its Practical Implications Ying Xu and Roch Gu´erin Department of Electrical and Systems Engineering, University of Pennsylvania (yingx,guerin)@ee.upenn.edu

Abstract. The focus of this paper is on developing and evaluating a practical methodology for determining if and when different types of traffic can be safely multiplexed within the same service class. The use of class rather than individual service guarantees offers many advantages in terms of scalability, but raises the concern that not all users within a class see the same performance. Understanding when and why a user will experience performance that differs significantly from that of other users in its class is, therefore, of importance. Our approach relies on an analytical model developed under a number of simplifying assumptions, which we test using several real traffic traces corresponding to different types of users. This testing is carried out primarily by means of simulation, to allow a comprehensive coverage of different configurations. Our findings establish that although the simplistic model does not accurately predict the absolute performance that individual users experience, it is quite successful and robust when it comes to identifying situations that can give rise to substantial performance deviations within a service class. As a result, it provides a simple and practical tool for rapidly characterizing real traffic profiles that can be safely multiplexed.

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Introduction

To design a successful QoS service model, it is often necessary to trade-off the performance guarantees that the service model can provide the associated operational and management complexity so that the QoS guarantees needed by end users can be provided while the service model is kept simple enough to meet deployment constraints. Most recently, there has been a renewed interest in investigating aggregate QoS solutions, due to the fact that they can greatly improve scalability, and therefore reduce the associated operational and management complexity. In a typical aggregate QoS service model, individual flows are multiplexed into a common service class and treated as a single stream when it comes to QoS guarantees, which eliminates the need for per-flow based state and processing. Such an approach is reflected in recent proposals such as the IETF Diff-Serv model [3]. By coarsening the different levels of QoS that the network offers into a small number of service classes, the Diff-Serv model is expected to 

This work was supported in part through NSF grant ITR00-85930.

M. Ajmone Marsan et al. (Eds.): QoS-IP 2003, LNCS 2601, pp. 1–18, 2003. c Springer-Verlag Berlin Heidelberg 2003 

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scale well. However, this gain in scalability through aggregation comes at the cost of losing awareness of the exact level of performance that an individual user experiences. More specifically, because performance is now monitored and enforced only at the aggregate class level, it is not clear whether performance guarantees extend to all individual users in the service class. In particular, it is possible that a given user experiences poor performance without this being noticed at the class level. This issue was explored in an earlier work [9], which focused on the loss probability as the relevant metric. [9] developed a number of models to evaluate the individual loss probabilities and the overall loss probability, in which user traffic are represented by either Markov ON-OFF sources or periodic sources. Using these analytical models, the deviation between individual loss probabilities and the overall loss probability was evaluated for a broad range of configurations. The major conclusion was that there are indeed cases where significant performance deviations can exist, and that user traffic parameters can have a major influence on whether this is the case or not. In this paper, we go beyond the work of [9] by developing a simple methodology capable of evaluating loss performance deviations in realistic settings. Specifically, we concentrate on the ability to predict performance deviations when aggregating traffic sources such as voice and video, which may not be accurately captured by the simplified source models introduced in [9]. In contrast to the existing body of work on call admission control, which is aimed at dynamically deciding whether or not to accept a flow-level request, our methodology is aimed at providing decisions about whether or not to assign different types of traffic streams to the same service class, given their source statistics. Our investigation starts with mapping real traffic sources onto “equivalent” Markovian sources. This mapping is, however, limited to matching first order statistics. Our rationale for using such an approach is, as is discussed later in the paper, based on our expectation that performance deviations are less sensitive to source modeling inaccuracies than absolute performance measures. The efficacy of this simple approach is then evaluated by means of simulations for a broad range of scenarios where multiple real-time traffic sources, i.e., voice and/or video sources, are aggregated, which we believe can also help gain a better understanding of whether and when an aggregate service model is suitable for supporting real-time applications. The reliability and robustness of the approach are further analyzed in Section 6, where we use worst case analysis to explicitly evaluate its intrinsic limitations in predicting performance deviations using only first order statistics. The rest of the paper is structured as follows: Section 2 describes our model and methodology for loss deviation prediction. Sections 3 and 4 report experimental results for two different boundary configurations, while results for the intermediate configuration are reported in Section 5. In Section 6, we conduct a worst case analysis of the performance of our solution. We concentrate on the main results, and most of the derivations are relegated to a technical report [10]. Finally, Section 7 summarizes the findings and implications of the paper.

On Evaluating Loss Performance Deviation

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3

Model and Methodology

The system we consider consists of multiple users that belong to a common service class, each of which is connected through its access link to an aggregation point, which is modeled as a single server, finite buffer, FIFO queue. In this section, we review the different configurations that we consider and the performance measures that we use to evaluate loss performance deviation. The voice and video traffic sources and their characteristics are then described together with the method we use for mapping them to sources that our analytical model can deal with. The simulation environment that we use is also briefly presented at the end of the section. Due to space constraints, we omit detailed descriptions of the analytical models used, as they were presented in [9]. 2.1

System Parameters and Loss Deviation Evaluation

System Parameters. The first parameter we vary is the number of users aggregated in the same service class, i.e., the number of traffic sources multiplexed in the FIFO queue. In particular, we focus on two cases: a two-source configuration and a “many-source” one, which correspond to two different boundary conditions, i.e., an environment where few large bandwidth connections share resources, and one where many “small” flows are multiplexed into the same queue. Another system parameter we consider is the size of the FIFO queue into which flows are multiplexed. In our simulations, we consider both a system with a relative small buffer size and another system with a relative large buffer size. In most cases, the qualitative behavior of the two systems is similar, and thus typically only results corresponding to one of them are reported. Evaluation Methodology. In a system with N users, let PL denote the overN all loss probability, PLi the loss probability of user i, and Pmax the maximum loss probability experienced by an individual user (without loss of generality, it is usually assumed to be user N ) among all the users. We first evaluate the amount of bandwidth C needed to ensure an overall loss probability PL ≤ Pmax , where Pmax corresponds to the target loss probability of the service N /PL . class. We then compute the loss probability ratio P LR = Pmax In addition, we also evaluate, the percentage by which the bandwidth N ≤ Pmax . allocated to the service class needs to be increased to ensure that Pmax In other words, if CN denotes the minimum amount of bandwidth needed so N that Pmax ≤ Pmax , we evaluate the quantity (CN − C)/C. The (maximum) loss probability ratio reflects the magnitude of the loss deviation when service guarantees are only provided at the aggregate level, and is therefore the metric we use to assess whether traffic aggregation is safe or not. Conversely, the additional bandwidth needed measures the cost of eliminating deviations for a given traffic mix. In addition to these two metrics, we also introduce a “consistency test” that measures the ability of our model to successfully predict scenarios where severe performance deviations will arise. The test relies

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on a “threshold” region, [P LRmin , P LRmax ], that is used to separate risky traffic mixes, i.e., mixes that give rise to large deviations, from safe ones. Specifically, if the loss probability ratio is less than P LRmin , the traffic mix is considered “definitely safe”, if it is greater than P LRmax , the traffic mix is deemed “definitely dangerous”, and if it falls between those two values, i.e., inside the threshold region, the traffic mix is flagged as potentially risky and requiring additional investigations. Ideally, the threshold region should be as narrow as possible, but depending on the accuracy of the model, too narrow a region may either yield a large number of false alarms or fail to properly identify harmful configurations. A wider threshold region reduces those problems at the cost of some imprecision in terms of classifying certain scenarios. We believe that introducing such a “grey” region provides greater flexibility, and can help minimize the impact of inaccuracies inherent in our evaluation methodology. Our hope is that a reasonably narrow threshold region is sufficient to flag the various traffic mixes for which the model might provide inaccurate answers. 2.2

Real-Time Traffic Traces and Mapping Methodology

Source Traces. The video traces we use to conduct our study are obtained from an online video trace library [2]. We chose this public library because of the diversity of the traces it provides. The library contains traces of 26 different hourlong video sequences, each encoded using two different standards (the MPEG4 and the H.263 standard), and under three different quality indices (low, medium and high). For each recorded trace, statistics reflecting its characteristics are also available. We refer to [4] for a detailed description of the trace collection procedure and the methodology used to extract the trace statistics. Table 1. Video Trace Statistics Trace Name Mean Frame Mean Bit Frame Size Frame Size Size (Bytes) Rate (Kb/sec) (Peak/Mean) (Covariance) Jurassic (low) 768.6 153.7 10.6 1.4 Jurassic (high) 3831.5 766.3 4.4 0.6 Lecture (low) 211.7 42.3 16.2 2.3

In our study, we rely mainly on 3 different sequences encoded using the MPEG4 codec with a frame rate of 25 frames/sec. These include the low quality and high quality traces of the movie Jurassic Park I and the low quality trace of a lecture video. The high quality trace of Jurassic Park I (Jurassic high) represents a video source that requires high transmission rate due to its quality requirement. The low quality trace of Jurassic Park I (Jurassic low) represents a lower rate source encoded from the same movie scene. At last, due to its scene characteristics, the low quality lecture trace (Lecture low) is selected because it has the lowest mean rate among all the traces in the video library. Several important statistics of the three video sources are given in Table 1.

On Evaluating Loss Performance Deviation

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Table 2. Voice Trace Statistics Trace Name Mean Spurt Mean Gap Peak Rate Utilization Length (ms) Length (ms) (Kb/sec) Voice 326 442 64 0.425

We also use voice traces from [7] in our investigation. In particular, the voice source that we choose corresponds to Fig. 4b in [7] and was generated using the NeVoT Silence Detector(SD) [8]. We refer to [7] for a complete description of the codec configuration and trace collection procedure. In Table 2 important statistics of the voice source are given. Converting to Markov ON-OFF Sources. Due to the nature of voice and video traffic generation, both the voice traffic and the video traffic inherit builtin ON-OFF patterns, which facilitates the usage of a Markov ON-OFF source to model them. A Markov ON-OFF source can be represented by a 3-tuple < R, b, ρ >, where R is the transmission (peak) rate when the source is active, b is the average duration of an active or ON period, and ρ represents the fraction of time that the source is active, or its utilization. Our task, is thus to capture a real traffic source using the above 3-tuple, based on its characteristics reflected by statistics given in Table 1 and 2. The raw video traffic consists of variable size frames that arrive at regular time intervals (40ms for the traces we use). In our study, we assume that a frame arrives instantaneously, so that the access link serves as a shaper, bounding the maximum rate of the output traffic by its own transmission speed. Assuming a fluid model, the output traffic can be thought of as a distorted version of the input traffic, where the frame transmission (ON period) extends over a time interval that is a function of the frame size and the input link speed. If the link speed is too slow to transmit a frame in 40ms, consecutive frames will be concatenated and form an extended burst. In the experiments that we conduct, we deliberately eliminate such frame concatenation by setting the link speed larger than the peak frame-level bit rate 1 . The shaped traffic emanated by the access link can thus be modeled by an equivalent ON-OFF source, with: R = Rlink ; b =

Favg b ; ρ= . Rlink 40 · 10−3

(1)

where Rlink is the access link speed and Favg is the average frame size of the video trace. We do not expect that such a simple source model will fully capture all the complex traffic characteristics of a video source. Specifically, although the mean of the burst duration is accurately captured, its distribution does not have to 1

We found that if the access link speed is less than the peak frame-level bit rate, then several extremely long bursts may occur and the delay at the access link could be quite large.

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be exponential. This may affect the accuracy of estimating the absolute loss probability. However, we believe this is still a reasonable approach based on the experience obtained from [9], where we saw that deviations were to a large extent a function of the first order statistics of a source, e.g., the peak rate, the utilization, and the average burst duration, among which the first two parameters usually played a dominant role. Furthermore, as discussed in Section 6, there are actually many cases for which the differences between the model’s prediction and the actual deviation can be shown to be small, and most important, independent of the burst duration distribution. As with video sources, the traffic of voice sources can be divided into “ON” and “OFF” periods, corresponding to the talk spurt and silence period in human speech. Again, while those periods need not always be exponentially distributed, our expectation is that this will only minimally impact our ability to predict loss probability ratios when mixing voice and other traffic sources. Hence, the mapping of voice sources onto ON-OFF sources is carried out using the values shown in Table 2, i.e., R = 64Kb/sec; b = 326ms and ρ = 0.425. Note that since voice traffic is reasonably smooth, i.e., during a burst period the voice source generates multiple packets of 80 Bytes with an equal spacing of 10ms, the peak rate of the equivalent ON-OFF voice source is fixed at 64Kb instead of equal to the link capacity2 . As we shall see later, this smoothness enables the voice source to avoid major performance degradation when aggregated with video sources, in spite of its small traffic contribution. Once video and voice sources have been mapped onto Markov ON-OFF sources, we can apply the analytical models developed in [9] to evaluate both individual and overall loss probabilities. Specifically, in the cases where only two sources are aggregated, we use Equations (1) and (2) in [9] to calculate both the individual and the overall loss probabilities. As in the many-source case, Equations (6) and (7) of [9] are applied. 2.3

Simulation Environment and Experimental Configuration

In order to assess the accuracy of our simplified model, we rely on simulations to evaluate the true loss probabilities and loss probability ratios. Moreover, in order to examine the cost associated with the aggregation process, we also conduct simulations to evaluate the amount of additional bandwidth needed. We use the NS2[1] simulator, as it can accurately model packet level behaviors. In all of our simulations, the packet size of the voice traffic is fixed at 80Bytes while the packet size of the video traffic is fixed at 100Bytes, so that a video frame larger than 100Bytes is fragmented into multiple packets. Throughout the paper, the threshold region is set as [3, 5] and the target loss probability Pmax , when fixed, is set to 10−4 . For simplicity, most of our experiments consider only two different types of sources, where one of the two types of sources is selected and has its parameters varied so that it experiences the larger loss probability. The parameters of the other type of sources are always fixed. 2

The peak rate will be equal to the access link speed only when it is less than 64Kb/sec, which is lower than the values assumed in this paper.

On Evaluating Loss Performance Deviation

3

7

Loss Deviation Prediction when Aggregating Two Sources

This section is devoted to scenarios with only two sources aggregated. This basic configuration, despite or rather because of its simplicity, provides useful insight in capturing the complex behavior of loss deviation. From [9], we know that a user experiences losses that differ significantly from the overall losses, if it both contributes significantly to the onset of congestion when active, and does it in a way that is undetected by resource allocation mechanism. When applied to two (few) sources, this rule indicates that the utilization of an individual source plays a dominant role in determining any loss deviation it experiences. Specifically, when multiplexing two sources, if one of them has a much smaller utilization than the other but a comparable peak rate, its total traffic contribution will be minor and unlikely to trigger the allocation of significant resources, yet its impact on congestion, and therefore losses, when active can be substantial. This observation was quantified in [9] using analytical models, and as we will see in this paper, also apply to the real-life traffic sources we consider. More important, we will establish that the simple methodology we have developed, is indeed capable of accurately capturing this qualitative behavior. 3.1

Aggregating Two Video Sources

In this sub-section, we consider scenarios consisting of aggregating two video sources. The first case involves multiplexing Jurassic low and Jurassic high, which corresponds to two video streams of similar characteristics but different quality and, therefore, bit rate. A second scenario considers the case of two video streams, Lecture low and Jurassic high, which differ in both characteristics and quality (bit rate). In each case, we increase the access speed of the lower bit rate sequence so that it has a larger peak rate and lower utilization than the higher bit rate sequence, and thus is expected to experience a larger loss probability. The buffer size is set to 5000 Bytes and to 2000 Bytes3 in the first and second scenarios, respectively. The loss probability ratio of each scenario is shown in Figure 1. From Figure 1(a), we see that when Jurassic low and Jurassic high are multiplexed, performance deviations can arise, as the loss probability ratio approaches a value of about 6. More important, the simple model we propose can be seen to accurately capture the trend and magnitude of this deviation. The relatively limited range of the loss probability ratio (it never exceeds 6) can be explained by the fact that although the two sources differ in utilization, the low bit rate source, Jurassic low, is not a negligible contributor to the overall traffic. This in turn limits the extent to which the performance experienced by the Jurassic low stream can deviate for the overall performance. In general, the impact of the relative traffic contribution of the two sources being multiplexed can be captured through an 3

We also explore different buffer size (200Bytes) but didn’t find significantly different results from the data here.

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upper bound on the loss probability ratio that only involves the mean rate of the two sources. Specifically, in a configuration with N sources being multiplexed, where, without loss of generality, the N -th source is the one experiencing the larger loss probability, the loss probability ratio satisfies: P LR =

N /rSN rN /rN 1 rL ≤ LN S = N . rL /rS rL /rS rS /rS

(2)

N and rSN correspond to the long term loss speed, i.e., the amount of where rL data lost per unit of time, and transmission speed of source N , and rL and rS correspond to the overall long term loss speed and transmission speed, respectively. Equation (2) states that the loss probability ratio P LR can never exceed a value that is inversely proportional to the fraction of traffic contributed by the worst performer in a service class. The smaller the fraction this user contributes, the larger the maximum loss probability ratio it may experience. In this example, Jurassic low is the source that loses more and from Table 1, we see that rS2 = 153.7Kb/sec, which is about 16.7% of the total traffic, resulting in a loss probability ratio satisfying P LR ≤ 6. As can be seen from Figure 1(a), as the access link speed of Jurassic low increases, the loss probability ratio will indeed approach (and never exceed) this value. Equation 2 indicates that when multiplexing two (or a small number of) sources, the more likely candidate for experiencing significant loss deviation is the source with the smallest bit rate. Furthermore, Equation 2, also shows that in the case of two sources, the higher bit rate source can never experience a loss probability of more than twice the overall loss probability.

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Fig. 1. Loss Probability Ratio When Aggregating Video Sources

Figure 1(b) displays the loss probability ratio when multiplexing Lecture low and Jurassic high, for which a maximum value even greater than that of the first scenario can be attained. In particular, we see that the Lecture low source

On Evaluating Loss Performance Deviation

9

can experience losses that are up to 20 times larger than the overall losses. This is primarily due to the lower (relative) rate of Lecture low, which only contributes about 5.2% of the total traffic. From equation (2), this implies that the loss probability ratio should satisfy P LR ≤ 19.1. From Figure 1(b), we see that as the link speed increases, the loss probability ratio indeed approaches this upper bound. The loss probability ratio predicted by the model is, however, not as accurate as in the case of Figure 1(a), as it consistently underestimates the actual loss probability ratio. This is because high order statistics of the traffic generated by both sources still influence the magnitude of the loss probability ratio. This impact notwithstanding, the model still generates a value that in most cases is sufficiently high to at least trigger a warning regarding to the potential danger of multiplexing these two sources. In particular, except for the lowest link speed, the loss probability ratio predicted by the model is always within or above the selected threshold region of [3, 5].

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Fig. 2. Additional Bandwidth Needed When Aggregating Video Sources Figure 2 provides a different view on the differences in performance between the two sources. It shows the additional bandwidth (in percentage) needed in order to ensure the desired loss probability for even the poorer performer of the two sources. As can be seen, this amount can be quite large (30% for the more benign case of Jurassic low and Jurassic high, and up to 60% for the more severe case of Lecture low and Jurassic high). This means that the observed differences in performance cannot be easily fixed through standard over-provisioning, and identifying such potentially dangerous scenarios is, therefore, important. 3.2

Aggregating One Video Source and One Voice Source

In this section, we study scenarios where one video source and one voice source are multiplexed. From Table 1 and Table 2, we can see that the voice source has a mean transmission rate that is much lower than that of the video source, for

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both the Jurassic low and Jurassic high sources. When used in equation (2) this translates into a relatively large upper bound for P LR, which could, therefore, indicate a potentially dangerous traffic mix. This turns out not to be the case because of the reasonably smooth nature of the voice source, which makes it mostly immune to performance deterioration when multiplexed with either the Jurassic low or the Jurassic high video sources. Instead, it is the video source that experiences somewhat poorer performance. The magnitude of this performance deviation is, however, limited, because the video source is the major contributor to the overall transmission rate (equation (2) gives an upper bound of 1.04 and 1.18 for the P LR for Jurassic low and Jurassic high, respectively). As a result, our main concern in these scenarios is whether the model will generate a false alarm, i.e., falsely predict that mixing a voice and a video sources is potentially dangerous.

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Fig. 3. Loss Probability Ratio When Aggregating One Video and One Voice The corresponding results are shown in Figure 3. From the graphs, we see that for both Jurassic low and Jurassic high, the model tracks the actual loss probability ratio reasonably accurately. More important, it will not generate any false alarm and will consistently identify the traffic mixes as safe. As an aside, the amount of additional bandwidth needed to ensure that both the voice and video sources experience the desired loss probability target can also be found to be small (less than 3%), which further confirms that mixing a voice and a video source should be fine in practice.

4

Loss Deviation Prediction when Aggregating Many Sources

The previous section dealt with the special case of only two sources, which while interesting in its own right, is clearly not the only or even most common scenario

On Evaluating Loss Performance Deviation

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one would expect to encounter in practice. In this section, we consider another set of possibly more realistic scenarios consisting of mixing many voice and video sources. As before, our goal is to determine whether the model is capable of accurately distinguishing between safe and unsafe traffic mixes. For sake of simplicity and in order to limit the number of combinations to consider, we limit ourselves to multiplexing two different types of sources. According to the discussion of Section 3, for one or more sources to experience substantially worse losses than other sources, the peak rate of the source should typically be high while its contribution to the total rate should be small enough to ensure that the losses experienced by itself only have a small impact on the overall loss probability. The latter typically implies a combination of a low average transmission rate and a small number of its peers. We therefore concentrate on such scenarios and evaluate the model’s ability to properly identify cases when severe loss deviations can occur. 4.1

A First Many-Source Example

In this first example, the dominant traffic contributors consist of 500 voice sources that are multiplexed with a , Jurassic low video source4 . The loss performance deviation is examined for a system where the buffer size is set to 5000 Bytes and for configurations where the access link speed of the video source increases from 5Mbps to 200Mbps, while the access link speed of the voice sources is fixed at 5Mbps. Given that the Jurassic low source has a reasonably high peak rate but only contributes a small amount to the total bit rate, we expect this scenario to be a prime candidate for generating significant differences in the loss probabilities that the voice and video sources experience. The resulting loss probability ratio is shown in Figure 4(a). As seen in Figure 4(a), as the video source’s access link speed grows, so does the loss probability ratio, and this evolution is accurately captured by the model even if it slightly over-estimates the actual value. This over-estimation does, however, not affect the model’s ability to correctly identify cases where significant deviations occur. The figure also shows that for the configurations considered, the range of possible deviations is substantially larger than that of the two-source scenarios of Section 3. This is not unexpected, as the traffic contributed by the video source is much smaller (only 1.12%) in comparison to the total traffic volume than was the case in the two-source scenarios. This very small contribution to the overall traffic translates into an upper bound of 89.5, when using Equation 2, and we can again see that this value is essentially achieved at high link speeds. As with the two-source case, we also investigate by simulation the amount of additional bandwidth needed to ensure that all sources experience at least the 4

We have conducted another set of experiments in which 500 voice sources and a single Jurassic high video source are aggregated. Since the results are similar to those reported in this section, both qualitatively and quantitatively, we omit reporting it here.

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Ying Xu and Roch Gu´erin 2 5 0

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Fig. 4. Aggregating 500 voice sources and one video source (Jurassic low) target performance of 10−4 . The results are shown in Figure 4(b), where we can again see that over-allocation is not an option in the cases where substantial performance deviations exist. In particular, when the link speed is high, more than twice the allocated bandwidth is required to guarantee adequate performance for the video sources. Based on the earlier discussion, significant performance deviation arises in the many-source case only when sources have both a high peak rate (high enough to trigger the onset of congestion when the source becomes active) and represent a small contribution to the overall bit rate (their higher losses do not contribute much to the overall loss probability). The one video source, many voice sources scenario is a perfect illustration of such an “unsafe” configuration. In contrast, a scenario with a small number of voice sources and many video sources would not result in any significant deviations and would be very close to what was observed in the previous section for a one voice source and one video source configuration. In the next section, we investigate the behavior of the system when it transits from an “unsafe” region to a “safe” one. 4.2

Transiting from Unsafe to Safe Traffic Mixes

In this section, we consider a number of scenarios consisting of a mixture of voice and video sources, and where the fraction of traffic contributed by each type of sources varies. Specifically, we start with a configuration consisting of 500 voice sources and one video source (Jurassic low). The access link speed of voice sources is taken to be 5 Mbps, while it is set to 200 Mbps for the video source. We then increase the number of video sources while keeping the total traffic rate fixed. As a result, the number of voice sources decreases and the total traffic contribution of video sources increases, which affects the possibility for performance deviations. In particular, as the traffic contribution from video sources becomes dominant, performance deviations are all but eliminated.

On Evaluating Loss Performance Deviation 2 5 0 s im u la tio n m o d e l

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Fig. 5. A Variable Traffic Mix Scenario

The results are shown in Figure 5(a), which illustrates that as the traffic contribution from the video sources first increases, the loss probability ratio experiences a sharp initial drop. This is followed by a slower decrease towards a level where performance deviations are essentially negligible. Specifically, when video sources contribute about 20% of the total traffic, the loss probability ratio has dropped to 4.6, down from 80 for a single video source. The loss probability ratio drops further to 2.3 for a video traffic contribution of 40%, and to 1.7 for a video traffic contribution of 60%. As illustrated in Figure 5(b), this general behavior is mirrored in the amount of additional bandwidth needed to eliminate the performance penalty incurred by video sources. More important from the perspective of assessing the ability of our model to accurately predict whether it is safe or not to mix traffic, the model consistently tracks the actual loss probability ratios across the range of scenarios. From a practical standpoint, this section provides an important guideline for determining when it is safe to mix traffic sources that differ significantly in both their peak and mean rates. Specifically, although there are a number of configurations for which it is safe to mix such sources, transiting from unsafe to safe configurations is not a well demarcated process. As a result, a generally safe practice is to altogether avoid multiplexing sources that differ too much in both their peak and mean rates.

5

Intermediate Configurations

As is seen in Section 3 and Section 4, the behavior of loss performance deviation differs significantly between the two-source and the many-source cases. Specifically, in the two-source case, source utilization alone can result in significant performance deviations, while in the many-source case both peak rate and utilization are involved. In this section, we study a few intermediate configurations that can help shed some light on the transition between the two-source

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and the many-source behaviors. Our goal is to ensure that this understanding is adequately incorporated into the simple methodology we propose to determine whether it is safe to multiplex different traffic sources.

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Fig. 6. Increasing the Number of Voice Sources The configuration we use for our investigation consists of multiplexing a variable (from 1 to 500) number of voice sources with one video source (Jurassic low). This allows us to explore the evolution from a safe, two-source traffic mix to an unsafe, many-source mix. The loss probability ratios and the additional bandwidth required (in percentage) are plotted for this range of scenarios in Figure 6(a) and Figure 6(b) respectively. As can be seen from the figure, the model is quite accurate in predicting the loss probability ratio across all scenarios. In addition, the transition from safe to unsafe regions is shown to be progressive, roughly following a linear function, but with a fairly steep slope. Specifically, mixing the video source with just 50 voice sources already yields a loss probability ratio close to 10, and it would take 50% more bandwidth to fix the problem. This is quite significant, especially in light of the fact that the traffic contribution of the video source is about one tenth of the total traffic, i.e., not an insignificant amount. This again highlights the fact that it is better to err on the side of caution when considering mixing traffic sources with rather disparate peak and mean rates.

6

Discussions of Prediction Errors

One of the main assumptions behind the approach used in this paper, is that while the underlying analytical model may be too simplistic to accurately compute it is capable of robust predictions when it comes to The obvious question that this assumption raises is “why would two wrongs make a right?” This section is an attempt at answering part of this question.

On Evaluating Loss Performance Deviation

6.1

15

Prediction Error in the Two-Source Case

The error in computing loss probabilities and, therefore, the loss probability ratio, originates from mapping the actual distribution of the burst duration into an exponential distribution. Specifically, the peak rate and the utilization (mean rate) of a source can usually be captured reasonably accurately, and the burst duration is the main parameter whose estimation in problematic. As a result, modeling a traffic source using a Markov ON-OFF source involves selecting a   burst duration chosen triplet of the form < R, b , ρ >, where b is an to yield the same loss probability as the one experienced by the actual source.  Because the choice of b is very much source dependent (see [5] for details on  a method for deriving estimates for b ) and although its value is often different from the average burst duration b, we nevertheless make the assumption that  b = b in our evaluation. This therefore represents the major source of error, when it comes to computing loss probabilities and the loss probability ratio. Our goal in this section is thus to provide a worst case analysis of the magnitude of this error. Consider a system consisting of two sources multiplexed onto the same link and where, without loss of generality, source 2 is the one that contributes the smallest amount of traffic. Denote P LRest as the loss probability ratio obtained from the approach proposed in this paper, and let EP LR be the possible difference between P LRest and the actual loss probability ratio P LR. possible value The determination of EP LR is based on evaluating the of |P LRest − P LR| as a function of the system parameters. Specifically, we first derive bounds (intervals) for both P LR and P LRest , and then derive the expression of EP LR based on the maximum distance between the boudaries of these intervals. Due to space constrain, we refer to [10](Appendix I) for details of the derivation, and only present the main results here. In [10], it is found that one can distinguish three main regions for which different bounds can be derived for P LR (and P LRest ): – Case 1: R1 ≤ C, R2 ≤ C – Case 2: R1 (R2 ) < C < R2 (R1 ) – Case 3: C ≤ R1 , C ≤ R2 where Case 2 can be further divided into two sub-regions depending on whether R1 is larger than R2 or not. In addition, because the allocated bandwidth C in actual system might be different from that estimated by the model (more precisely, it should be denoted as Cest ) 5 , the total number of regions need to be considered is actually nine (all possible combinations). In [10], the expression of EP LR is derived for all the nine cases, and the results are given in Table 3: From the table, we can infer that in many cases the value of EP LR will be reasonably small. The only cases where a potentially large estimation error can 5

This is because the capacity allocated in the model is based on the assumption that the ON period is exponentially distributed with mean b, while the actual capacity allocated incorporate the effect of the real source statistics.

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Table 3. Worst Case Prediction Error: EP LR

Actual Situation

Model Prediction

Case 1

Case 2

R 2)

1 1 * ] -1 (r 1 /R > r 2 /R , R >R ) S 1 S 2 1 2 r /rS 1 + R 1/R 2 2 S

R /R 1 *( 1 2 ) rS2 /rS 1 + R 1 /R 2 r 2 /R , R >R ) S 1 S 2 1 2 rS /rS 1 + R 1/R 2

1 1 max[2, 2 * ] -1 (r 1 /R > r 2 /R , R >R ) S 1 S 2 1 2 rS /rS 1 + R 1/R 2

R /R 1 *( 1 2 ) rS2 /rS 1 + R 1 /R 2

1 R /R *( 1 2 ) rS2 /rS 1 + R 1 /R 2

(R 1 PL2 , and since it is then the major traffic contributor (source 1) that loses more, P LR = PL1 /PL . This implies that P LR can never exceed rS /rS1 , which is less than 2. This then yields EP LR ≤ 1. In other scenarios, as long as neither system falls into Case 3, it is possible to show that EP LR will be a decreasing function of both the fraction of traffic contributed by source 2 and  the difference between  R1 and R2 . This is reflected in the expressions R1 /R2 1 max 1, r2 1/rS · 1+R11 /R2 − 1 and r2 /r · 1+R for the cases R1 > R2 and 1 /R2 S S S R1 < R2 , respectively. In those cases, EP LR will be large only when both the value of rS2 /rS is small (the traffic contribution of source 2 is much smaller than that of source 1) and R1 /R2 is close to 1. The only other cases where we commit it is possible for EP LR to be large is, as mentioned earlier, when either the modeled or the actual system correspond to Case 3. In this case, either P LR or P LRest can be anywhere in the range 1 to rS /rS2 , so that EP LR = rS /rS2 − 1, which can be arbitrarily large if the traffic contribution of source 2 is very small. The question is then to determine how common this configuration is. A brief and arguably limited review of the many different configurations we tested found that this scenario occurred only when multiplexing video sources with rather different rates, e.g., Lecture low and Jurassic high. In those cases, the modeled system fell (erroneously) in Case

On Evaluating Loss Performance Deviation

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3 while the actual system is in Case 2. This indeed translated into substantial differences between the loss probability ratio predicted by the model and the value of P LR obtained in the simulations, as is seen in Figure 1. However, it is worth noting that in spite of those differences, the tests performed using the model to determine if it was safe or not to multiplex the sources, still provided a correct answer in most cases. In other words, the methodology based on the average burst duration still successfully captured the trend in loss probability ratio and thus, was able to correctly identify the potential danger of mixing the traffic sources. 6.2

Prediction Error in the Many-Source Case

In the many-source case, the equations used to predict the loss probability ratio, i.e., Equation (6) and (7) of [9], are derived assuming a bufferless model. For such a system, the loss probability ratio is only affected by the peak rate and the utilization [6]. This is because data losses occur when the arrival rate is greater than the link capacity, and thus are determined only by their difference. As a result, the loss probability ratio does not depend on the statistics of burst duration. Instead, the model’s accuracy depends only on how good a fit a bufferless model is for the real system. This is a function of both the buffer size and the relative burstiness of the source(s). When the number of sources is large, the ability of a buffer, even a large one, to accommodate many large bursts is very limited, so that a bufferless model is often quite accurate. From the simulations of Section 4 and Section 5, we have indeed seen that a buffer size of 5000 Bytes gives results that are barely distinguishable from those of a bufferless system, even in cases where the number of sources is moderate. In other simulations that are not included in the paper due to lack of space, similar observations were made for systems with much larger buffers, i.e., 100 KBytes. In those cases, although there were instances where the absolute prediction was not entirely accurate, it always remained sufficient to clearly identify when it was dangerous to multiplex sources of different types. As a result, we believe that the performance of an approach based on a bufferless model should remain robust across a wide range of buffer sizes, as long as the number of sources being multiplexed is large enough.

7

Conclusions

This paper is concerned with the problem of deciding when it is possible to multiplex different traffic sources into a common service class, when both resource allocation and performance monitoring is done at the class level. Our goal is to develop a reasonably simple methodology for identifying traffic mixes that can generate significant performance deviations. The methodology we propose is based on a set of analytical tools developed in [9], and which are used together with a simple method for mapping real traffic sources onto source models that the analysis is capable of handling.

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The effectiveness of the methodology is evaluated through simulations by exploring its prediction ability across a number of scenarios involving real traffic sources. The paper establishes that the methodology, though simple, is quite successful and robust in identifying traffic mixes that can result in severe loss performance deviations. In particular, it reliably identifies cases where large deviations would occur and mostly avoids false alarms. In addition, the region for which it gives somewhat inconclusive results, its so-called threshold region, is relatively narrow. Furthermore, the paper also shows that in most cases where large performance deviations are observed, the amount of additional bandwidth needed to provide all users in the service class with the desired performance, can often be quite large. This indicates that simply over-provisioning the bandwidth allocated to the service class cannot easily eliminate loss performance deviations, when present. As a result, providing a simple yet accurate method for identifying potentially dangerous traffic mixes is important when contemplating deploying class-based services.

8

Acknowledgement

The authors would like to acknowledge Wenyu Jiang from Columbia University for providing the voice traffic traces, and Frank Fitzek from the Technical University of Berlin, Germany, for providing the video traffic traces.

References [1] The network simulator – ns-2. http://www.isi.edu/nsnam/ns/. [2] Video trace library. http://www-tkn.ee.tu-berlin.de/research/trace/trace.html. [3] S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss. An architecture for differentiated services. Request For Comments (Proposed Standard) RFC 2475, IETF, December 1998. [4] F. Frank and R. Martin. MPEG-4 and H.263 video traces for network performance evaluation. IEEE Network Magazine, 15(6):40–54, November 2001. [5] L. G¨ un. An approximation method for capturing complex traffic behavior in high speed networks. Performance Evaluation, 19(1):5–23, January 1994. [6] U. Mocci J. W. Roberts and J. Virtamo, editors. Broadband Network teletraffic Final Report of Action COST 242, volume 1155. Springer-Verlag, 1996. [7] W. Jiang and H. Schulzrinne. Analysis of on-off patterns in voip and their effect on voice traffic aggregation. In The 9th IEEE International Conference on Computer Communication Networks, 2000. [8] H. Schulzrinne. Voice communication across the Internet: a network voice terminal. Technical Report 92–50, Department of Computer Science, University of Massachusetts, Amherst, MA, USA, 1992. [9] Y. Xu and R. Gu´erin. Individual QoS versus aggregate QoS: A loss performance study. In Proceedings of the IEEE Infocom, NYC, USA, June 2002. [10] Y. Xu and R. Gu´erin. On evaluating loss performance deviation: A simple tool and its practical implications. Technical report, University of Pennsylvania, September 2002. (Available at http://einstein.seas.upenn.edu/mnlab/publications.html).

Extending the Network Calculus Pay Bursts Only Once Principle to Aggregate Scheduling Markus Fidler Department of Computer Science, Aachen University Ahornstr. 55, 52074 Aachen, Germany [email protected]

Abstract. The Differentiated Services framework allows to provide scalable network Quality of Service by aggregate scheduling. Services, like a Premium class, can be defined to offer a bounded end-to-end delay. For such services, the methodology of Network Calculus has been applied successfully in Integrated Services networks to derive upper bounds on the delay of individual flows. Recent extensions allow an application of Network Calculus even to aggregate scheduling networks. Nevertheless, computations are significantly complicated due to the multiplexing and de-multiplexing of micro-flows to aggregates. Here problems concerning the tightness of delay bounds may be encountered. A phenomenon called Pay Bursts Only Once is known to give a closer upper estimate on the delay, when an end-to-end service curve is derived prior to delay computations. Doing so accounts for bursts of the flow of interest only once end-to-end instead of at each link independently. This principle also holds in aggregate scheduling networks. However, it can be extended in that bursts of interfering flows are paid only once, too. In this paper we show the existence of such a complementing Pay Bursts Only Once phenomenon for interfering flows. We derive the end-to-end service curve for a flow of interest in an arbitrary aggregate scheduling feed forward network for rate-latency service curves, and leaky bucket constraint arrival curves, which conforms to both of the above principles. We give simulation results to show the utility of the derived forms.

1

Introduction

The Differentiated Services (DS) architecture [2] is the most recent approach of the Internet Engineering Task Force (IETF) towards network Quality of Service (QoS). DS addresses the scalability problems of the former Integrated Services approach by an aggregation of micro-flows to a small number of different traffic classes, for which service differentiation is provided. Packets are identified by simple markings that indicate the respective class. In the core of the network, routers do not need to determine to which flow a packet belongs, only which aggregate behavior has to be applied. Edge routers mark packets and indicate whether they are within profile or, if they are out of profile, in which case they might even be discarded by a dropper at the edge router. A particular marking on M. Ajmone Marsan et al. (Eds.): QoS-IP 2003, LNCS 2601, pp. 19–34, 2003. c Springer-Verlag Berlin Heidelberg 2003 

20

Markus Fidler

a packet indicates a so-called Per Hop Behavior (PHB) that has to be applied for forwarding of the packet. Currently, the Expedited Forwarding (EF) PHB [9], and the Assured Forwarding (AF) PHB group are specified. The EF PHB is intended for building a service that offers low loss, low delay, and low delay jitter, namely a Premium service. The specification of the EF PHB was recently redefined to allow for a more exact and quantifiable definition [5]. Especially the derivation of delay bounds is of interest, when providing a Premium service. In [4] such bounds are derived for a general topology and a maximum load. However, these bounds can be improved, when additional information concerning the current load, and the special topology of a certain DS domain is available. In [15] a central resource management for DS domains called a Bandwidth Broker (BB) is presented. A BB is a middleware service which controls and facilitates the dynamic access to network services of a particular administrative domain [10]. The task of a BB in a DS domain is to perform a careful admission control, and to set up the appropriate configuration of the domain’s edge routers, whereas the configuration of core routers is intended to remain static to allow for scalability. While doing so, the BB knows about all requests for capacity of certain QoS classes. Besides it can easily learn about the DS domains topology, either statically, or by implementing a listener for the domains routing protocol. Thus, a BB can have access to all information that is required, to apply the mathematical methodology of Network Calculus [3,13], in order to base its admission control on delay boundaries that are derived for the current load, and the special topology of the administrated domain [19]. In this paper we address the derivation of end-to-end delay guarantees based on Network Calculus. We derive a closed form solution for the end-to-end delay in feed forward First In First Out (FIFO) networks, for links that have a ratelatency property, and flows that are leaky bucket constraint. In particular this form accounts for bursts of interfering flows only once, and thus implements a principle for aggregate scheduling that is similar to the Network Calculus Pay Bursts Only Once principle [13]. The derived boundaries can be applied as a decision criterion to perform the admission control of a DS domain by a BB. The remainder of this paper is organized as follows: In Section 2 the required background on Network Calculus, and the notation that is applied in the sequel are given. Section 3 introduces two examples, which show how bursts of interfering flows worsen the derived delay bounds and, which prove the existence of a counterpart to the Pay Bursts Only Once phenomenon for interfering flows in aggregate scheduling networks. The first example can be satisfactorily solved by direct application of current Network Calculus, whereas to our knowledge for the second example a tight solution is missing in current literature. This missing piece is addressed in Section 4, where a tight closed form solution for arbitrary feed forward networks with FIFO rate-latency service curves and leaky bucket constraint arrival curves is derived. In Section 5 we describe the implementation of the admission control in a DS BB that is based on worst-case delay bounds. Numerical results on the performance gain that is achieved by applying the previously derived terms are given. Section 6 concludes the paper.

Extending the Network Calculus Pay Bursts Only Once Principle

2

21

Network Calculus Background and Notation

Network Calculus is a theory of deterministic queuing systems that is based on the early work on the calculus for network delay in [6,7], and on the work on Generalized Processor Sharing (GPS) presented in [16,17]. Further extensions, and a comprehensive overview on current Network Calculus are given in [12,13], and from the perspective of filtering theory in [3]. Here only a few concepts are covered briefly, to give the required background, and to introduce the notation that is mainly taken over from [13]. In addition since networks consisting of several links n that are used by a flow of interest, and a number of interfering flows m are investigated, upper indices j indicate links, and lower indices i indicate flows in the sequel. The scheduler on an outgoing link can be characterized by the concept of a service curve, denoted by β(t). A special characteristic of a service curve is the rate-latency type that is given by βR,T (t) = R · [t − T ]+ with a rate R and a latency T . The term [x]+ is equal to x, if x ≥ 0, and zero otherwise. Service curves of the rate-latency type are implemented for example by Priority Queuing (PQ), or Weighted Fair Queuing (WFQ). The latency of a PQ scheduler is given in [5] for variable length packet networks with a Maximum Transmission Unit (MTU) according to T = MTU/R. Nevertheless, routers can implement additional nonpreemptive layer 2 queues on their outgoing interfaces for a smooth operation, which can add further delay to a layer 3 QoS implementation [20]. Thus T = (l2 + 1) · MTU/R might have to be applied, whereby l2 gives the layer 2 queuing capacity in units of the MTU. Flows are defined either by their arrival functions denoted by F (t), or by their arrival curves α(t), whereas α(t2 − t1 ) ≥ F (t2 ) − F (t1 ) for all t2 ≥ t1 . In DS networks, a typical characteristic for incoming flows can be given by the leaky bucket constraint αr,b (t) = b + r · t that is also known as sigma-rho leaky bucket in [3]. Usually the ingress router of a DS domain meters incoming flows against a leaky bucket algorithm, and either shapes, or drops non-conforming traffic, which justifies the application of leaky bucket constraint arrival curves. If a link j is traversed by a flow i, the arrival function of the output flow Fij+1 , which is the input arrival function for an existing, or an imaginary subsequent link j + 1, can be given according to (1) for t ≥ s ≥ 0 [12]. Fij+1 (t) ≥ Fij (t − s) + β j (s)

(1)

From (1) the term in (2) follows. The operator ⊗ denotes the convolution under the min-plus algebra that is applied by Network Calculus. Fij+1 (t) ≥ (Fij ⊗ β j )(t) = inf [Fij (t − s) + β j (s)] t≥s≥0

(2)

that Further on, the output flow is upper constrained by an arrival curve αj+1 i is given according to (3), with  denoting the min-plus de-convolution. (t) = (αji  β j )(t) = sup[αji (t + s) − β j (s)] αj+1 i s≥0

(3)

22

Markus Fidler

If the path of a flow i consists of two or more links, the formulation of the concatenation of links can be derived based on (4). ≥ β j+1 (t − s) Fij+2 (u) − Fij+1 (u − (t − s)) j+1 j β j (s) Fi (u − (t − s)) −Fi (u − t) ≥ j+2 j j+1 Fi (u) −Fi (u − t) ≥ β (t − s) + β j (s)

(4)

The end-to-end service curve is then given in (5), which covers the case of two links, whereas the direct application of (5) also holds for n links. β j+1,j (t) = (β j+1 ⊗ β j )(t) = inf [β j+1 (t − s) + β j (s)] t≥s≥0

(5)

The maximal virtual delay d for a system that offers a service curve of β(t) with an input flow that is constraint by α(t), is given as the supremum of the horizontal deviation according to (6).   (6) d ≤ sup inf[τ ≥ 0 : α(s) ≤ β(s + τ )] s≥0

For the special case of service curves of the rate-latency type, and sigma-rho leaky bucket constraint arrival curves, simplified solutions exist for the above equations. The arrival curve of the output flow according to (3) is given in (7) for this case, whereas the burst size of the output flow bi + ri · T j is equal to the maximum backlog at the scheduler of the outgoing link. αj+1 (t) = bi + ri · T j + ri · t i

(7)

The concatenation of two rate-latency service curves can be reduced to (8). β j+1,j (t) = min[Rj+1 , Rj ] · [t − (T j+1 + T j )]+

(8)

Finally, (9) gives the worst case delay for the combination of a rate-latency service curve, and a leaky bucket constraint arrival curve. d ≤ T j + bi /Rj

(9)

If a flow i traverses two links j and j + 1, two options for the derivation of the end-to-end delay exist. For simplicity, the service curves are assumed here to be of the rate-latency type, and the arrival curve is chosen to be leaky bucket constraint. At first the input arrival curve of flow i at link j + 1 can be computed as in (7). Then the virtual end-to-end delay is derived to be the sum of the virtual delays at link j and j + 1 according to (9). Doing so results in d ≤ T j + bi /Rj + T j+1 + (bi + ri · T j )/Rj+1 . The second option is to derive the end-to-end service curve as is done in (8), and compute the delay according to (9) afterwards, resulting in d ≤ T j + T j+1 + bi / min[Rj+1 , Rj ]. Obviously, the second form gives a closer bound, since it accounts for the burst size bi only once. This property is known as the Pay Bursts Only Once phenomenon from [13]. Until now only networks that perform a per-flow based scheduling, for example Integrated Services networks, have been considered. The aggregation or

Extending the Network Calculus Pay Bursts Only Once Principle

23

the multiplexing of flows can be given by the addition of the arrival functions F1,2 (t) = F1 (t) + F2 (t), or arrival curves α1,2 (t) = α1 (t) + α2 (t). For aggregate scheduling networks with FIFO service curves, families of per-flow service curves βθ (t) according to (10) with an arbitrary parameter θ ≥ 0 are derived in [8,13]. βθj (t) gives a family of service curves for a flow 1 that is scheduled in an aggregate manner in conjunction with a flow 2 on a link j. 1t>θ is zero for t ≤ θ. βθj (t) = [β j (t) − α2 (t − θ)]+ 1t>θ

(10)

The parameter θ has to be set to zero in case of blind multiplexing. In FIFO j j+1 (v) ≤ F1,2 (t)], the conditions F j (u) ≤ F j+1 (t), networks for u = sup[v : F1,2 j + j+1 + (t) with u = u+,  > 0 hold for the sum of both flows, and and F (u ) ≥ F for the individual flows, too. These additional constraints allow to derive (10) for an arbitrary θ > 0. The complete derivation is missed out here. It can be found in [13]. From (10) it cannot be concluded that supθ [βθj ], or inf θ [βθj ] is a service j j curve, but for the output flow αj+1 1 (t) = inf θ≥0 [(α1  βθ )(t)] can be given [13]. For the special case of rate-latency service curves, and leaky bucket constraint arrival curves, (11) can be derived from (10) to be a service curve for flow 1 for r1 + r2 < Rj . (11) β j (t) = (Rj − r2 ) · [t − (T j + b2 /Rj )]+ The methodology that is shown up to here already allows to implement the algorithmic derivation of delay bounds in a DS domain by a BB, with the restriction that the domain has to be a feed forward network. In non feed forward networks analytical methods like time stopping [3,13] can be applied. Nevertheless, for an algorithmic implementation, it is simpler to prevent from aggregate cycles, and transform the domains topology into a feed forward network, to allow for the direct application of Network Calculus. Such a conversion of the network topology can be made by means of breaking up loops by forbidding certain links, for example by turn prohibition as presented in [21] for networks that consist of bidirectional links. Doing so, the BB can inductively derive the arrival curves of micro-flows at each outgoing link, then compute the service curve of each link from the point of view of each micro-flow, and concatenate these to end-to-end service curves, to give upper bounds on the worst case delay for individual flows.

3

Extended Pay Bursts Only Once Principle

Though Section 2 gives the required background to derive per micro-flow based end-to-end delay bounds in aggregate scheduling networks, these bounds are likely to be unnecessarily loose. Figure 1 gives a motivating example of a simple network consisting of two outgoing links that are traversed by two flows. This example is given to introduce a similar concept to the Pay Bursts Only Once principle [13] for aggregate scheduling. Flow 1 is the flow of interest, for which the end-to-end delay needs to be derived. According to the Pay Bursts Only Once principle, at first the end-to-end service curve for flow 1 has to be derived, and then the delay is computed, instead of computing the delay at each link

24

Markus Fidler I

II

1 2

Fig. 1. Two Flows Share Two Consecutive Links

independently, and summing these delays up. A similar decision has to be made, when deriving the service curve for flow 1 by subtracting the arrival curve of flow 2 from the aggregate service curves. Either this subtraction is made at each link independently before concatenating service curves, or the subtraction is made after service curves have been concatenated. To illustrate the difference the two possible derivations of the end-to-end service curve for flow 1 are given here for rate-latency service curves, and leaky bucket constraint arrival curves. For the first option, which is already drafted at the end of Section 2, the service curve of link I from the point of view of flow 2 can be derived to be of the rate-latency type with a rate RI − r1 and a latency T I + b1 /RI . Then, the arrival curve of flow 2 at link II can be given to be leaky bucket constraint with the rate r2 and the burst size b2 + r2 · (T I + b1 /RI ). The service curves at link I and II from the point of view of flow 1 can be given to be rate-latency service curves with the rates RI − r2 , respective RII − r2 , and the latencies T I + b2 /RI , respective T II + (b2 + r2 · (T I + b1 /RI ))/RII . The concatenation of these two service curves yields the rate-latency service curve for flow 1 given in (12). β I,II (t) = min[RI − r2 , RII − r2 ] · [t − (T I + b2 /RI ) − (T II + (b2 + r2 · (T I + b1 /RI ))/RII )]+

(12)

The second option requires that the service curves of link I and II are convoluted prior to subtraction of the flow 2 arrival curve [19]. The concatenation yields a service curve of the rate-latency type with a rate of min[RI , RII ] and a latency of T I + T II . After subtracting the arrival curve of flow 2 from the concatenation of the service curves of link I, and II, (13) can be given for flow 1. β I,II (t) = (min[RI , RII ] − r2 ) · [t − (T I + T II + b2 / min[RI , RII ])]+

(13)

Obviously, the form in (13) offers a lower latency than the one in (12), which accounts for the burst size of the interfering flow 2 twice, once with the size b2 at link I, and then with b2 + r2 · (T I + b1 /RI ) at link II. The increase of the burst size of flow 2 at link II is due to the aggregate scheduling of flow 2 with flow 1 at link I. Thus, based on (12), and (13) a counterpart to the Pay Burst Only Once phenomenon has been shown for interfering flows in aggregate scheduling networks. However, most problems of interest cannot be solved as simple as the one in Figure 1. One such example is shown in Figure 2. Flow 2 is the flow of interest, for which the end-to-end service curve needs to be derived. Links I and II can

Extending the Network Calculus Pay Bursts Only Once Principle I

II

25

III

1 2 3

Fig. 2. Three Flows Share Three Consecutive Links

be concatenated after the arrival curve of flow 3 is subtracted from the service curve of link II. Then the arrival curve of flow 1 can be subtracted from the concatenation of the service curves of link I and II. Unfortunately the direct application of the Network Calculus terms given in Section 2 then requires that the arrival curve of flow 3 at link III is subtracted from the service curve of link III independently, which violates the extended Pay Bursts Only Once principle. An alternative derivation is possible, if the arrival curve of flow 1 is subtracted from the service curve of link II before links II and III are concatenated. Doing so does unfortunately encounter the same problem.

4

Closed Form Solution for Feed Forward Networks

Consider an end-to-end path of a flow of interest i in an arbitrary aggregate scheduling feed forward network with FIFO service curve elements. Further on, assume that a concatenation of consecutive links offers a FIFO characteristic, too. The path consists of n links that are indexed by j in ascending order from the source to the destination of the flow of interest i. These links are given in the set Ji . Further on, the links of the path of flow i are used in an aggregate manner by an additional number of flows m that are indexed by k. The paths of the flows k are given by the sets Jk . For each link j a set Kj is defined to hold all other flows k that traverse the link, not including flow i. Note that flows may exist that share a part of the path of the flow of interest i, then follow a different path, and afterwards again share a part of the path of flow i. These flows are split up in advance into as many individual flows as such multiplexing points exist. Thus, all resulting flows do have only one multiplexing point with flow i. In [13] the term Route Interference Number (RIN)  is defined to hold the quantity of such multiplexing points. Then, the set Ki = j∈Ji Kj is defined to hold all m flows that use thecomplete path or some part of the path of flow i. Further on, the set Ji,k = Ji Jk holds all links of a sub-path that are used by both flow i and a flow k. Based on these definitions, on the terms in (4), and on the rules for multiplexing, (14) can be given for time pairs tj+1 − tj ≥ 0 for all j ∈ Ji . The time indices are chosen here to match link indices, since arrival functions are observed at these time instances at the belonging links.    Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ β j (tj+1 − tj ) − (Fkj+1 (tj+1 ) − Fkj (tj )) (14) j∈Ji

k∈Ki j∈Ji,k

26

Markus Fidler

Now, the arrival functions of the interfering flows can be easily split up and subtracted from the relevant links. Like for the derivation of (10) in [13], FIFO conditions can be defined on a per-link basis. Doing so, pairs of arrival functions Fkj+1 (tj+1 ) − Fkj (tj ) can be replaced by their arrival curves αjk (tj+1 − tj − θj ) for tj+1 −tj > θj , with the arbitrary per link parameters θj ≥ 0. Nevertheless, doing so results in paying the bursts of all interfering flows at each link independently. However, FIFO conditions can in addition to per link be derived per subpath Ji,k . With j∈Ji,k (Fkj+1 (tj+1 ) − Fkj (tj )) = Fkjmax +1 (tjmax +1 ) − Fkjmin (tjmin ), whereby jmax = max[j ∈ Ji,k ], and jmin = min[j ∈ Ji,k ], (15) can be derived for tjmax +1 − tjmin > θk , based on (10).   j β j (tj+1 − tj ) − αkmin (tjmax +1 − tjmin − θk ) (15) Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ j∈Ji

k∈Ki

To motivate the step from (14) to (15), the FIFO conditions that are applied, are shown exemplarily for the small network in Figure 2. The derivation, is a direct application of the one given in [13] for the form in (10). Define an u1 , and u3 for flow 1, respective flow 3 according to (16), and (17). u1 = sup{v : F1I (v) + F2I (v) ≤ F1III (t3 ) + F2III (t3 )}

(16)

u3 = sup{v : F2II (v) + F3II (v) ≤ F2IV (t4 ) + F3IV (t4 )}

(17)

I I Now, from (16), and with u+ 1 = inf{v : v > u1 }, t1 ≤ u1 ≤ t3 , F1 (u1 ) + F2 (u1 ) ≤ III III I + I + III III F1 (t3 ) + F2 (t3 ), and F1 (u1 ) + F2 (u1 ) ≥ F1 (t3 ) + F2 (t3 ) can be given. Due to the per sub-path FIFO conditions, the above terms also hold for the III individual flows 1, and 2, for example F1I (u1 ) ≤ F1III (t3 ), and F1I (u+ 1 ) ≥ F1 (t3 ). Similar conditions can be derived for flows 2, and 3 from (17). The following term in (18) can be set up based on (4).

F2IV (t4 ) − F2I (t1 ) ≥ β III (t4 − t3 ) + β II (t3 − t2 ) + β I (t2 − t1 ) − (F3IV (t4 ) − F3II (t2 )) − (F1III (t3 ) − F1I (t1 ))

(18)

III II + IV With F1I (u+ 1 ) ≥ F1 (t3 ), and F3 (u3 ) ≥ F3 (t4 ), (19) can be derived.

F2IV (t4 ) − F2I (t1 ) ≥ β III (t4 − t3 ) + β II (t3 − t2 ) + β I (t2 − t1 ) II I + I − (F3II (u+ 3 ) − F3 (t2 )) − (F1 (u1 ) − F1 (t1 ))

(19)

Choose two arbitrary parameters θ1 ≥ 0, and θ3 ≥ 0. If u1 < t3 − θ1 , F1I (u+ 1) ≤ F1I (t3 − θ1 ) holds. Further on, t3 − t1 > θ1 can be given in this case, since u1 ≥ t1 . With a similar condition for flow 3, the form in (20) is derived. F2IV (t4 ) − F2I (t1 ) ≥ β III (t4 − t3 ) + β II (t3 − t2 ) + β I (t2 − t1 ) − α3 (t4 − t2 − θ3 ) − α1 (t3 − t1 − θ1 )

(20)

Else, for u1 ≥ t3 − θ1 , the FIFO condition F2III (t3 ) ≥ F2I (u1 ) is applied. Further on, the term F2III (t3 ) − F2I (t1 ) ≥ β I,II (t3 − t1 ) can be set up, with β I,II denoting

Extending the Network Calculus Pay Bursts Only Once Principle

27

the service curve for flow 2 that is offered by link I, and II. Substitution of t1 by u1 , yields F2III (t3 ) ≥ F2I (u1 ) + β I,II (t3 − u1 ). Hence, β I,II (t3 − t1 ) = 0 is a trivial service curve for u1 ≥ t3 − θ1 . Similar forms can be derived for u3 ≥ t4 − θ3 . In the following the form in (15) is solved for the simple case of rate-latency service curves, and leaky bucket constraint arrival curves. Proposition 1 (End-to-End Service Curve) i βR,T αr,b

  

 βi (t) = min Rj − rk · t − Tj − j∈Ji

k∈Kj

j∈Ji

k∈Ki

bjkmin

+

minj∈Ji,k [Rj ]

(21)

The form in (21) gives an intuitive result. The end-to-end service curve for flow i has a rate R, which is the minimum of the remaining rates at the traversed links, after subtracting the rates of interfering flows that share the individual links. The latency T is given as the sum of all latencies along the path, plus the burst size of interfering flows at their multiplexing points indicated by jmin , divided by the minimum rate along the common sub-path with the flow of interest i. Thus, bursts of interfering flows account only once with the maximal latency that can be evoked by such bursts along the shared sub-paths. Proof 1 In (22) the form in (15) is given for rate-latency service curves, and leaky bucket constraint arrival curves for tjmax +1 − tjmin > θk . 

Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ Rj · [tj+1 − tj − T j ]+ j∈Ji

−



bjkmin + rk · (tjmax +1 − tjmin − θk )

(22)

k∈Ki

Here, we apply a definition of the per flow θk by per link θj according to (23). Now the failure of any of the conditions tjmax +1 − tjmin > θk requires the failure of at least one of the conditions tj+1 − tj > θj for any j with jmax ≥ j ≥ jmin .  θk = θj (23) j∈Ji,k

Reformulation of (22) yields (24) for tj+1 − tj > θj , with j ∈ Ji,k . 

Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ Rj · [tj+1 − tj − T j ]+ j∈Ji

−



k∈Ki

bjkmin + rk ·



 (tj+1 − tj − θj )

(24)

j∈Ji,k

Next, the fact that (10) gives a service curve for any setting of the parameter θ with θ ≥ 0 is used. Thus, the per-flow θk can be set arbitrarily with θk ≥

28

Markus Fidler

0, whereas this condition can according to (23) be fulfilled by any θj ≥ 0. Hence, (24) gives a service curve for any θj ≥ 0. We define an initial setting of the parameters θj , for which an end-to-end service curve for flow i is derived for all tj+1 −tj > θj . Then, for the special cases in which tj+1 −tj > θj does not hold for one or several links j, θj is redefined. We show for these cases by means of the redefined θj that the end-to-end service curve that is derived before still holds true. Thus, we prove that this service curve is valid for all tj+1 − tj ≥ 0. The definition of different settings of the parameters θj is not generally allowed to derive a service curve. As already stated in Section 2, it cannot be concluded that for example inf θ βθ (t) is a service curve [13]. Nevertheless, there is a difference between doing so, and the derivation that is shown in the following. Here, a service curve βθj is derived for fixed θj for all tj+1 − tj > θj . This service curve is not modified later on, but only proven to hold for any tj+1 −tj ≥ 0 by applying different settings of the θj . The initially applied setting of the θj is given in (25). The θj are defined to be the latency of the scheduler on the outgoing link j plus the burst size of interfering flows k, if j is the multiplexing point of the flow k with flow i, divided by the minimum rate along the common sub-path of flow k and i.  bjkmin (25) θj = T j + minj  ∈Ji,k [Rj  ] j k∈K

|j=jmin

With (25) the term in (24) can be rewritten according to (26) for all tj+1 −tj > θj . Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ −





Rj · [tj+1 − tj − T j ]+



j∈Ji

bjkmin

 tj+1 − tj − T j − + rk ·

bjkmin  minj  ∈Ji,k

j k ∈K |j=jmin

j∈Ji,k

k∈Ki



 (26)

[Rj  ]

+ Some reordering, while up the subtrahends by adding [. . . ] conditions, scaling and a replacement of k∈Ki j∈Ji,k by j∈Ji k∈Kj yields (27).

Fin+1 (tn+1 ) − Fi1 (t1 ) ≥

    Rj − rk · [tj+1 − tj − T j ]+ k∈Kj

j∈Ji

 j  bkmin − rk · −

Fin+1 (tn+1 ) − Fi1 (t1 ) ≥  k∈Ki

j∈Ji,k

by





j∈Ji

 (27)

j

minj  ∈Ji,k [R ]

k∈Kj ,

(28) can be derived.

    Rj − rk · [tj+1 − tj − T j ]+ j∈Ji

−



k∈Ki

bjkmin 

j∈Ji,k k ∈Kj|j=jmin

k∈Ki

With the replacement of



bjkmin +

k∈Kj

  j∈Ji k∈Kj

rk ·

 j k ∈K |j=jmin

bjkmin 

minj  ∈Ji,k [Rj  ]

 (28)

Extending the Network Calculus Pay Bursts Only Once Principle

Further on

k∈Ki

bjkmin =

Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ −







j∈Ji

j|j=j min

k ∈K

29

bjkmin yields (29). 

    rk · [tj+1 − tj − T j ]+ Rj − k∈Kj

j∈Ji





bjkmin − 

j∈Ji k ∈Kj|j=j

min

rk ·

k∈Kj



bjkmin 

 (29)

j

minj  ∈Ji,k [R ]

j|j=j min

k ∈K

Applying the common denominator, while scaling up the subtrahend, and with  j ∈ Ji,k and thereby Rj ≥ minj  ∈Ji,k [Rj ] with k  ∈ Kj , (30) can be derived. Fin+1 (tn+1 ) − Fi1 (t1 ) ≥

    Rj − rk · [tj+1 − tj − T j ]+ j∈Ji

k∈Kj

    Rj − − rk · k∈Kj

j∈Ji



bjkmin 

j k ∈K |j=jmin



minj  ∈Ji,k [Rj  ]

(30)

Then, (30) can be reformulated according to (31), still for tj+1 − tj > θj .    Fin+1 (tn+1 ) − Fi1 (t1 ) ≥ Rj − rk j∈Ji

k∈Kj

 · [tj+1 − tj − T j ]+ −

 j k ∈K |j=jmin

bjkmin  minj  ∈Ji,k

 [Rj  ]

(31)

The inf (tj+1 −tj >θj )|j∈Ji of (31) can be derived to be the form that is given in (21). Thus, the service curve in (21) is approved for all tj+1 − tj > θj with the parameter settings of θj according to (25). Now, if some of the conditions tj+1 − tj > θj fail, the θj that are given in (25) can be redefined according to (32), based on the arbitrary parameters δkj ≥ 0 with j∈Ji,k δkj = 1.  δkj · bjkmin θj = T j + (32) minj  ∈Ji,k [Rj  ] k∈Kj

bjkmin

The burst size of interfering flows is arbitrarily accounted for by θj in (25), whereas, if an interfering flow k traverses more than one link, the burst size bjkmin could be part of any θj , with j ∈ Ji,k . For such redefined θj , it can be shown that the same derivation as above holds, resulting in (33). Again, applying the inf (tj+1 −tj >θj )|j∈Ji leads to the same form (21), as shown for (31) before. Fin+1 (tn+1 ) − Fi1 (t1 ) ≥

   rk Rj − j∈Ji

k∈Kj

  · [tj+1 − tj − T j ]+ −

 δkj  · bjkmin  (33)  minj  ∈Ji,k [Rj ]

k ∈Kj

30

Markus Fidler

However, there can be pairs of tj+1 − tj ≥ 0, for which no setting of the parameters δkj according to (32) allows a redefinition of θj , for which tj+1 − tj > θj for all j ∈ Ji can be achieved. A condition tj+1 − tj > θj can fail for δkj = 0 for all k ∈ Kj , if tj+1 − tj ≤ T j , without violating any of the per-flow conditions tjmax +1 − tjmin > θk . In this case the terms that are related to link j in (33) are nullified immediately by the [. . . ]+ condition. Nevertheless, if some of the per flow conditions tjmax +1 − tjmin > θk  are violated for a number of flows k ∈ Li , the service curves of the sub-paths k∈Li Ji,k have according to the derivation of (10) to be set to zero. However, setting the service curves of sub-paths to zero is the same as setting the service curves of all links along these paths to zero. Regarding (33), it can be seen that any links for which the service curve is set to zero possibly increase the resulting rate of the service curve, compared to (21), whereas the resulting maximum latency is not influenced. This holds true for any θj according to (32), respective for any δkj with j∈Ji,k δkj = 1. Thus, also the case  of δkj = 0 for all k ∈ Ki \{Li }, and j ∈ k∈Li Ji,k is covered. The latter setting ensures that bursts of flows that share part of the sub-paths that are set to zero, but that also traverse further links, are accounted for at these links. Then by scaling down the term minj∈Ji \{Ji,k|k∈L } [Rj − k∈Kj rk ] to minj∈Ji [Rj − k∈Kj rk ], (21) i

is also a service curve for cases in which tj+1 − tj ≤ θj , and finally holds for any  tj+1 − tj ≥ 0 with j ∈ Ji . Finally, (34) gives a tight end-to-end service curve for flow 2 in Figure 2. As intended, the bursts of the interfering flows 1, and 3 are accounted for only once, with their initial burst size at the multiplexing, or route interference point. β2 (t) = min[RI − r1 , RII − r1 − r3 , RIII − r3 ] +

b3 b1 − · t − T I − T II − T III − I II II III min[R , R ] min[R , R ]

5

(34)

Numerical Results

In this section we give numerical results on the derivation of edge-to-edge delay bounds in a DS domain, which can be efficiently applied for the definition of socalled Per Domain Behaviors (PDBs) [14]. We compare the options of applying either the Extended Pay Burst Only Once principle, the Pay Bursts Only Once principle, or none of the two principles. We implemented an admission control for an application as a BB in a DS domain. The BB currently knows about the topology of its domain statically, whereas a routing protocol listener can be added. Requests for Premium capacity are sent via socket communication to the BB. The requests consist of a start, and an end time to allow for both immediate, and advance reservation, a Committed Information Rate (CIR), a Committed Burst Size (CBS), and a target maximum delay. Whenever the BB receives a new request, it computes the edge-to-edge delay for all requests that are active during the period of time of the new request, as described in Section 2. If none of the target maximum per-flow delays is violated, the new request is accepted, which otherwise is rejected.

Extending the Network Calculus Pay Bursts Only Once Principle

31

For performance evaluation we implemented a simulator that generates such Premium resource requests. Sources and sinks are chosen uniformly from a predefined set. Start, and end times are modelled as negative exponentially distributed with a mean λ, respective μ, that is a mean of ρ = μ/λ requests are active concurrently. This modelling has been found to be appropriate for user sessions, for example File Transfer Protocol (FTP) sessions in [18]. The target delay, CIR, and CBS are used as uniformly distributed parameters for the simulations. The topology that is used is shown in Figure 3. It consists of the level one, and level two nodes of the German Research Network (DFN) [1]. The level one nodes are core nodes. End systems are connected to the level two nodes that are edge nodes. In detail, we connect up to five sources and sinks to each of the level two nodes. Links are either Synchronous Transfer Mode (STM) 4, STM 16, or STM 64 connections. The link transmission delay is assumed to be 2 ms. Shortest Path First (SPF) routing is applied to minimize the number of hops along the paths. Further on, Turn Prohibition (TP) [21] is used, to ensure the required feed forward property of the network. Figure 3 shows how loops are broken within the level one mesh of the DFN topology by the TP algorithm. The nodes have been processed by TP in the order of their numbering. For example the turn (8; 7; 9) that is the turn from node 8 via node 7 to node 9 is prohibited, whereas for instance the turn (8; 7; 6), or simply the use of the link (8; 7) is permitted. For the DFN topology the SPF TP algorithm does only increase the length of one of the paths by one hop compared to SPF routing. Further on, the TP algorithm can be configured to prohibit turns that include links with a comparably low capacity with priority [21], as is shown in Figure 3, and applied by our BB. The Premium service is implemented based on PQ. Thus, service curves are of the rate-latency type with a latency set to the time it takes to transmit 3 MTU of 9.6 kB, to account for non-preemptive scheduling, due to packetization, and a router internal buffer for 2 Jumbo frames [20]. The performance measure that we apply is the ratio of accepted requests divided by the overall number of requests, and as an alternative the distribution of the derived delay bounds. Simulations have been run, until the 0.95 confidence interval of the acceptance ratio was smaller than 0.01. Initial-data deletion [11] has been applied to capture only the steady-state behavior, and the replication and deletion approach for means, that is for example shown in [11], was used. The results are given for different settings of the requested maximum delay, CBS, and CIR, and for a varying load ρ = μ/λ in Figure 4, and 5. In addition Figure 6 shows the fraction of flows for which a delay bound that is smaller than the delay given on the abscissa was derived. As one of our main results we find a significant performance gain, when accounting for the Extended Pay Bursts Only Once phenomenon. The Pay Bursts Only Once principle alone allows to derive noticeable tighter delay bounds, based on edge-to-edge service curves, compared to an incremental delay computation, as described already in Section 2. The advantage can further on be seen in terms of the acceptance ratio in Figure 4, and 5, whereas the importance of the Pay Bursts Only Once phenomenon increases, if a larger CBS is used. In addition

32

Markus Fidler

7

7

5

6

5 6

0 9

0

8

9

4 4

8

3

2

2 1 3

1 Level 1 Prohibited Turns:

Level 1 Site STM 64 Connection STM 16 Connection STM 4 Connection

Level 2 Site 2 STM 16 Connections 2 STM 4 Connections

not on any shortest path alternative path with the same length exists prohibits a shortest path

Fig. 3. DFN Topology and Example Level 1 Prohibited Turns

the Extended Pay Bursts Only Once principle is of major relevance, if the load on the network is high, and if large bursts are permitted. In case of a high load, flows are likely to share common sub-paths, and the interference of such flows with each other is much more accurately described by the Extended Pay Bursts Only Once principle. Thus, the form presented in (21), allows to derive tighter delay bounds, and thus to increase the acceptance ratio. In particular, as Figure 6 shows, the delay bound for the 99-percentile of the flows is reduced from above 112 ms to 81 ms in case of the Pay Bursts Only Once principle, and than to 59 ms in case of the extended principle for aggregate scheduling. For the 95-percentile, 85 ms, 63 ms, and 49 ms can be given. Further on, the load, up to which an acceptance ratio of for example 0.95 can be achieved, can be multiplied, when accounting for the Extended Pay Bursts Only Once phenomenon.

6

Conclusions

In this paper we have shown that a counterpart to the Pay Bursts Only Once phenomenon exists for interfering flows in aggregate scheduling networks. We then have derived a closed form solution for the end-to-end per-flow service curve in arbitrary feed forward aggregate scheduling networks, where links are of the rate-latency type, and flows are sigma-rho leaky bucket constraint. Our solution accounts for the known Pay Bursts Only Once principle, and extends it to aggregate scheduling in that bursts of interfering flows are paid only once, too. Thus, our form allows to give significantly closer bounds on the delay, while the intuitive form reduces computational complexity, if for example applied as a decision criterion for a Differentiated Services admission control in a Bandwidth Broker. A significant performance gain has been shown by simulation results.

Extending the Network Calculus Pay Bursts Only Once Principle 1

0,9

0,8

0,7

0,6

0,5

0,4

0,3 CIR = uniform random[10...80] Mb/s CBS = uniform random[1...8] Mb delay = uniform random[40...80] ms

0,2

Extended Pay Bursts Only Once Principle Pay Bursts Only Once Principle Incremental Delay Computation

0,1

0 0

10

20

30

40

50 Offered Load

60

70

80

90

100

9

10

Fig. 4. Acceptance Ratio versus Load 1

0,9

0,8

0,7

0,6

0,5

0,4

0,3 CIR = uniform random[10...80] Mb/s delay = uniform random[40...80] ms load = 50

0,2

Extended Pay Bursts Only Once Principle Pay Bursts Only Once Principle Incremental Delay Computation

0,1

0 0

1

2

3

4 5 6 Committed Burst Size (Mb)

7

8

Fig. 5. Acceptance Ratio versus Committed Burst Size 1

0,9

0,8

0,7

0,6

0,5

0,4

0,3 CIR = uniform random[10...80] Mb/s CBS = uniform random[1...8] Mb load = 50

0,2

Extended Pay Bursts Only Once Principle Pay Bursts Only Once Principle Incremental Delay Computation

0,1

0 0

20

40

60 Delay (ms)

80

100

Fig. 6. Fraction of Flows with a smaller Delay Bound

120

33

34

Markus Fidler

Acknowledgements This work was supported by the German Research Community (DFG) under grant graduate school (GRK) 643 ”Software for Communication Systems”.

References 1. Adler, H.-M., 10 Gigabit/s Plattform f¨ ur das G-WiN betriebsbereit, DFN Mitteilungen, Heft 60, November 2002. 2. Blake, S., et al., An Architecture for Differentiated Services RFC 2475, 1998. 3. Chang, C.-S., Performance Guarantees in Communication Networks, Springer, TNCS, 2000. 4. Charny, A., and Le Boudec, J.-Y., Delay Bounds in a Network with Aggregate Scheduling, Springer, LNCS 1922, Proceedings of QofIS, 2000. 5. Charny, A., et al., Supplemental Information for the New Definition of EF PHB (Expedited Forwarding Per-Hop-Behavior) RFC 3247, 2002. 6. Cruz, R. L., A Calculus for Network Delay, Part I: Network Elements in Isolation, IEEE Transactions on Information Theory, vol. 37, no. 1, pp 114-131, 1991. 7. Cruz, R. L., A Calculus for Network Delay, Part II: Network Analysis, IEEE Transactions on Information Theory, vol. 37, no. 1, pp 132-141, 1991. 8. Cruz, R. L., SCED+: Efficient Management of Quality of Service Guarantees, IEEE Infocom, 1998. 9. Davie, B., et al., An Expedited Forwarding PHB RFC 3246, 2002. 10. Foster, I., Fidler, M., Roy, A., Sander, V., Winkler, L., End-to-End Quality of Service for High-End Applications Elsevier Computer Communications Journal, in press, 2003. 11. Law, A. M., and Kelton, W. D., Simulation, Modeling, and Analysis McGraw-Hill, 3rd edition, 2000. 12. Le Boudec, J.-Y., and Thiran, P., Network Calculus Made Easy, Technical Report EPFL-DI 96/218. Ecole Polytechnique Federale, Lausanne (EPFL), 1996. 13. Le Boudec, J.-Y., and Thiran, P., Network Calculus A Theory of Deterministic Queuing Systems for the Internet, Springer, LNCS 2050, Version July 6, 2002. 14. Nichols, K., and Carpenter, B., Definition of Differentiated Services Per Domain Behaviors and Rules for their Specification, RFC 3086, 2001. 15. Nichols, K., Jacobson, V., and Zhang, L., A Two-bit Differentiated Services Architecture for the Internet, RFC 2638, 1999. 16. Pareck, A. K., and Gallager, R. G., A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single-Node Case, IEEE/ACM Transactions on Networking, vol. 1, no. 3, pp. 344-357, 1993. 17. Pareck, A. K., and Gallager, R. G., A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Multiple-Node Case, IEEE/ACM Transactions on Networking, vol. 2, no. 2, pp. 137-150, 1994. 18. Paxson, V., and Floyd, S., Wide Area Traffic: The Failure of Poisson Modeling IEEE/ACM Transactions on Networking, vol. 3, no. 3, pp. 226-244, 1995. 19. Sander, V., Design and Evaluation of a Bandwidth Broker that Provides Network Quality of Service for Grid Applications, Ph.D. Thesis, Aachen University, 2002. 20. Sander, V., and Fidler, M., Evaluation of a Differentiated Services based Implementation of a Premium and an Olympic Service, Springer, LNCS 2511, Proceedings of QofIS, 2002. 21. Starobinski, D., Karpovsky, M., and Zakrevski, L., Application of Network Calculus to General Topologies using Turn-Prohibition, Proceedings of IEEE Infocom, 2002.

Mod elli n g th e Ar r i v a l P r oces s f or P a ck et Au d i o In g e m a r K a j1a n d Ia n M a rs h 1

2

D e p t . o f M a t h e m a t i c s , U p p s a l a U n i v e r s i t y , Sw e d e n i k a j @ m a th.u u .s e 2 I a n M a r s h , C N A L a b , SI C S, Sw e d e n i a n m @ s i cs .s e

Ab s tr a ct. P a c k e t s i n a n a u d i o s t r e a m c a n b e d i s t o r t e d r e l a t i v e t o o n e a n o t h e r d u rin g th e tra v e rs a l o f a p a c k e t s w itc h e d n e tw o rk . T h is d is to rtio n c a n b e m a in ly a ttrib u te d to q u e u e s in ro u te rs b e tw e e n th e s o u rc e a n d th e d e s tin a tio n . T h e q u e u e s c a n c o n s is t o f p a c k e ts e ith e r fro m o u r o w n fl o w , o r fro m o th e r fl o w s . T h e c o n trib u tio n o f th is w o rk is a M a rk o v m o d e l fo r th e tim e d e la y v a ria tio n o f p a c k e t a u d i o i n t h i s s c e n a r i o . O u r m o d e l i s e xt e n s i b l e , a n d s h o w t h i s b y i n c l u d i n g s e n d e r s ile n c e s u p p re s s io n a n d p a c k e t lo s s in to th e m o d e l. B y c o m p a rin g th e m o d e l to w id e a r e a tr a ffi c tr a c e s w e s h o w th e p o s s ib ility to g e n e r a te a n a u d io a r r iv a l p r o c e s s s im ila r to th o s e c re a te d b y re a l c o n d itio n s . T h is is d o n e b y c o m p a rin g th e p ro b a b ility d e n s ity fu n c tio n s o f o u r m o d e l to th e re a l c a p tu re d d a ta .

1

K ey w or d s : P a c k e t d e l a y , V o I P , M a r k o v c h a i n , St e a d y s t a t e

I n tr od u cti on M o d e llin g th e a r r iv a l p r o c e s s f o r a u d io p a c k e ts th a t h a v e p a s s e d th r o u g h a s e r ie s o f ro u te rs is th e p ro b le m w e w ill a d d re s s . F ig u re 1illu s tra te s th is s itu a tio n : P a c k e ts c o n ta in in g a u d io s a m p le s a re s e n t a t a c o n s ta n t ra te fro m a s e n d e r, s h o w n in s te p o n e . T h e

Se n d e r

R e c e iv e r 3 . J itte r b u ffe r

1. O r i g i n a l s p a c in g c ro s s tra ffic

R o u te r

R o u te r

2. D i s t o r t a t i o n d u e t o q u e u e i n g F ig . 1 . T h e n e tw o rk s e ffe c t o n p a c k e t a u d io s p a c in g

M . A j m o n e M a r s a n e t a l . (E d s . ): Q o S-I P 20 0 3 , L N C S 26 0 1, p p . 3 5 – 4 9 , 20 0 3 . c Sp r i n g e r -V e r l a g B e r l i n H e i d e l b e r g 20 0 3 

4 . R e s to re d s p a c in g

3 6

In g e m a r K a j a n d Ia n M a rsh

s p a c in g b e tw e e n p a c k e ts is c o m p r e s s e d a n d e lo n g a te d r e la tiv e to e a c h o th e r. T h is is d u e t o t h e b u f f e r i n g i n i n t e r m e d i a t e r o u t e r s a n d m i xi n g w i t h c r o s s -t r a f fi c , s h o w n i n s t e p tw o . In o rd e r to re p la y th e p a c k e ts w ith th e ir o rig in a l s p a c in g , a b u ffe r is in tro d u c e d a t th e r e c e iv e r, c o m m o n ly r e f e r r e d to a s a jitte r b u ff e r s h o w n in s te p th r e e . T h e o b je c tiv e o f t h e b u f f e r i s t o a b s o r b t h e v a r i a n c e i n t h e i n t e r -p a c k e t s p a c i n g i n t r o d u c e d b y t h e d e l a y s d u e t o c r o s s t r a f fi c , a n d (p o t e n t i a l l y ) i t s o w n d a t a . I n s t e p f o u r , u s i n g i n f o r m a t i o n c o d e d in to th e h e a d e r o f e a c h p a c k e t, th e p a c k e ts a re re p la y e d w ith th e ir o rig in a l tim in g re s to re d . T h e m o tiv a tio n f o r th is w o r k d e r iv e s f r o m th e in a b ility o f u s in g k n o w n a r r iv a l p r o c e s s e s t o a p p r o xi m a t e t h e p a c k e t a r r i v a l p r o c e s s a t t h e r e c e i v e r . U s i n g a k n o w n a r r i v a l p r o c e s s , e v e n a c o m p l e xo n e , i s n o t a lw a y s r e a l i s t i c a s t h e m o d e l d o e s n o t i n c l u d e c h a r a c t e r i s t i c s t h a t r e a l a u d i o s t r e a m s e xp e r i e n c e . F o r e xa m p l e t h e u s e o f s i l e n c e s u p p r e s s i o n o r t h e d e l a y /j i t t e r c o n t r i b u t i o n o f c r o s s t r a f fi c . O n e a l t e r n a t i v e i s t o u s e r e a l t r a f fi c tr a c e s . A lth o u g h th e y p r o d u c e a c c u r a te a n d r e p r e s e n ta tiv e a r r iv a l p r o c e s s e s , th e y a r e i n h e r e n t l y s t a t i c a n d d o n o t o f f e r m u c h i n t h e w a y o f fl e xi b i l i t y . F o r e xa m p l e , o b s e r v i n g t h e a f f e c t o f d i f f e r e n t p a c k e t s i z e s w i t h o u t r e -r u n n i n g t h e e xp e r i m e n t s . W h e n t e s t i n g t h e p e r f o r m a n c e o f j i t t e r b u f f e r p l a y o u t a l g o r i t h m s , f o r e xa m p l e , t h i s i n fl e xi b i l i t y i s u n d e s ira b le . T h u s , a n im p o rta n t c o n trib u tio n o f th is p a p e r is to a d d re s s th e d e fi c ie n c ie s o f th e s e a p p ro a c h e s b y c o m b in in g th e a d v a n ta g e s o f b o th a m o d e l o f th e p ro c e s s , w ith d a ta fro m re a l tra c e s . T h is p a p e r p r e s e n ts in a d e s c r ip tiv e m a n n e r, a p a c k e t d e la y m o d e l, b a s e d o n th e m a in a s s u m p tio n th a t p a c k e ts a re s u b je c te d to in d e p e n d e n t tra n s m is s io n d e la y s . It is in te n d e d th a t re a d e rs n o t c o m p le te ly fa m ilia r w ith M a rk o v ia n th e o ry c a n fo llo w th e d e s c rip tio n . W e a s s u m e n o p rio r k n o w le d g e o f th e m o d e l a s it is b u ilt fro m fi rs t p rin c ip le s s ta rtin g in s e c t i o n 2. W e g i v e r e s u l t s f o r t h e m e a n a r r i v a l a n d i n t e r a r r i v a l t i m e s o f a u d i o p a c k e t s i n th is s e c tio n . W e a d d s ile n c e s u p p re s s io n to th e m o d e l in s e c tio n 3 a n d p a c k e t lo s s in th e n e xt s e c t i o n , 4 . R e a l d a t a i s i n c o r p o r a t e d i n s e c t i o n 5 , r e l a t e d w o r k f o l l o w s i n s e c t i o n 6 a n d w e c u s to m a rily ro u n d o ff w ith s o m e c o n c lu s io n s in s e c tio n 7 .

2

T h e P a ck et D ela y Mod el T h e re a re tw o c a u s e s o f d e la y fo r p a c k e t a u d io s tre a m s . F irs tly , th e d e la y c a u s e d b y o u r o w n tr a ffi c , i.e . p a c k e ts q u e u e d u p b e h in d o n e s f r o m th e s a m e fl o w , th is w e r e f e r t o a s t h e s e q u e n t i a l d e l a y . Se c o n d l y , t h e d e l a y c o n t r i b u t e d b y c r o s s t r a f fi c , u s u a l l y T C P W e b tra ffi c , w h ic h w e c a ll tra n s m is s io n d e la y in th is p a p e r. It is im p o rta n t to s ta te w e c o n s id e r th e s e tw o d e la y s a s s e p a ra te , b u t s tu d y th e ir c o m b in e d in te ra c tio n o n th e o b s e r v e d d e la y s a n d in te r a r r iv a ls . P r o p a g a tio n a n d s c h e d u lin g d e la y a r e n o t m o d e lle d a s p a rt o f th is w o rk . I n t h i s m o d e l p a c k e t s a r e t r a n s m i t t e d p e r i o d i c a l l y u s i n g a p a c k e t i s a t i o n t i m e o f 20 m illis e c o n d s . F o r c o n v e n ie n c e , th e p a c k e tis a tio n in te rv a l is u s e d a s th e tim e u n it fo r th e m o d e l . Sa y i n g t h a t a p a c k e t i s s e n t a t t i m e k s i g n i fi e s t h a t t h i s p a r t i c u l a r p a c k e t i s s e n t a t c l o c k t i m e 20k m s i n t o t h e d a t a s t r e a m . T h e fi r s t p a c k e t i s s e n t a t t i m e 0. W e b e g i n w i t h t h e t r a n s m i s s i o n d e l a y o f a p a c k e t . Su p p o s e t h a t p a c k e t k c o u l d b e s e n t is o la te d fro m th e re s t o f th e a u d io s tre a m a n d le t Yk = t r a n s m i s s i o n d e l a y o f p a c k e t k (n o . o f 20 m s p e r i o d s ).

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io

3 7

T o s e e th e im p a c t o f th e s e q u e n tia l d e la y , le t k ≥ 1.

Tk = t h e a r r i v a l t i m e o f p a c k e t k a t t h e j i t t e r b u f f e r ,

T h e m o d e l u s e d i n t h i s p a p e r i s s h o w n i n F i g u r e 2. T h e fi g u r e s h o w s p a c k e t s b e i n g t r a n s -

0

k + 1 k

k − 1

Se n d e r

T im e T ra n s m itte d P a c k e ts

R e c e iv e d P a c k e ts Tk R e c e iv e r

V k

T k + 1 U k

F i g . 2 . Tk a r r i v a l t i m e s b e f o r e p l a y o u t , Vk o b s e r v e d d e l a y s , Uk o b s e r v e d i n t e r a r r i v a l tim e s m th fe w

itte e ir re n e d

d fro m a s e n d e r a t re g u la r in te rv a ls . T h e y tra v e rs e th e n e tw o rk , w h e re a s s ta te d , o r i g i n a l s p a c i n g i s d i s t o r t e d . P a c k e t k a r r i v e s a t t i m e Tk a t t h e r e c e i v e r . T h e d i f c e in tim e b e tw e e n w h e n it d e p a r te d a n d a r r iv e d w e c a ll th e o b s e r v e d d e la y , w h ic h e n o te Vk = a r r i v a l t i m e − d e p a r t u r e t i m e = Tk − k + 1 k ≥ 1.

T h e t i m e w h e n t h e n e xt p a c k e t (n u m b e r e d k + 1) a r r i v e s i s Tk+1 a n d s o t h e o b s e r v e d i n t e r a r r i v a l t i m e s a r e o b t a i n e d a s t h e d i f f e r e n c e s b e t w e e n Tk+1 a n d Tk , d e n o t e d Uk = Tk+1 − Tk . A p a c k e t k, s e n t a t t i m e k−1, r e q u i r e s t i m e Yk t o p r o p a g a t e t h a r r i v e s t h e r e f o r e a t Tk = k − 1 + Yk , a s l o n g a s i t i s n o t d e l a y e d p a c k e t s (w h i c h w e c a l l s e q u e n t i a l d e l a y s ). I t m a y h o w e v e r c a t c t r a n s m i t t e d e a r l i e r (1 → k − 1). T h i s p a c k e t i s f o r c e d t o w a i t b e f p la y o u t b u ff e r. T h is s h o w s th a t th e a c tu a l a r r iv a l tim e s s a tis f y : T1 = Y1 Tk = max(Tk−1 , k − 1 + Yk ),

ro u g h th e n fu rth e r b y h u p to a u o re b e in g s

k ≥ 2.

e tw o o th e r d io p to re d

rk a n d a u d io a c k e ts in th e

(1)

Si n c e Tk−1 a n d Yk a r e i n d e p e n d e n t , w e c o n c l u d e f r o m t h e r e l a t i o n a b o v e (1) t h a t Tk f o r m s a t r a n s i e n t M a r k o v c h a i n . M o r e o v e r , t h e i n t e r a r r i v a l t i m e s s a t i s f y Uk = Tk − Tk−1 = max(0, k − 1 + Yk − Tk−1 ) k ≥ 2.

(2)

3 8

In g e m a r K a j a n d Ia n M a rsh

T h e a r r i v a l t i m e s (Tk ), i n t e r a r r i v a l t i m e s (Uk ) a n d o b s e r v e d d e l a y s (Vk ) c a n b e e a s i l y o b s e r v e d f r o m t r a f fi c t r a c e s . A s a n e xa m p l e , F i g u r e 3 s h o w s t h e h i s t o g r a m f o r a n 2 5 0

2 0 0

fre q u e n c y

1 5 0

1 0 0

5 0

0 0

2 0

4 0

F ig . 3 . H is to g ra m

6 0 in te r a r r iv a l tim e s , m s

8 0

1 0 0

1 2 0

o f t h e i n t e r a r r i v a l t i m e s (Uk )

e m p ir ic a l s e q u e n c e o f in te r a r r iv a l tim e s . T h e d a ta is f r o m a r e c o r d in g o f a V o ic e o v e r I P s e s s i o n b e t w e e n A r g e n t i n a a n d Sw e d e n , m o r e d e t a i l s o f t h e t r a f fi c t r a c e s a r e g i v e n i n s e c t i o n 5 . 1. T h e t r a n s m i s s i o n d e l a y s e q u e n c e (Yk ) s h o u l d b e o n t h e o t h e r h a n d c o n s i d e r e d a s n o n -o b s e r v a b l e . T h e a p p r o a c h i n t h i s s t u d y i s t o c o n s i d e r (Yk ) h a v i n g a g e n e r a l (u n k n o w n ) d i s t r i b u t i o n a n d i n v e s t i g a t e t h e r e s u l t i n g p r o p e r t i e s o f t h e o b s e r v e d d e l a y (Vk ) a n d i n t e r a r r i v a l t i m e s (Uk ). Si n c e t h e l a t t e r s e q u e n c e s c a n b e e m p i r i c a l l y o b s e rv e d , th is le a d s to th e q u e s tio n to w h e th e r th e tra n s m is s io n d e la y d is trib u tio n c a n b e re c o n s tru c te d u s in g s ta tis tic a l in fe re n c e . In th is d ire c tio n w e w ill in d ic a te s o m e m e th o d s th a t c o u ld b e u s e d to c o m p a re th e th e o re tic a l re s u lts w ith th e g a th e re d e m p iric a l d a ta . T o c a r r y o u t t h e s t u d y , w e a s s u m e f r o m t h i s p o i n t t h e s e q u e n c e (Yk ) i s i n d e p e n d e n t a n d id e n tic a lly d is trib u te d , w ith d is trib u tio n fu n c tio n

a n d fi n ite s tu d y , ty p ju s tifi e d f to a llo w d 2 .1

m e a n ic a l v o r th e e p e n d

F (x) = P (Yk ≤ x), k ≥ 1, ∞ t r a n s m i s s i o n d e l a y ν = 0 (1 − F (x)) dx < ∞. F o r t h e d a t a i n o u r a l u e s o f ν a r e 20 -4 0 , i . e . 4 0 0 -8 0 0 m s . W e c o n s i d e r t h e s e a s s u m p t i o n s p u rp o s e o f s tu d y in g a re fe re n c e m o d e l, o b v io u s ly it w o u ld b e d e s ira b le e n c e o v e r tim e .

Mea n Ar r i v a l a n d I n ter a r r i v a l T i m es

I t i s i n t u i t i v e l y c l e a r t h a t i n t h e l o n g r u n E(Uk ) ≈ 1 a s o n a v e r a g e p a c k e t s a r r i v e w i t h 20 m s s p a c i n g , w h i c h w e w i l l n o w v e r i f y f o r t h e m o d e l . T h e r e p r e s e n t a t i o n (1) f o r Tk c a n b e w ritte n

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io

3 9

Tk = max(Y1 , 1 + Y2 , . . . , k − 1 + Yk ) k ≥ 1, w h ic h g iv e s th e a lte r n a tiv e r e p r e s e n ta tio n  ), Tk = max(Y1 , 1 + Tk−1

k≥2

(3 )

w h e re o n th e rig h t s id e  = max(Y2 , 1 + Y3 , . . . , k − 2 + Yk ) Tk−1

h a s t h e s a m e m a r g i n a l d i s t r i b u t i o n a s Tk−1 b u t i s i n d e p e n d e n t o f Y1 . F r o m t h a t w e c a n w r i t e {Tk > t} a s a u n i o n o f t w o d i s j o i n t e v e n t s , a s

(3 ) f o l l o w s

  > t} ∪ {Y1 > t, 1 + Tk−1 ≤ t}. {Tk > t} = {1 + Tk−1  H e n c e , u s i n g t h e i n d e p e n d e n c e o f Tk−1 a n d Y1 ,   > t) + P (Y1 > t, 1 + Tk−1 ≤ t) P (Tk > t) = P (1 + Tk−1 = P (1 + Tk−1 > t) + P (Y1 > t)P (1 + Tk−1 ≤ t)

a n d so



∞

E(Tk ) =

P (Tk > t) dt  ∞ P (Y1 > t)P (Tk−1 ≤ t − 1) dt. = E(1 + Tk−1 ) + 0

(4 )

1

T h e re fo re

 E(Uk ) = 1 +

∞

P (Y1 > t)P (Tk−1 ≤ t − 1) dt → 1,

k→∞

(5 )

1

∞ (s i n c e ν = 0 P (Y1 > t) dt < ∞ a n d Tk → ∞, t h e d o m i n a t e d c o n v e r g e n c e t h e o r e m a p p l i e s f o r c i n g t h e i n t e g r a l t o v a n i s h i n t h e l i m i t ). A f u r t h e r c o n s e q u e n c e o f (4 ) i s o b t a i n e d b y i t e r a t i o n ,  ∞ k−1  E(Tk ) = k − 1 + E(Y1 ) + P (Y1 > t) P (Ti ≤ t − 1) dt. 1

i=1

If w e in tro d u c e N (t) = t h e n u m b e r o f a r r i v i n g p a c k e t s i n t h e t i m e i n t e r v a l (0, t], s o t h a t {N (t) ≥ n} = {Tn ≤ t}, t h i s c a n b e w r i t t e n 

∞

E(Vk ) = E(Y1 ) +

P (Y1 > t) 1

k−1 

P (N (t − 1) ≥ i) dt,

(6 )

i=1

w h i c h , a s k → ∞, g i v e s a n a s y m p t o t i c r e p r e s e n t a t i o n f o r t h e a v e r a g e o b s e r v e d d e l a y a s  ∞ E(Vk ) → ν + P (Y1 > t)E(N (t − 1))) dt. (7 ) 1

4 0

2 .2

In g e m a r K a j a n d Ia n M a rsh

S tea d y S ta te D i s tr i b u ti on s

B y (1), P (Tk ≤ x) =

k 

P (i + Yi ≤ x + 1) =

i=1

k−1 

F (x − i),

i=0

a n d t h e r e f o r e t h e s e q u e n c e (Vk ), w h i c h w e d e fi n e d b y Vk = Tk − k + 1, k ≥ 1, s a t i s fi e s P (Vk ≤ x) =

k−1 

F (x + k − 1 − i) =

i=0

k−1 

F (x + i) x ≥ 0.

i=0

T h i s s h o w s t h a t (Vk ) i s a M a r k o v c h a i n w i t h s t a t e s p a c e t h e p o s i t i v e r e a l l i n e a n d a s y m p to tic d is tr ib u tio n g iv e n b y P (V∞ ≤ x) =

∞ 

F (x + i) x ≥ 0.

(8 )

i=0

F u rth e rm o re , fo r x≥0 P (Uk ≥ x) = P (k − 1 + Yk − Tk−1 ≥ x) = P (Vk−1 ≤ Yk + 1 − x)  ∞ = P (Vk−1 ≤ y + 1 − x) dF (y), 0

w h e r e i n t h e s t e p o f c o n d i t i o n i n g o v e r Yk w e u s e t h e i n d e p e n d e n c e o f Yk a n d Vk−1 . T h e r e f o r e t h e s e q u e n c e (Uk ) h a s t h e a s y m p t o t i c d i s t r i b u t i o n  ∞ ∞ P (U∞ ≤ x) = 1 − F (y − x + i) dF (y) x ≥ 0, (9 ) 0

i=1

in p a rtic u la r a p o in t m a s s in z e ro o f s iz e  P (U∞ = 0) = 1 − 0

∞ ∞

F (y + i) dF (y).

(10 )

i=1

T h i s d i s t r i b u t i o n h a s t h e p r o p e r t y t h a t E(U∞ ) = 1 f o r a n y g i v e n d i s t r i b u t i o n F o f Y w i t h ν = E(Y ) < ∞. I n f a c t , t h i s f o l l o w s f r o m 5 u n d e r a s l i g h t l y s t r o n g e r a s s u m p t i o n o n Y (u n i f o r m i n t e g r a b i l i t y ), b u t c a n a l s o b e v e r i fi e d d i r e c t l y b y i n t e g r a t i n g (9 ). F i g u r e d P (U∞ ≤ 4 s h o w s n u m e r i c a p p r o xi m a t i o n s o f t h e (n o n -n o r m a l i s e d ) d e n s i t y f u n c t i o n dx x) o f (9 ) f o r t h r e e c h o i c e s o f F . A l l t h r e e d i s t r i b u t i o n s s h o w a c h a r a c t e r i s t i c p e a k c l o s e t o t i m e 1c o r r e s p o n d i n g t o t h e b u l k o f p a c k e t s a r r iv i n g w i t h m o r e o r l e s s c o r r e c t s p a c i n g o f 20 m s . A f r a c t i o n o f t h e p r o b a b i l i t y m a s s i s fi xe d a t x = 0 i n a c c o r d a n c e w i t h (10 ), b u t n o t s h o w n e xp l i c i t l y i n t h e fi g u r e . T h e s e f e a t u r e s o f t h e d e n s i t y f u n c t i o n s c a n b e c o m p a r e d w i t h t h e s h a p e o f t h e h i s t o g r a m i n F i g u r e 3 w i t h i t s p e a k a t t h e 20 m s s p a c i n g . A l s o , c l o s e t o t h e o r i g i n i s a s m a l l p e a k w h i c h c o r r e s p o n d s t o p a c k e t s a r r i v i n g b a c k -t o b a c k u s u a lly a r r iv in g a s a b u r s t, p r o b a b ly d u e to a d e la y e d p a c k e t a h e a d o f th e m . I n F ig u re 4 th e d e n s ity fu n c tio n w ith th e h ig h e s t p e a k c lo s e to 1tim e u n it is a G a u s s ia n d i s t r i b u t i o n w i t h a r b i t r a r i l y s e l e c t e d p a r a m e t e r s m e a n 5 a n d v a r i a n c e 0 . 2. O f t h e t w o e xp o n e n t i a l d i s t r i b u t i o n s , t h e o n e w i t h t h e h i g h e r v a r i a n c e (E xp (3 )) h a s a l o w e r p e a k a n d m o r e m a s s a t z e r o c o m p a r e d w i t h a n e xp o n e n t i a l w i t h s m a l l e r v a r i a n c e (E xp (2)).

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io

4 1

1 .5

1

0 .5

0 0

0 .5

1

1 .5

2

2 .5

3

3 .5

4

F i g . 4 . D e n s i t y f u n c t i o n s o f U f o r N (5 , 0 . 2), E xp (2) a n d E xp (3 )

3

S i len ce S u p p r es s i on Mech a n i s m

In th is su p p re tra n s m a c c o u n o n th e

s e c tio n w e s s io n in to th it p a c k e ts w ts fo r a b o u t n e tw o rk . A s

in c o e m o h e n h a lf s ig n

rp o ra te a n d e l . Si l e n c th e re is n o o f th e to ta to p a c k e t n

a d d itio n a l s o u rc e o f ra n d o m e s u p p re s s io n is e m p lo y e d a t s p e e c h a c tiv ity . D u r in g a n o l n u m b e r o f p a c k e ts , c o n s id e r u m b e r kth e q u a n tity

d e la th e s rm a l a b ly

y s d u e to s e n d e r so a s c o n v e rs a tio re d u c in g th

ile n c e n o t to n th is e lo a d

Xk = d u r a t i o n o f s i l e n t p e r i o d b e t w e e n p a c k e t s k − 1 a n d k. A s ile n t p e rio d is th e tim e in te rv a l d u rin g w h ic h th e s ile n c e s u p p re s s io n m e c h a n is m is i n e f f e c t . W e a s s u m e t h a t t h e s i l e n c e s u p p r e s s i o n i n t e r v a l s a r e i n d e p e n d e n t o f (Yk )k≥1 a n d a r e g i v e n b y a s e q u e n c e o f i n d e p e n d e n t r a n d o m v a r i a b l e s X1 , X2 , . . ., s u c h t h a t G(x) = P (Xk ≤ x),

1 − α = G(0) = P (Xk = 0) > 0,

μ = E(Xk ) < ∞.

T h e (s m a l l ) p r o b a b i l i t y α = P (Xk > 0) r e p r e s e n t s t h e c a s e w h e r e s i l e n c e s u p p r e s s i o n is a c tiv a te d ju s t a f te r p a c k e t k−1is tr a n s m itte d f r o m th e s e n d e r. N o te th a t Sk =

k 

Xi = t o t a l t i m e o f s i l e n c e s u p p r e s s i o n a f f e c t i n g p a c k e t k,

i=1

w h ic h im p lie s th a t th e d e liv e r y o f p a c k e t k f r o m k − 1 + Sk . T h e r e p r e s e n t a t i o n (1) t a k e s t h e f o r m T1 = S1 + Y1 ,

th e s e n d in g u n it n o w

Tk = max(Tk−1 , k − 1 + Sk + Yk ),

s ta rts a t tim e

k ≥ 2,

(11)

4 2

In g e m a r K a j a n d Ia n M a rsh

h e n c e Uk = Tk − Tk−1 = max(0, k − 1 + Sk + Yk − Tk−1 ) k ≥ 2.

(12)

Si m i l a r l y , Vk = a r r i v a l t i m e − d e p a r t u r e t i m e = Tk − k + 1 − Sk

k ≥ 1.

T h e a l t e r n a t i v e r e p r e s e n t a t i o n (3 ) i s  ), Tk = X1 + max(Y1 , 1 + Tk−1

(13 )

w h e re  Tk−1 = max(Y2 + S2 − X1 , 1 + Y2 + S2 − X1 , . . . , k − 2 + Yk + Sk − X1 )

h a s t h e s a m e m a r g i n a l d i s t r i b u t i o n a s Tk−1 b u t i s i n d e p e n d e n t o f X1 a n d Y1 . I n a n a l o g y w i t h t h e c a l c u l a t i o n o f t h e p r e v i o u s s e c t i o n l e a d i n g u p t o (4 ), t h i s r e l a t i o n g i v e s  ∞  E(Tk ) = E(X1 + 1 + Tk−1 ) + P (X1 + Y1 > t, X1 + Tk−1 ≤ t − 1) dt. (14 ) 1

E xc h a n g i n g t h e o p e r a t i o n s o f i n t e g r a t i o n a n d e xp e c t a t i o n s h o w s t h a t t h e l a s t i n t e g r a l c a n b e w ritte n  ∞   E 1{Y1 > t − X1 , Tk−1 > t − X1 − 1} dt 1+X1

w h e r e w e h a v e a l s o u s e d t h a t t h e i n t e g r a n d v a n i s h e s o n t h e s e t {t ≤ 1 + X1 }.  A p p l y ∞  t h e c h a n g e -o f -v a r i a b l e s t → t − X1 t o g e t E 1 1{Y1 > t, Tk−1 > t − 1} dt . T h e n s h i f t i n t e g r a t i o n a n d e xp e c t a t i o n a g a i n t o o b t a i n f r o m (14 ) t h e r e l a t i o n s  ∞ P (Y1 > t)P (Tk−1 ≤ t − 1) dt E(Tk ) = 1 + E(X1 ) + E(Tk−1 ) + 0



a n d E(Uk ) = 1 + E(X1 ) +

∞

P (Y1 > t)P (Tk−1 ≤ t − 1) dt.

1

H e n c e w i t h s i l e n c e s u p p r e s s i o n , a s k → ∞,  E(Uk ) → 1 + μ,

E(Vk ) → ν +

∞

P (Y1 > t)E(N (t − 1)) dt,

(15 )

1

u s in g th e s a m e a rg u m e n ts a s in th e s im p le r c a s e o f th e p re v io u s s e c tio n .

4

I n clu d i n g P a ck et L os s i n th e Mod el W e re tu rn to th e o rig in a l m o d e l w ith o u t s ile n c e s u p p re s s io n b u t c o n s id e r in s te a d th e e f f e c t o f l o s t p a c k e t s . Su p p o s e t h a t e a c h I P p a c k e t i s s u b j e c t t o l o s s w i t h p r o b a b i l i t y p, in d e p e n d e n tly o f o th e r p a c k e t lo s s e s a n d o f th e tra n s m is s io n d e la y s . L o s t p a c k e ts a re

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io

4 3

u n a c c o u n t e d f o r a t t h e r e c e i v e r a n d h e n c e , i n t h i s s e c t i o n , t h e s e q u e n c e (Tk ) r e c o r d s a r r i v a l t i m e s o f n o n -l o s t p a c k e t s o n l y . T o k e e p t r a c k o f t h e i r d e l i v e r y t i m e s f r o m t h e s e n d e r in tro d u c e Kk = n u m b e r o f a t t e m p t s r e q u i r e d b e t w e e n s u c c e s s f u l p a c k e t s k − 1 a n d k,

k ≥ 1,

w h i c h g i v e s a s e q u e n c e (Kk )k≥1 o f i n d e p e n d e n t , i d e n t i c a l l y d i s t r i b u t e d r a n d o m a b le s w ith th e g e o m e tric d is trib u tio n P (Kk = j) = (1 − p)pj ,

v a ri-

j ≥ 0.

M o re o v e r, Lk = K1 + . . . + Kk =n u m b e r o f a tte m p ts re q u ire d fo r ks u c c e s s fu l p a c k e ts is a s e q u e n c e o f r a n d o m v a r ia b le s w ith a n e g a tiv e b in o m ia l d is tr ib u tio n . T h e a r r iv a l tim e s o f p a c k e ts a r e n o w g iv e n b y T1 = K1 − 1 + YK1 ,

Tk = max(Tk−1 , Lk − 1 + YLk ),

k ≥ 2.

D u e t o t h e i n d e p e n d e n c e w e m a y r e -i n d e x t h e s e q u e n c e o f YLk ’ s t o o b t a i n T1 = K1 − 1 + Y1 , a n d th u s

Tk = max(Tk−1 , Lk − 1 + Yk ),

 ), Tk = K1 − 1 + max(Y1 , 1 + Tk−1  Tk−1

w i t h K1 , Y1 a n d a ll in d e p e n d e n t, T h i s i s t h e s a m e r e l a t i o n a s (13 ) w i t h 1 E(Uk ) → 1 + E(K1 − 1) = 1−p , e s tim a te p a c k e t lo s s b a s e d o n o b s e rv e d s u p p re s s io n a n d p a c k e t lo s s ,

a n d a g a i n Tk−1 a X1 r e p l a c e d b y k → ∞, w h i c h in te r a r r iv a l tim e

E(Uk ) → 1 + E(X) + E(K1 − 1) = μ +

5

k ≥ 2.

k≥2  Tk−1

n d id e n K1 − 1 a n d p ro v id e s a s . Si m i l a r l y , 1 , 1−p

(16 ) tic a h e n s im c o m

lly d is trib u te d . c e , a s i n (15 ), p le m e th o d to b in in g s ile n c e

k → ∞,

(17 )

I n cor p or a ti n g R ea l D a ta 5 .1

T r a ce D a ta

W e g iv e a b r ie f d fo r th e p a ra m e te w e re se n t fro m a o f w e e k s 1. T h e im p lie s th e p a c k s i t e i s a p p r o xi m

e s c rip tio n o f rs in th e m o s ite in B u e n s tre a m s a re e ts le a v e th e a t e l y 12, 0 0 0

t h e e xp e r i m e n t s w e p e r f o r m e d i n o r d e r t o o b t a i n e s t i m a t e s d e l . P u l s e C o d e M o d u l a t e d (P C M ) p a c k e t a u d i o s t r e a m s o s A i r e s , A r g e n t i n a t o St o c k h o l m , Sw e d e n o v e r a n u m b e r s e n t w i t h a 6 4 k b i t s /s e c r a t e i n 16 0 b y t e p a y l o a d s . T h i s s e n d e r w i t h a i n t e r -p a c k e t s p a c i n g o f 20 m s . T h e r e m o t e k i l o m e t r e s , 25 I n t e r n e t h o p s a n d f o u r t i m e z o n e s f r o m

4 4

In g e m a r K a j a n d Ia n M a rsh

o b s e r v e d d e la y s , m s

6 8 0

6 6 0

6 4 0

6 2 0

6 0 0 1 7 0 0

1 7 2 0

1 7 4 0

1 7 6 0

1 7 8 0 1 8 0 0 1 8 2 0 p a c k e t s e q u e n c e n u m b e r

1 8 4 0

1 8 6 0

1 8 8 0

1 9 0 0

1 7 2 0

1 7 4 0

1 7 6 0

1 7 8 0 1 8 0 0 1 8 2 0 p a c k e t s e q u e n c e n u m b e r

1 8 4 0

1 8 6 0

1 8 8 0

1 9 0 0

in te r in te r v a l tim e s , m s

8 0

6 0

4 0

2 0

0 1 7 0 0

F i g . 5 . F o u r s e c o n d a u d i o p a c k e t t r a c e s : a )d e l a y s b )i n t e r a r r i v a l t i m e s o u r re w h e n se c o n le a v e se q u e

c e th d s th n c

iv e r. e sp e a n d e se n e

T h e to o l is a k e r is s ile n w ith s u p p re d e r a n d th e

c a p t. W s s io a b s

a b le o f s ile n c e s u p ith o u t s ile n c e s u p p n 20 6 4 a r e s e n t . W o lu te a r r iv a l tim e s

p re s s io n , in w h ic re s s io n , 3 5 6 3 p a c e re c o rd th e a b s o a t th e r e c e iv e r. T

h p a c k e k e ts a re lu te tim h is g iv e

ts se e s s

a re n o t se n t n t d u rin g 7 0 th e p a c k e ts a n o b se rv e d

vk = a r r i v a l t i m e n o k − d e p a r t u r e t i m e n o k o f t h e M a r k o v c h a i n (Vk ). I n p a r t i c u l a r , t h e s a m p l e m e a n v¯ i s a n e s t i m a t e o f t h e o n e -w a y d e l a y . Si m i l a r l y , uk = a r r i v a l t i m e n o k − a r r i v a l t i m e n o (k − 1) i s a s a m p l e o f t h e i n t e r a r r i v a l t i m e s e q u e n c e (Uk ). A ty p ic a l s e q u e n c e o f tra c e d a ta u s e d in th is s tu d y w ith o u t s ile n c e s u p p re s s io n is s h o w n i n F i g u r e 5 , w h i c h s h o w s (vk ) a n d (uk ) f o r a s m a l l s e q u e n c e o f 20 0 p a c k e t s (1700 ≤ k < 1900), c o r r e s p o n d i n g t o f o u r s e c o n d s o f a u d i o . T o f u r t h e r i l l u s t r a t e s u c h t r a c e d a t a , F i g u r e 6 s h o w s a h i s t o g r a m o f t h e d e l a y s (vk ) a n d F i g u r e 3 a h i s t o g r a m f o r t h e i n t e r a r r i v a l t i m e s (uk ). I t c a n b e n o t e d t h a t l a r g e v a l u e s o f i n t e r a r r i v a l t i m e s a re s o m e tim e s fo llo w e d b y v e ry s m a ll o n e s , m a n ife s tin g th a t a s e v e re ly d e la y e d p a c k e t f o r c e s s u b s e q u e n t p a c k e t s t o a r r i v e b a c k -t o -b a c k . T h e f r a c t i o n o f p a c k e t s a r r i v i n g i n th is m a n n e r c o rre s p o n d s to th e h e ig h t o f th e le ftm o s t p e a k in th e h is to g ra m o f F ig u re 3 . R e tu r n in g to tr a c e s w ith s ile n c e s u p p r e s s io n , F ig u r e 7 g iv e s th e s ta tis tic s o f th e re c o rd e d v o ic e s ig n a l u s e d . T h e u p p e r p a rt s h o w s a h is to g ra m o f th e ta lk s p u rts a n d th e l o w e r p a r t t h e c o r r e s p o n d i n g h i s t o g r a m f o r t h e n o n -z e r o p a r t o f t h e d i s t r i b u t i o n G o f 1

A v a ila b le fro m

h t t p : //w w w . s i c s . s e /˜ i a n m /C O ST 26 3 /c o s t 26 3 . h t m l

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io

4 5

3 0 0

2 5 0

fre q u e n c y

2 0 0

1 5 0

1 0 0

5 0

0

5 0 0

5 5 0

6 0 0

6 5 0 o b s e r v e d d e la y tim e s , m s

7 0 0

7 5 0

8 0 0

o f t h e o b s e r v e d d e l a y s (Vk )

F ig . 6 . H is to g ra m

t h e s i l e n c e i n t e r v a l s X d i s c u s s e d i n s e c t i o n 3 . T h e p r o b a b i l i t y α = P (X = 0) a n d t h e e xp e c t e d v a l u e μ = E(X) w e r e e s t i m a t e d t o α∗ = 0.0456

5 .2

μ∗ = 25.7171.

N u m er i ca l E s ti m a tes

In m c a sa

th is s e c tio n w e in d ic a te a fe w s im p le n u m e ric a l te c h n iq a te s b a s e d o n tra c e d a ta . In p rin c ip le s u c h m e th o d s b a s e d n b e u s e d fo r s y s te m a tic s tu d ie s o f th e d e la y s a n d lo s s e s m p le d in d iffe re n t e n v iro n m e n ts . C o n s id e rin g fi rs t th e c a s e o f n o s ile n c e s u p p re s s io n , it t h a t g i v e n a n o b s e r v e d r e a l i z a t i o n (uk )nk=1 o f (Uk ), a p o i n p r o b a b i l i t y p i s o b t a i n e d f r o m (17 ) (w i t h μ = 0), u s i n g 20 p =1− , u ¯ ∗

O u r m e a s u re m e n ts g a v e c o n s is te n tly b i l i t i e s o f t h e o r d e r 10−4 . N e xt w e l o o k a t a n e xp e r i m e n t w d iffe re n t tim e s u s in g s ile n c e s u p p re s c e iv e r d u r in g e a c h tr a n s m is s io n . T a b th e e s tim a te d μfro m th e tra c e fi le s . o f t h e o r d e r 0.5 m i l l i s e c o n d s i n t h e

u e s th a t g iv e p a r a m e te r e s tio n th e m o d e l p re s e n te d h e re a n d fo r c o m p a ris o n o f tra c e s w a s p o in te d o u t in s e c tio n 4 t e s tim a te o f th e p a c k e t lo s s

1 u ¯= uk m s . n n

k=1

u ¯ ≈ 20.002 − 20.005 m s , i n d i c a t i n g l o s s p r o b a h e r e t h e p r e -r e c o r d e d v o i c e s io n , a n d th e in te r a r r iv a l tim l e 1 s h o w s t h e e xp e c t e d s i l e T h e o b ta in e d e s tim a te s in d m e a n v a lu e s o f th e s ile n c e

is tra n s m e s m e a su n c e in te rv ic a te a s y su p p re ss

itte d a t s e v e n re d a t th e re a l E(X) a n d s te m a tic b ia s io n in te rv a ls .

4 6

In g e m a r K a j a n d Ia n M a rsh

N o o f o b s e r v a tio n s

4 0

3 0

2 0

1 0

0 0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0 2 5 0 0 3 0 0 0 L e n g th o f ta lk s p u r ts , m s

3 5 0 0

4 0 0 0

4 5 0 0

5 0 0 0

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0 2 5 0 0 3 0 0 0 L e n g th o f s ile n t in te r v a ls , m s

3 5 0 0

4 0 0 0

4 5 0 0

5 0 0 0

N o o f o b s e r v a tio n s

4 0

3 0

2 0

1 0

0

F ig . 7 . L e n g th s o f ta lk s p u rts a n d s ile n c e p e rio d s T a b le 1 . Si l e n c e I n t e r v a l P a r a m e t e r s T tra tra tra tra tra tra tra

P a c k e t lo s s e s d o n o t s e e m to s iv e s ta tis tic a l a n a ly s is m ig h p re lim in a ry in v e s tig a tio n w e W e n o w c o n s id e r th e p ro g i v e n a fi xe d l e n g t h s a m p l e d e la y s . O n e m e th o d fo r th is I n d e e d , r e w r i t i n g (8 ) a s t h e s

ra c e c e c e c e c e c e c e

c e 1 2 3 4 5 6 7

25 26 26 26 26 26 26

E (X ) .7 4 9 2 . 220 4 . 228 4 . 216 4 . 218 6 . 2124 . 220 9

E (X 0 .0 0 .4 0 .5 0 .4 0 .5 0 .4 0 .5

) - μ∗ 3 21 6 3 9 113 9 9 3 0 15 9 5 3 0 3 8

e xp l a i n f u l l y t h e o b s e r v e d d e v i a t i o n . A m o r e c o m p r e h e n t re v e a l th e s o u rc e o f th is s lig h t m is m a tc h . F o r th e p re s e n t fi n d th e n u m e ric a l e s tim a te s s a tis fa c to ry . b le m o f e s tim a tin g th e d is trib u tio n F o f p a c k e t d e la y s Y o b s e r v a t i o n (vk ) o f t h e M a r k o v c h a i n (Vk ) f o r o b s e r v e d c a n b e b a s e d o n t h e s t e a d y s t a t e a n a l y s i s i n s e c t i o n 2. 2. im p le re la tio n

P (V∞ ≤ x) = F (x)

∞ 

F (x + i) = F (x) P (V∞ ≤ x + 1)

i=1

s h o w s t h a t i f w e l e t F¯V d e n o t e a n e m p i r i c a l d i s t r i b u t i o n f u n c t i o n o f V , t h e n w e o b t a i n a n e s t i m a t e F¯ o f F b y t a k i n g F¯V (x) F¯ (x) = ¯ FV (x + 1)

x ≥ 0,

(18 )

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io

4 7

w h e r e w e r e c a l l t h a t t h e v a r i a b l e x i s m e a s u r e d i n u n i t s o f 20 m s i n t e r v a l s . A n a p p l i c a t i o n o f t h i s n u m e r i c a l a l g o r i t h m t o t h e t r a c e d a t a o f t h e p r e v i o u s fi g u r e s (5 a n d 6 ) y i e l d s a n e s tim a te d d e n s ity f u n c tio n f o r Y a s in F ig u r e 8 . T h e n u m e r ic a l s c h e m e is s e n s itiv e 1 .2

1

e s tim a te d fr e q u e n c y

0 .8

0 .6

0 .4

0 .2

0

5 0 0

5 5 0

6 0 0

6 5 0 d e la y tim e s , m s

7 0 0

7 5 0

8 0 0

F ig . 8 . E s tim a te d d e n s ity o f Y fo th la in th th

6

r s m a ll c h a n g e s in th e d a ta , s o it is d iffi c u lt to e d i s t r i b u t i o n o f F . A s e xp e c t e d t h e g r a p h i s y s , F ig u re 6 , b u t w ith c e rta in d iffe re n c e s d u e t h e s e q u e n c e (Vk ) a s o p p o s e d t o t h e i n d e p e e s h ift to w a rd s s m a lle r v a lu e s fo r Y in c o m p a e i n e q u a l i t y F¯ (x) ≥ F¯V (x) v a l i d f o r a l l x, w

d ra w v e ry to th n d e n ris o n h ic h

c o n c lu s io n s o n th e fi n e r d e ta s im ila r to th a t o f th e o b s e rv e e M a rk o v ia n d e p e n d e n c e s tru c e i n (Yk ). T h e m a i n d i f f e r e n to th o s e o f V. T h is c o r r e s p o n i s o b v i o u s f r o m (18 ).

ils d d c tu c e d s

o f e re is to

R ela ted W or k

M a n y re s e a rc h e rs h a v e lo o k e d a t th e n e e d s in te rm s o f b u ffe r s iz e fo r p a c k e t s tre a m s c h a r a c t e r i s e d b y M a r k o v (s e m i o r m o d u l a t e d ) b e h a v i o u r e s p e c i a l l y i n t h e c a s e o f m u l t i p l e xe d s o u r c e s . T h e i r g o a l w a s t o d e r i v e t h e w a i t i n g t i m e o f p a c k e t s s p e n t i n t h e b u f f e r s h o w n a s p r o b a b ility d e n s ity f u n c tio n o f th e w a itin g tim e s . R e la tiv e ly f e w , h o w e v e r, h a v e lo o k e d a t th e a r r iv a l p r o c e s s u s in g a s ta g e o f b u ff e r s a n d id e n tif y in g e m b e d d e d M a rk o v c h a in s fro m a s in g le s o u rc e . A d d itio n a lly w e c o n c e n tra te o n th is s c e n a rio , in c lu d in g b o th s tre a m s w ith a n d w ith o u t s ile n c e s u p p re s s io n . A d d itio n a lly a s fa r a s w e k n o w , n o -o n e h a s u s e d r e a l t r a c e d a t a t o e n h a n c e a n d v e r i f y t h e i r m o d e l s t o t h e l e v e l w e sh o w . So m e e a r l y a n a l y t i c a l w o r k o n t h e b u f f e r s i z e r e q u i r e m e n t s f o r p a c k e t i s e d v o i c e i s s u m m a r i s e d b y G o p a l e t a l . [1]. O n e o f t e n c i t e d p i e c e o f w o r k i s B a r b e r i s [2]. A s p a r t o f t h i s w o r k h e a s s u m e s t h e d e l a y s e xp e r i e n c e d b y p a c k e t s o f t h e s a m e t a l k s p u r t a r e i . i . d a c c o r d i n g t o a n e xp o n e n t i a l d i s t r i b u t i o n p(t) = λe−λT w h e r e 1/λ i s t h e a v e r a g e

4 8

In g e m a r K a j a n d Ia n M a rsh

tra n s m is s io n d e la y a n d s ta n d a rd d e v ia tio n . b u f f e r r e q u i r e m e n t s [3 ] m o d e l t h e a r r i v a l p r [1 − F (j, n − j + 1)] o f t h e e v e n t “ n o a r r i v a o u tc o m e o f th e tria l is re p re s e n te d b y th e ra n  1if p a c k e t j h a s k(j, n) = 0o th e rw is e .

M o c l y d o

.K . e ss e t” m v

M a s a t a r

e h m e a B e e a c h ia b le

t A li e t a l. in th e ir w o rk o f rn o u lli tria l w ith p ro b a b ility in te r v a l u p to its a r r iv a l. T h e k(j, n):

a r r iv e d a t o r b e f o r e tim e n

F e r r a n d i z a n d L a z a r i n [4 ] l o o k a t t h e a n a l y s i s o f a r e a s in g le c h a n n e l n o d e a n d c o m p u te its p e rfo rm a n c e p a ra m m o d e l p r im itiv e s . T h e y d o n o t u s e a n y M a r k o v ia n a s s u m w h i c h u s e s a s e r i e s o f o v e r l o a d a n d u n d e r -l o a d p e r i o d s . D d is c a r d e d . T h e y d e r iv e a n a d m is s io n c o n tr o l s c h e m e b a s e d a r r iv a l r a te . V a n D e r W a l e t a l. d e r iv e a m o d e l f o r th e e n d to i n l a r g e s c a l e I P n e t w o r k s [5 ]. T h e i r m o d e l i n c l u d e s d i f f e th e d e la y b u t n o t th e a r r iv a l p r o c e s s o f a u d io p a c k e ts p e r s d e s c r i b e d h e r e i s a l s o d i s c u s s e d i n t h e b o o k [6 ].

7

a l tim e p a c k e t s e s s io n o v e r e te rs a s a fu n c tio n o f th e ir p tio n s , ra th e r a n a p p ro a c h u rin g o v e rlo a d p a c k e ts a re o n a n a v e ra g e o f th e p a c k e t e n d d e la y fo r v o ic e p a c k e ts re n t fa c to rs c o n trib u tin g to e . T h e m a th e m a tic a l m o d e l

C on clu s i on s

W e h a v e a d d r e s s e d th e p r o b le m o f m o d e llin g th e a r r iv a l p r o c e s s o f a s in g le p a c k e t a u d io s tre a m . T h e m o d e l c a n b e u s e d to p ro d u c e p a c k e t a u d io s tre a m s w ith c h a ra c te ris tic s , a t le a s t, q u ite s im ila r to th e p a rtic u la r tra c e s w e h a v e o b ta in e d . T h e m o d e l is s u ita b le fo r g e n e ra tin g s tre a m s b o th w ith a n d w ith o u t s ile n c e s u p p re s s io n a p p lie d a t th e s o u rc e , in a d d itio n th e c a s e w h e re p a c k e ts a re lo s t h a s b e e n in c lu d e d . T h e w o r k c a n b e g e n e r a lly a p p lie d to r e s e a r c h w h e r e m o d e llin g a r r iv in g p a c k e t a u d i o s t r e a m s n e e d s t o b e p e r f o r m e d . A n a t u r a l n e xt s t e p i s t o u s e t h e a r r i v a l m o d e l p re s e n te d h e re fo r e v a lu a tio n o f jitte r b u ffe r p e rfo rm a n c e , s u c h a s in v e s tig a tin g w a itin g tim e s a n d p o s s ib le p a c k e t lo s s in th e jitte r b u ffe r. W e o b s e rv e d fro m o u r m o d e l th a t th e i n t e r a r r i v a l t i m e s a r e n e g a t i v e l y c o r r e l a t e d (a s m e n t i o n e d Se c t i o n 5 . 1). T h i s w i l l h a v e a n im p a c t o n th e d y n a m ic s a n d p e rfo rm a n c e o f a jitte r b u ffe r. W ith a n a c c u ra te m o d e l, b a s e d o n re a l d a ta m e a s u re m e n ts , a re a lis tic tra ffi c g e n e ra to r c a n b e w ritte n . In s e p a ra te w o r k w e h a v e g a t h e r e d n e a r l y 25 , 0 0 0 V o I P t r a c e s f r o m t e n g l o b a l l y d i s p e r s e d s i t e s w h ic h w e c a n u tilis e fo r ’p a ra m e te ris in g ’ th e m o d e l, d e p e n d in g o n th e d e s ire d s c e n a rio .

R ef er en ces [1] P r a b a n d h a m M . G o p a l , J . W . W o n g , a n d J . C . M a j i t h i a , “ A n a l y s i s o v o i c e t r a n s m i s s i o n u s i n g p a c k e t s w i t c h i n g t e c h n i q u e s ,” P e r f o r m a n c e 1, p p . 11– 18 , F e b . 19 8 4 . [2] G i u l i o B a r b e r i s , “ B u f f e r s i z i n g o f a p a c k e t -v o i c e r e c e i v e r , ” I E E E T r n i c a t i o n s , v o l . C O M -29 , n o . 2, p p . 15 2– 15 6 , F e b . 19 8 1. [3 ] M e h m e t M . K . A l i a n d C . M . W o o d s i d e , “ A n a l y s i s o f r e -a s s e m b l y a p a c k e t v o i c e n e t w o r k ,” i n P r o c e e d i n g s o f t h e C o n f e r e n c e o n C o m ( I E E E I n f o c o m ) , B a l H a r b o u r (M i a m i ), F l o r i d a , A p r . 19 8 6 , I E E E , p p

f p la y o u t s tra te g ie s fo r E v a lu a tio n , v o l. 4 , n o . a n s a c tio n s o n C o m m u b u ffe r re q u ire m e n ts in p u te r C o m m u n ic a tio n s . 23 3 – 23 8 .

M o d e llin g th e A r r iv a l P r o c e s s f o r P a c k e t A u d io [4 ] J o s e p M . F e r r a n t r a f fi c ,” T e c h n i c tio n s R e s e a rc h , [5 ] W a l m v a n d e r W tiv e s e r v ic e s o n [6 ] I n g e m a r K a j , S In d u s tria l a n d A

d iz a n d A u re l A . L a z a r, “ M o d e lin g a n d a a l R e p o r t T e c h n i c a l R e p o r t N u m b e r 119 C o l u m b i a U n i v e r s i t y , N e w Y o r k 10 0 27 , a l, M a n d je s M ic h e l, a n d R o b K o o ij, “ E a l a r g e -s c a l e I P n e t w o r k , ” i n I F I P , J u n e to c h a s tic M o d e lin g fo r B ro a d b a n d C o m p p lie d M a th e m a tic s , P h ila d e lp h ia , P A , U

d m is s io n c o n tro l o f re a l tim e p a -8 8 -4 7 , C e n t e r f o r T e l e c o m m u n 19 8 8 . n d -t o -e n d d e l a y m o d e l s f o r i n t e 19 9 9 . m u n i c a t i o n s S y s t e m s , So c i e t y SA , 20 0 2, P r e p a r e d w i t h L A T E X

4 9 c k e t ic a ra c fo r .

On Packet Delays and Segmentation Methods in IP Based UMTS Radio Access Networks G´ abor T´ oth and Csaba Antal Traffic Analysis and Network Performance Laboratory, Ericsson Research Laborc u. 1, Budapest, H-1037, Hungary {gabor.toth,csaba.antal}@eth.ericsson.se

Abstract. In UMTS radio access networks (UTRAN), the delay requirement - bandwidth product of real-time classes is small, therefore large packets need to be segmented. Furthermore, low priority segmented packets may also have real-time requirements. Assuming that UTRAN traffic is characterized as the superposition of periodic sources with random offset, we propose analytic results and we show simulation results for the delay distribution of real-time classes in a priority system. We then compare segmentation methods considering the delay requirements of all real-time classes.

1

Introduction

UMTS Terrestrial Radio Access Networks (UTRAN) [1] will be based on packet switched technologies to utilize the gain of multiplexing services with various QoS requirements. First UTRAN networks will be deployed with ATM infrastructure, IP based UTRAN networks will be introduced in later releases. As opposed to generic multiservice networks, most traffic types in UTRAN have real-time requirements. It is well-known that voice traffic, which is expected to be the dominant traffic type at first UMTS systems, has inherent real-time requirements. In addition to that, applications used at mobile terminals also have real-time requirements [2] in the access network due to the timing requirements of the Radio Link Control (RLC) protocol and the support of soft handover. The end-to-end delay requirement of real-time data packets, however, is less stringent (15-40 ms) than that of voice (5-7 ms) [3]. Other traffic types that do not span to the air interface are synchronization of base stations, which has the most stringent delay requirement, and the non-real-time operation and maintenance and non-UTRAN traffic in IP based UTRAN. RLC protocol provides reliable transmission between mobile terminals and the corresponding radio network controller via a retransmission mechanism to overcome packet losses at the air interface. Therefore, it tolerates packet losses in the transport network. Accordingly, both voice and data applications have in the radio access network. A special property of real-time traffic types over the transport network is periodicity; that is, mobile terminals and RNCs emit RLC-blocks periodically. M. Ajmone Marsan et al. (Eds.): QoS-IP 2003, LNCS 2601, pp. 50–63, 2003. c Springer-Verlag Berlin Heidelberg 2003 

On Packet Delays and Segmentation Methods

51

The initial phase of periodic flows is random, hence the traffic can be modeled as a superposition of independent periodic streams with a random initial offset. In the general case, periodic streams are modulated with an on-off process due to Discontinuous Transmission (DTX) for voice sources and higher layer protocols for data applications. Packet size of real-time flows is heterogeneous. Synchronization and voice packet are small (30-50 bytes), while the size of data packets might be large. For example if the transmission time interval of data packets, i.e. period length, is 20 ms and the bitrate of the bearer is 384 kbps then the packet size is larger than 1000 bytes. The exact packet size including all protocol overheads depends on the applied technologies. The above characteristics of UTRAN networks indicate that to assure optimal operation for real-time traffic with the most stringent delay requirements, small packets (such as voice, some signalling and synchronization) should be differentiated from real-time data traffic in routers and switches. It is also apparent that real-time data traffic has to have preference over maintanence and best effort non-UTRAN traffic. Therefore, in IP based UTRAN, which will be based on the DiffServ concept [4], multiple real-time classes should be distinguished in the routers. Furthermore, even if voice has absolute priority over real-time data traffic, the delay of voice packets is significantly increases due to data packets (a 1000 byte long data packet may increase the voice delay by 4 ms at an E1 link). To minimize this effect, large data packets are segmented. In ATM based UTRAN ATM does this task, while in IP UTRAN layer 2 segmentation is applied based on the PPP Multilink Protocol (MP) [5]. If multiple QoS classes are needed at layer 2 then multi-class extension of MP [6] should also be supported. Segmentation of real-time data packets, however, has an effect on the delay of data packets themselves. Therefore, all real-time classes should be included in the delay analysis of the system. The aim of this paper is to derive new analytical results that allow the evaluation of the effect of segment size and segmentation methods on the delay of all real-time classes. Therefore, we analyze the packet delay distribution in a two-class strict-priority system, where traffic sources generate packets periodically with random initial offset and packets are segmented at the entry of the queues. Thus, results presented in this paper are based on a constant bitrate source model. Approximation for the delay distribution of on-off sources is also possible based on the presented results if the methods presented in [2] are applied. The rest of the paper is structured as follows. In Section 2, we propose analytic results for the exact packet delay distribution for high priority packets in a priority system. We derive then the low priority packet delay distribution for the case of a single low priority source in Section 3. In Section 4, we verify the analytic results by simulations. We propose new segmentation methods in Section 5 and we evaluate their performance in Section 6. Finally, we draw the conclusions in Section 7.

52

2 2.1

G´ abor T´ oth and Csaba Antal

Analytic Evaluation of High Priority Packet Delay Prior Work

The delay distribution of high priority constant bit-rate traffic has been analyzed since the idea of transmitting real-time traffic over packet switched networks emerged. The N*D/D/1 system, which means that deterministic periodic sources are served by a single deterministic server, received dedicated attention at the beginning of the 90s. The exact virtual waiting time distribution was expressed first in [7] and in [8]. These results were extended to more general cases and a closed form approximation was also proposed in several papers including [9], [10] and [11]. For a detailed review of the work on N*D/D/1 systems see [12] and [13]. Denoting the number of voice sources by NH and assuming that they generate a bH long packet in each T long time period, the CDF of the queuing delay of a voice packet can be expressed based on equation 3.2.2 in [12] as 

FDq (t) = 1 − tC b

0, otherwise it is 0. The first term In the second term of (2), Pr(A|B) si Pr(si ) can be expressed by using that Pr(A|BC) = min(1, tC , ¯ si ), Pr(C|B) = S NL bL and Pr(B) = T C−NH bH . After substituting these formulae into (2) we get the CDF that yields the probability density function by derivation, which has the following form:  Cki fDs (t) = p0 δ(t) + (3) T C − NH b H ∀i:si >tC

where p0 = 1 − and δ(x) is the Dirac delta function. The PDF of the total voice delay, fD (t), then is obtained by convolving the d FDq (t), and that density functions of the preemptive voice delay, fDt (t) = dt of the residual transmission time of data segments, fDs (t). Accomplishing the necessary calculations, the PDF is obtained:    si  ci FDt (t) − FDt (t − ) − ci FDt (t) (4) fD (t) = −p0 fDt (t) + C NL bL T C−NH bH

∀i:si 0 : t0 ∈ (t − τm , t − τm + dt] : ν(t0 , td ) = m : Vt = 0.

Using the new notations PC can be expressed as  Pr(Z|X, Y, W ) Pr(W |X, Y ) Pr(Y |X) Pr(X) PC = l

(11)

m

The rightmost probability is the probability that the length of a randomly chosen burst is l, multiplied with the probability that the arrival of the data packet occurs when a voice packet is being served. Pr(X) = Pr(B0 = l|V0 > 0) Pr(V0 > 0) =

lbH Pr(B = l) N bH E(B) TC

(12)

where the distribution of busy period length P r(B = l) and the mean busy period length E(B) is expressed based on [16]. The probability of event X has the form of:    l  N −l−1 N bH lbH N lbH Pr(X) = 1− 1− (13) l TC TC TC The next probability to be calculated is the probability that the service of the data packet starts in a specific dt long time interval given that the length of the served voice busy period is l. As the arrival time of the packet is distributed evenly over the time-interval of the served voice burst, the second probability is Pr(Y |X) = if l >

tC−bL bH

− m and 0 otherwise.

C dt lbH

(14)

56

G´ abor T´ oth and Csaba Antal

To calculate the Pr(W |X, Y ) probability, we remove the l packet long voice busy period from the high priority system, and we take only the reduced N*D/D/1 system into account where T  = T − lbCH and N  = N − l. In this system, we determine the probability that m arrivals occur in a τm long time interval, given that the system is empty at the beginning of the interval. We use parameters with apostrophe for the truncated system. Applying the Bayesformula, the wanted probability can be formalized as Pr(W |X, Y ) = Pr(ν  (t , t + τm ) = m|Vt = 0) = Pr(Vt = 0|ν  (t , t + τm ) = m) Pr(ν  (t , t + τm ) = m) Pr(Vt = 0)

(15)

The probability Pr(Vt = 0|ν  (t , t + τm ) = m) can be divided into two parts depending on whether the virtual waiting time at t + τm reaches the threshold Vˆ = T C−NCbH −bL or not. If the virtual waiting time exceeds Vˆ at t + τm then the system can not empty until t + T  , so Pr(Vt = 0|ν  (t , t + τm ) = m, Vt +τm > Vˆ ) = 0. That is, Pr(Vt = 0|ν  (t , t + τm ) = m) can be expressed as the product of two probabilities: Pa = Pr(Vt = 0|ν  (t , t + τm ) = m, Vt +τm < Vˆ ) and Pb = Pr(Vt +τm < Vˆ |ν  (t , t + τm ) = m). < Vˆ , so it can be There is some idle period in (t + τm , t + T  ) if V  t +τm

T C−N bH −bL handled as an individual N*D/D/1, which yields Pa = T C−(l+m)b . For the H −bL calculation of probability Pb , the virtual waiting time distribution of a system with m users and τm long period can be used as an approximation. Pb is the value of this distribution at Vˆ .

Pb = 1 −



n m    m 1 − NTbCH R(N + n) − 1 R(m)−m

n+1−m n 1 − R(N + n) + R(m) n=n

(16)

0

L where n0 = TbHC (1 − R(N )) and R(x) = xbHT +b C . Probability Pb is independent of l, so it will be referred to as Km in the following. The next two unknown probabilities of (15) are Pr(ν  (t , t + τm ) = m) =   N −l−m  N −l mb +b m mbH +bL bH H L and Pr(Vt = 0) = TTC−N 1 − T C−lbH T C−lbH C−lbH .Therefore, m

the final form of Pr(W |X, Y ) is T C−N b −b mbH +bL m   N − l Km T C−NHbH L T C−lb H Pr(W |X, Y ) ≈ T C−(m+l)bH −bL l+m+1−N m

(17)

T C−lbH

To express the last probability we use that ν(t0 , td ) = m and td = t0 + This is the empty probability at an arbitrarily chosen time instant in such an N*D/D/1 system where there are m sources with period length of mbH +bL : Pr(Z|X, Y, W ) = mbHbL+bL C mbH +bL . C

On Packet Delays and Segmentation Methods

57

Composing the product of the conditional probabilities calculated above and substituting l + m with k we obtain N N −m

m−1   1 − R(N ) dt m k−m Km R(0)R(m) PC ≈ (18)

k+1−N T R(k − m)m+1−k 1 − R(k) tC−b ∀m k>

bH

L

The next step is to calculate the probability PD , which is for the case when the low priority packet arrives into an empty system. It follows from the preemptive operation, that the service time in this case can only take such a value that exactly equals to mbHC+bL , where m is a non-negative integer that is less than or equal to N . Therefore, the probability that the delay of the low priority packet is in a certain dt period equals to the sum (over all m) of the probabilities that m high priority packets arrive during the service time of the low priority packet. That is, the mbHC+bL value falls in the given dt long time interval. m max  

(19) Pr V0 = 0, Vt = 0, ν 0, τm = m PD = m=mmin L L and mmax = (t+dt)C−b . Following the same train of where mmin = tC−b bH bH thoughts as in the continuous case we can get the following expression for the PD probability

  m max  N R(0) 1 − R(N ) R(m)m−1 PD ≈ Km (20)

m+1−N m 1 − R(m) m=m min

Applying that Pr(t < D ≤ t + dt) = PC + PD , and substituting this into (5) we get the formula of N N −m

m−1 1 − R(N ) 1  m k−m Km R(0)R(m) fD (t) ≈ (21)

k+1−N T R(k − m)m+1−k 1 − R(k) tC−b ∀m k>

+

 m

3.2

bH

L



  mbH + bL N R(0) 1 − R(N ) R(m)m−1 ) Km δ(t −

m+1−N C m 1 − R(m)

Non-preemptive System with Segmentation

In this section we show how the analytic results obtained for the preemptive system can be applied to the non-preemptive case. Fig. 2 illustrates the preemptive and non-preemptive systems with the same arrival process. In the non-preemptive case, the data packet is segmented according to the method depicted in the upper-left corner of the figure. In the preemptive case, it does not matter whether the data packet is segmented or not (if we neglect segmentation overhead), so for the sake of comparability we assumed that the packet is segmented according to the same method. In Fig.

58

G´ abor T´ oth and Csaba Antal

Fig. 2. Timeline of serving packets in preemptive and non-preemptive systems 2 it can be observed that the service of the data segment is started in such a time instant in the non-preemptive case when the voice queue is empty and all data segments preceding the observed one have already been served. Thus, if the stability criteria for the system are met, the start times of the segments in the non-preemptive system are the same as in the preemptive case. Since the service of a segment can not be interrupted in the non-preemptive system, the total service time of the data packet can be calculated as the sum of two components. One is the delay that a bˆL = bL − Sl long low priority packet suffers in a preemptive system, the other is the transmission time of a Sl long segment at full service rate. Thus the CDF of the delay of a single bL long data packet in a preemptive system with segmentation is   Sl (22) FD (t) = FˆD t − |ˆ C bL =bL −Sl where Sl is the length of the last segment, FˆD (t) is the CDF of the delay of a ˆbL long data packet in a preemptive system and C is the server rate.

4

Verification

We have carried out simulations to verify the analytic results for various scenarios. Here we present results for a router with a 1920 kbps (E1) link, which carries the multiplexed traffic of 1 data and 80 voice sources. The length of the voice and data packets are 44 and 1013 bytes, respectively, and the period is 20 ms for each sources. The comparison was done for two different segmentation sizes. The data packets are divided into two segments in both cases. In the first case, the sizes of the first and second segment are 800 and 213 bytes, in the second case, they are 506 and 507 bytes. Fig. 3(b) and Fig. 3(a) show the complement of the normalized cumulative histograms and the cumulative density functions of the delays for both cases. In

On Packet Delays and Segmentation Methods 10

10

10

− 1

10

− 2

10

0

− 1

− 2

10

10

10

1− F

1− F

D

D

(t)

(t)

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59

− 3

10 Ca Ca Ca Ca

− 4

s e− s e− s e− s e−

1s 1a 2s 2a

im n im n

u l a t ed a ly tic u l a t ed a ly tic

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− 5

0

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10 12 D el a y [ m s ]

14

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(a) Complementary distribution functions of the data delay

10

− 3

Ca Ca Ca Ca

− 4

s e− s e− s e− s e−

1s 1a 2s 2a

im n im n

u a ly u a ly

l a t ed tic l a t ed tic

− 5

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0 .5

1

1. 5

2

2. 5 D el a y [ m s ]

3

3 .5

4

4 .5

5

(b) Complementary distribution functions of the voice delay

Fig. 3. Verification of the analytic formulae the figures it is apparent that the simulated and the analytical results are hardly distinguishable.

5

Segmentation Methods

In this section we investigate how the segmentation affects the delay of high and low priority packets. We also show that the simplest segmentation method, which is widely applied in current equipments, is suboptimal in this sense. First consider the voice traffic. As it was shown in Section 2, the voice delay is the sum of two independent random variables of which only fDs depends on the segmentation of the data packet. The quantiles of the total delay are minimized via proper segmentation in practical cases if the quantiles of the segmentationdependent component are also minimized. This can be reached by setting the size of the . Now let us consider how segmentation effects data delay. We have shown in this paper that the delay distribution of the data traffic in a non-preemptive system is determined by the size of the last segment of the segmented data packet. How the former part of the packet is segmented does not play an important role in forming the distribution. Since the service of the last data segment in the non-preemptive system can not be interrupted once it is started, that the data packet suffers given that the total packet size is fixed. 5.1

Basic Segmentation Algorithm

The simplest method for segmenting packets cuts the packet into MSS (maximum segment size) long segments until the remaining part is shorter than the MSS. Thus, the last segment contains the remaining bytes only. This relatively simple procedure is suboptimal for both voice and data delay because the largest data segment could be smaller and the last segment could be smaller.

60

G´ abor T´ oth and Csaba Antal

Two alternative modifications can be applied to the basic segmentation algorithm as follows. 5.2

Segmentation Method 1

This method ensures that the largest segment of a packet is as small as possible given that the number of segments (n) is the same as it is in the basic method P at a given MSS setting: n = MSS

where P is the total packet size and M SS is the maximum segment size. This is to avoid the segmentation of packets into arbitrarily small pieces, which would result in too large header overhead. At these constraints voice delay is optimal when data packets are segmented such that the size of segments is set as even as possible. The algorithm produces two types of segments with sizes of S1 and S2 that can be calculated as S1 = Pn and S2 =  Pn . The number of the S1 -size segments is n1 = mod (P, n) and the number of S2 -size segments is n2 = n − n1 . Segments can be sent in an arbitrary sequence because one byte difference does not have a noticeable effect on data delay. Even though, the main purpose of this algorithm is to further reduce the tail distribution of the voice delay, it can be seen that this algorithm never produces shorter last segment than the basic algorithm does, thus this algorithm may also increase the performance of the data traffic. 5.3

Segmentation Method 2

The largest last segment provides the best performance for data traffic. For not to increase the delay of the voice packets, the algorithm keeps the original maximum segment size (MSS) as a parameter. The size of the segment to be sent at last is set to the largest possible value i.e. MSS, while the remaining part of the packet is segmented into n − 1 pieces that are equal in size to the extent possible. The method used to calculate the size of these n − 1 pieces of segments is identical to the one described at . It can be seen that this algorithm never produces more MSS sized segments than the basic algorithm does, thus the quantile of the segmentation-dependent part of the voice delay may decrease. Therefore, besides decreasing the tail distribution of the data delay, the algorithm might also increase the performance of the voice traffic.

6

Comparison of Segmentation Methods

To illustrate how the described algorithms reduce delays when two different traffic classes are carried over the same link, a simple network scenario was investigated using the analytical results obtianed in Section 2. The investigated system includes a 1920 kbps link (E1) that carries the multiplexed periodic voice and data traffic. Each high priority voice source transmits one 44-byte packet every 20 milliseconds, and each low priority data source transmits one 1013byte long packet every 20 milliseconds, which corresponds to a 384 kbps bearer in IP UTRAN. The traffic mix includes the traffic of 80 voice sources and one

On Packet Delays and Segmentation Methods

61

data source. The header overhead introduced by the segmentation was neglected during the investigation because it does not influence the comparison.

q u a n t i l e o f t h e v o i c e d el a y [ m s ]

18 17 16 15 B a s ic M et h o d 1 M et h o d 2

14

− 3

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10

− 3

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19

12 0

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120 0

5 .5 5 4 .5 4 3 .5 3 B a s ic M et h o d 1 M et h o d 2

2. 5 2 1. 5 0

20 0

4 0 0 M a x im u m

6 0 0 8 0 0 S eg m en t a t i o n S i z e

10 0 0

120 0

(b) Quantiles of the voice delay

Fig. 4. 10−3 quantiles of the delays in the case of 80 voice and 1 data flows

Fig.4(a) shows the resulted 10−3 quantile of the data delay as a function of the maximum segmentation size. Fig.4(b) shows the 10−3 quantile of the voice delay as the function of the MSS. The difference between the shapes of curves can be attributed to the way segment sizes depend on MSS at the studied methods. Data delay curve at the basic algorithm is monotonously increasing if the number of segments (n) does not change because then the size of the last segment decreases at increasing MSS. However, if the number of segments is decremented (due to the increased MSS) then the size of the last segment has a jump (from 0 to MSS), which results in a jump in the data delay curve as well. Segmentation Method 1 also has jumps in the data delay curve when the number of segments changes. It is constant otherwise because S1 and S2 depends only on n and not on M SS. At Segmentation Method 2, the size of the last segment is always equal to M SS, so the data delay curve is continuous. Regarding voice delay we can observe that the Basic Method and Method 2 have continuous curves because the size of the largest segment is equal to M SS. At Method 1, the largest segment size is Pn , so the voice delay is constant if n is constant. It can be observed that using either Segmentation Method 1 or Segmentation Method 2, the 10−3 quantile of both voice and data delays are always smaller than or equal to that of the basic segmentation method. No improvement achieved at all regarding voice delay when Method 2 is used with such an MSS where the data packet is divided into two pieces. In this case, the length of the produced data segments are the same as the basic algorithm would produce, but in reverse order. Therefore, the PDFs of the segmentation-dependent part of the voice delays, and thus the PDFs of the total voice delays are the same in the two cases. It can be concluded from Fig.4(b) that the quantile of voice delay

62

G´ abor T´ oth and Csaba Antal

is reduced the most if Method 1 is used. Regarding data delay, however, Method 2 significantly overperforms Method 1. We do not have analytical formulae to calculate the delay distributions for the case when more than one data source generate traffic in the system. Therefore, we made simulations to show that the segmentation algorithms improve the performance of both classes in these cases too. The simulated systems are identical to the one we had before, only the number of voice and data users is changed to 36 and 3, respectively. Fig.5(b) and Fig.5(a) show the output of the simulations. It can be realized, that the curves are very similar to those of the analytical results for one data source, which means that Method 1 and Method 2 provides the best performance regarding voice and data delay, respectively.

5 q u a n t i l e o f t h e v o i c e d el a y [ m s ]

18

17 . 5 B a s ic M et h o d 1 M et h o d 2

17

4 .5 4 3 .5 3 2. 5 2 1. 5

B a s ic M et h o d 1 M et h o d 2

10

10

− 3

− 3

q u a n t i l e o f t h e d a t a d el a y [ m s ]

18 . 5

16 . 5 0

20 0

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6 0 0 8 0 0 S eg m en t a t i o n S i z e

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1 0 .5 0

(a) Quantiles of the data delay

20 0

4 0 0 M a x im u m

6 0 0 8 0 0 S eg m en t a t i o n S i z e

10 0 0

120 0

(b) Quantiles of the voice delay

Fig. 5. 10−3 quantiles of the delays in the case of 36 voice and 3 data flows

7

Conclusions and Future Work

We have shown that the delay quantile of voice and real-time data packets depends significantly on the segmentation method applied for large data packets. We proposed two methods that decrease the delay of both data and voice packets compared to conventional segmentation methods. We have concluded based on analytic and simulation results that the best segmentation method regarding data delay is if the size of the data segment that is sent last has the maximum size allowed by the MSS parameter. On the other hand, voice performance is optimal when data segments are as even as possible. As applying these methods makes it possible to admit more connections from both traffic classes without violating their delay constraints, the bandwidth efficiency of small links in IP UTRAN networks can be increased. For the performance evaluation of the proposed methods, we have also derived analytic results for a two-class single server strict priority system where both high priority and low priority traffic are superpositions of periodic constant bit-rate sources with real-time requirements. We have derived the exact delay distribution of voice packets assuming that the low

On Packet Delays and Segmentation Methods

63

priority buffer is not saturated. We have also expressed the low priority delay distribution for the case when there is a single low priority session in the system. Extending the analytic results to cases of many low priority sources and for more traffic classes is in progress. The investigation of the sources modulated with an on-off process is also planned in the future.

References 1. 3GPP ”UTRAN overall description,” Technical Specification, TS 25.401. 2. Sz. Malomsoky, S. Racz, Sz. Nadas, ”Connection admission control in UMTS radio access networks,” Computer Communications - Special Issue on 3G Wireless and Beyond, Fall, 2002 3. 3GPP, ”Delay budget within the access stratum,” Technical Report, TR 25.853, V4.0.0, May 2001 4. 3GPP, ”IP Transport in UTRAN,” Work Task Technical Report, TR 25.933 V1.0.0, March 2001 5. K. Sklower, B. Lloyd, G. McGregor, D. Carr, T. Coradetti, ”The multilink PPP protocol,” RFC 1990, August 1996 6. C. Bormann, ”The multi-class extension to multi-link PPP,” RFC 2686, Sept. 1999 7. A. Bhargava, P. Humblet and H. Hluchyj, ”Queuing analysis of continuous bit stream transport in packet networks,” Globecom ’89, Dallas, TX, October 1989. 8. I. Norros, J. W. Roberts, A. Simonian and J. Virtamo, ”The superposition of variable bitrate sources in ATM multiplexers,” IEEE Journal on Selected Areas in Communications, 9(3):378-387, April 1991. 9. B. Hajek, ”Heavy traffic limit theorems for queues with periodic arrivals,” In ORSA/TIMS Special Interest Conference on Applied Probability in the Engineering, Informational and Natural Sciences, pp. 44, January 1991 10. B. Sengupta, ”A queue with superposition of arrival streams with an application to packet voice technology,” Performance’90, pp. 53-60, North-Holland 1990. 11. J. Roberts and J. Virtamo, ”The superposition of periodic cell arrival streams in an ATM multiplexer,” IEEE Trans. Commun., vol. 39, pp. 298-303 12. COST 242 Management Committee, ”Methods for the performance evaluation and design of broadband multiservice networks,” The COST 242 Final Report, Part III., June 1996 13. J. He, K. Sohraby, ”On the Queueing Analysis of Dispersed Periodic Messages,” IEEE Infocom 2000, March 26-30, Tel-Aviv, Israel 14. K. Iida, T. Takine, H. Sunahara, Y. Oie, ”Delay analysis of CBR traffic under static-priority scheduling,” IEEE/ACM Trans. On Networking, Vol. 9, No. 2, pp.177-185 15. M. J. Karam, F. A. Tobagi, ”Analysis of the Delay and Jitter of Voice Traffic over the Internet,” IEEE Infocom 2001, April 22-26, Anchorage, Alaska, USA 16. J.T. Virtamo, ”Idle and busy period distribution of an infinite capacity N*D/D/1 queue,” 14th International Teletraffic Congress - ITC 14, Antibes Juan-les-Pins, France, June 1994.



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The RAMON Module: Architecture Framework and Performance Results Aldo Roveri1, Carla-Fabiana Chiasserini2 , Mauro Femminella3 , Tommaso Melodia1 , Giacomo Morabito4 , Michele Rossi5 , and Ilenia Tinnirello6 1

University of Rome La Sapienza; 2 Polytechnic of Turin 3 University of Perugia 4 University of Catania 5 University of Ferrara 6 University of Palermo

Abstract. A design study of a Re-configurable Access Module for Mobile Computing Applications is described. After a presentation of its cross-layered architecture, Control Parameters (CPs) of the module are introduced. The set of CPs both describes the functional state of the communication process in relation to the time-varying transport facilities and provides, as input of suitable Algorithms, the control information to re-configure the whole protocol stack for facing modified working conditions. The paper also presents the structure of the simulator realized to demonstrate the feasibility of the design guidelines and to evaluate reconfigurability performances.

1

Introduction

This paper presents a first insight in the design of a Re-configurable Access module for MObile computiNg applications (called RAMON in the sequel) and discusses some preliminary results of a feasibility study of this module which is being carried out within an Italian research program1, with the participation of six academic research groups2. The framework of RAMON is given by mobile users in a TCP/IP environment ( ). The mobility is allowed in different communication environments ( ). These REs are identified in a WAN cellular system (e.g., UMTS or GPRS) and in a local area access system (e.g., IEEE 802.11 or Bluetooth). In wireless communications, much effort will have to be put in the ability to re-configure all layers of the communication process to the time-varying transport facilities, in order to assure the respect of QoS requirements. The adaptability to different communication environments led us to overtake the OSI layered approach and to adopt the idea of 1 2

The RAMON project was partially funded by MIUR (Italian Ministry of Research). The address of the reference Author is: [email protected]

M. Ajmone Marsan et al. (Eds.): QoS-IP 2003, LNCS 2601, pp. 471–484, 2003. c Springer-Verlag Berlin Heidelberg 2003 

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, which appears to be particularly appealing to enable dynamic optimization among all layers of the communication process. The idea has already been presented in [1], [2] as a design methodology for adaptive and multimedia networks. RAMON provides a first example of use of this methodology. The remaining of the paper is organized as follows. In Section 2 we describe the RAMON Functional Architecture. Section 3 defines the relevant that constitute the basis of the re-configuration action and the main algorithms which perform it. Section 4 presents the overall RAMON simulator developed in the ns-2 framework [3] to demonstrate the feasibility of the design guidelines and to evaluate the reconfigurability performances, while Section 5 contains some samples of performance results.

2

The Architecture

RAMON allows the deployment of control algorithms which are independent of the specific RE considered. A (MS), equipped with RAMON, becomes a , i.e. an MS which supports common to all the REs. Such functionalities are obtained from the of each RE, by means of , as described below. Figure 1 shows the RAMON functional architecture. It includes a plane ( ) and an plane ( ), which is divided in as many parts ( ) as the number of different REs involved. In the case of Figure 1 the number of different REs is let equal to two for the sake of simplicity. Below the A-plane, functionalities ( ) for each RE (denoted as for the i-th RE) are located. An RE-independent service development ( ) is offered to the overlying Application layer. CC-plane functions, which are also RE-independent, are grouped in three , according to the classical model adopted for wireless communications: i) ( ); ii) ( ); iii) ( ).

Fig. 1. Overall system architecture.

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The A-plane translates: 1) exchanged between the CC-plane and the NC-plane for each RE; 2) (CP) data passed from the plane ( ) to the CC-plane. Two different types of interfaces can be identified: i) the α , between the CC-plane and the A-plane; ii) the β , between the A-plane and the NC-plane of each RE. Figure 2 completes Figure 1. In its right part the CCplane and the A-plane are depicted, with the relevant α and β interfaces. In its left part, which is concerned with two generic REs, the relevant NC-planes and NU-planes are shown. Figure 2 helps us showing the way the SC-c, MM-c and RRC-c functionalities interact with the corresponding , and (i=1,2) of the two REs through the translation performed by the A planes (A/RE-1, A/RE-2). The relations between the NC-planes and NU-planes are highlighted and particularly how the SC-i, MM-i and RRC-i functionalities are related with (PHYi), (MAC-i) and (RLC-i) functions is shown. Finally, , and layers, which are part of the NU-plane, directly interact with the CC-plane.

Fig. 2. Basic interactions among Control and User planes.

3

Reconfigurability Parameters

The main idea is to dynamically adapt the whole stack to the perceived QoS by means of adequate control actions. QoS measurements are passed to the RAMON entity by means of CP data.

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Cross-layer interaction requires control information sharing among all layers of the protocol stack in order to achieve dynamic resource management. It may be performed in two directions: i) : upper layers parameters may be configured to adapt to the variable RE characteristics; ii) : MAC, RLC and PHY layer parameters can adapt to the state of Transport and Application layer parameters. Thus, e.g., the behavior of the TCP congestion window may be forced to adapt to the timevarying physical channel characteristics (upward), while lower layer parameters may be re-configured, with the aim of serving distinct applications with different QoS requirements (downward). As shown in Figure 3, CP data flow from all layers of the NU-plane of each RE and are processed by running in the CC-plane. The output of the Algorithms consists of , which are passed to all layers of the protocol stack. For lower layers, which are RE-dependent, these primitives have to be interpreted by the pertinent A-plane; for higher layers, which are typical of the Internet stack, the primitives can act without any mediation.

Fig. 3. Information flows in RAMON.

The effect of the Command Primitives, in concurrence with the variations of the RE transport characteristics, gives rise to modifications in the perceived QoS. These modifications cause corresponding change of the CP data. The CC-plane performs re-configuration actions only if they entail appreciable improvements in the QoS perceived. The most important Algorithms adopted in the RAMON design are: – –

Algorithm; Algorithm;

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– Algorithm; – RRC Algorithm for – RRC Algorithm for The first two algorithms will be analyzed respectively in Sections 3.1 and 3.2; the other three will be briefly described in the following. QoS and MM capabilities are carried out by means of the Mobile IP protocol, improved with an function. This last is called ( ), is described in [7] and operates in a framework. In addition, we assumed that a [8] is adopted within the wireless domain: the scope is to hide local handoffs from Home Agent/Correspondent Nodes, thus reducing handoff latency. To preserve information integrity of packet transmission over the radio channel while meeting the desired QoS and energy constraints, an algorithm for Error Control has been developed within the RRC functional set, which is suitable for a UMTS environment: it provides optimal operational conditions and parameter setting at the RLC layer. The performance results of the application of the algorithm to the UMTS RE are being published [10] and a module which implements it in the RAMON overall simulator has been developed. An open, re-configurable scheduling algorithm called CHAOS (CHannel Adaptive Open Scheduling) has been defined, which is part of the RRC-c functional set. The Algorithm defines a scheduling strategy for efficient resource sharing control. It is adaptive to and . Different CPs may be chosen to represent both variables. Traffic conditions may be represented by transmission buffer occupancy or queue age associated to packets in the transmission buffers; physical channel conditions may be expressed by averaged (SIR) and/or . The basic CHAOS principles can be applied in a RAMON module residing in a VBS managing radio resources of different REs. The specific adaptations studied for UTRA-TDD and Bluetooth (whose description can be found in [11]) correspond to A-plane entities of the RAMON architecture. 3.1

Handover Algorithm

RAMON includes an abstract handover algorithm, running at the Virtual MS (VMS), based on the virtualization of the functions necessary for Mobility Management. This operation allows making handover services programmable and independent of the underlying technologies. In a re-configurable wireless scenario, the selection of the “best” access point at any moment is not simply related to the physical channel quality, but implies also a technology choice as a trade-off between performance, cost, power consumptions, etc. Moreover, the roaming across different systems requires solving addressing and authentication problems, maintaining a low latency to prevent the adverse effects of TCP congestion control. In order to develop a platform-independent handover algorithm, similarly to [4], [5] we have decoupled these problems. By hiding the implementation details

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of the MM algorithms from handover control systems, the handover decision can be managed separately from handover execution, so that the same detection mechanisms can interface with many different access networks. The algorithm is based on a generic (MCHO) style: handover decisions and operations are all done at the VMS. RAMON keeps track of a list of (VBS) in its coverage area. The rationale is that some REs do not provide MCHO capabilities. Therefore, the entire RE is considered as a unique VBS. Conversely, for MCHO systems, a VBS coincides with a BS. Periodically, for each VBS, the VMS collects CPs as QoS measures (possibly querying the VBS) and estimates cell load condition. According to the definition criterion of the best VBS, if the best serving VBS is not the one in use for a given period of time, the VMS hand-offs to it. We can identify three main logical functional blocks: i) the , which re-configures the decision metrics, according to the user requirements; ii) the , based on system-dependent available functions and signaling; iii) the , which compares abstract performance metrics computed on the basis of the measurements and of the user profile. The cost of using a BSn at a given time is function of the available Bn , the related Pn , the Cn of the network the BSn belongs to. While the last two parameters are easy to compute (mobile host battery life and service type cost), the bandwidth parameter is more complex. In order to account for the real available bandwidth, channel quality perceived by the MS and cell occupancy status have to be considered. The cost function of the BSn is then evaluated as: fn = wb · N (1/Bn ) + wp · N (Pn ) + wc · N (Cn )

(1)

where wb , wp and wc are the weights of each parameter, which sum to 1, and N (x) is the normalized version of the parameter x. The reciprocal of the bandwidth is considered in order to minimize the cost function of the best access BS. Weights can be modified by the user at run-time, and can be set to zero for those parameters that are not of concern to the user: e.g., if high performance has to be pursued, we can assign wb = 1, wp = 0 and wc = 0. Thus, by minimizing the cost function, we achieve load balancing across different REs. 3.2

Session Control Algorithm

Due to the low Mobile IP performance, the MS migrating from a RE to another may be unreacheable for time periods of the order of seconds, which considerably impacts the TCP operation. In particular, several consecutive RTOs (Retransmission Time Out) occur. This results in a very low value of the which, upon each RTO expiration, is updated as follows: ssthresh = max(cwnd/2, 2 · M SS)

(2)

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where cwnd denotes the current . Therefore, as the inter-RE handover is successfully completed, the sender immediately enters the phase and cwnd increases slowly. This causes low throughput performance. In order to solve this problem, the TCP sender implementation has been modified, still maintaining compatibility with standard TCP implementations. We observe that, after an inter-RE handover, the connection path may change dramatically. Consequently, what the TCP sender learned in terms of available bandwidth and estimations of the RTT (Round Trip Time) and RTO is not valid anymore. Based on the above observation, after the inter-RE handover is completed, the TCP sender resets its internal parameters (i.e., , , and ), and enters into the so-called phase during which it rapidly estimates the available bandwidth and the RTT characterizing the connection in the new RE. Moreover, in order to avoid useless segment transmissions which would only result in power consumption, the TCP sender transmitting any data as the handover begins and as the handover is successfully completed. The information about the beginning and the end of handovers is provided by command primitives. The above Algorithm [6], which will be referred to as TCP-RAMON in the sequel, has been integrated in the overall RAMON simulator, and is effective when the MS, acting as a mobile host, is the TCP sender. Otherwise, a similar behavior can be obtained as follows. Before initiating the handover, the MS generates an ACK which informs the TCP sender that the ( ) is equal to 0. This results in a of the TCP sender and avoids consecutive RTO expirations. When the handover is completed, the TCP receiver generates a new ACK with the original value of : this occurrence resumes the communication.

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The Simulative Approach

In this section the RAMON simulator (Figure 4) is described with reference to UMTS-TDD and Bluetooth REs. An 802.11 implementation has also been developed. The simulator is based on the ns package [3] (ver. 2.1b7a). Specifically, modifications have been carried out to the Wireless Node object ( class). One protocol stack for every simulated RE is created in the same MobileNode object. The RAMON module and the A-plane modules are interposed between Agents (RTAgent, MIP Agent, etc.) and radio access layers (LL, MAC, etc.). On the left part of Figure 4 the UMTS-TDD protocol stack is shown with its specific Adaptation plane ( in figure), where as the Bluetooth stack is on the right side with its A-plane ( ). On top of the stacks the RAMON module is directly linked to the TCP (or UDP) layer, to the MIP layer ( ) and to the routing Agent (NOn AdHoc routing agent [13]). The UMTS-TDD protocol stack has been developed for this project. The Bluetooth protocol stack is derived from the ns simulator [12] and modified to

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Fig. 4. Overall simulator architecture.

adapt the Bluetooth node object to the ns MobileNode object. The α interface in Figure 4 defines the messages exchanged between CC-plane and A-planes. The functions of the α interface can be related to the Command Primitives and the parameters they exploit to the CPs. A list of the most important of these functions follows: – get(parameters name): gets the parameters name parameter value. – attach(): is used to create an and to register the node to the ( ). – detach() deletes registration from the FA. – monitor(RE): returns a quality metric for the requested RE. – set(parameters name,value): sets the value value to parameters name parameter. – send(packet,options) – receive(options) In particular, the “get” function is used to read the CPs from the A-planes for optimization purposes. CPs originated at different layers can be associated to different optimization tasks: i) physical layer CPs are related to power control and battery life saving; ii) link layer CPs are directly connected to link reliability and packet delay; iii) transport layer CPs are directly related to the QoS perceived from the user application in terms of packet delay and throughput. The “set” function is needed to pass some values to the A/RE-i modules: in fact, with this primitive, some CPs can be modified by the CC-plane. Both the “set” and the “get” functions are also defined for the interactions between the CCplane and RE-independent upper layers protocols. The other functions defined above are Command Primitives (for the α interface).

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Two more primitives (named respectively start handover notification() and end handover notification()) are defined for interaction between the CCplane and the transport layer. The first one notifies the TCP about the beginning of the handover while the second one notifies the end of it. The most important CPs passing through the α interface are briefly discussed in the following for the main layers interacting with RAMON. . CPs detectable at such layer are strongly dependent on the considered RE. A very useful CP is the (BAT LEVEL), used to maximize the MS life, e.g., by attaching the MS to the less power demanding RE. Moreover, (TX POWER) and (SIR) measurements, if available, are used to detect temporary link failures or high interference conditions: e.g., if the physical channel in a given instant is detected to be in an interference prone situation, the Link layer can be set in a “wait” status to avoid energy wastage. . A description of the at such layer is significant in order to characterize the packet error process affecting the Application layer. Such a description can be achieved by translating the Link layer packet success/failure transfer process into a simple [14], which is analytically tractable and RE independent; hence RE independent algorithms can easily be deployed which exploit such model. The CPs for the models are: at the link layer (P LOSS LINK), at link (LINK PACKET SIZE), layer (BURST ERR) and (ERR PR). Other useful CPs are the allowed in the link layer (MAX LINK RETR) and the (AVG LINK RETR); the last one is related to the energy spent per useful information bit, i.e., the amount of energy wasted due to Link layer retransmissions. . At this layer, the MS should be able to collect information regarding the packet process. When the TCP protocol is considered, in addition to the packet error rate, it communicates to RAMON the average and instantaneous value (AVG TH and ACT TH), the estimated (RTT) and the actual RTO. These CPs are used to control the behavior of TCP state variables and to avoid their incorrect setting as packet errors occur. In particular, it is well known that TCP reacts to packet losses as if a congestion had occurred, i.e., by reducing the maximum flow that the sender is allowed to put into the network at a time. However, in a wireless environment this is not the correct way to proceed because errors affecting a wireless link are very often transient and do not represent at all a measure of network congestion. On the contrary they are a measure of the temporary link QoS. Moreover, performance measured at this level is directly related with the QoS perceived by the user, so it can be weighted in a cost function in order to derive an estimate of the actual QoS. Such an estimate is then compared against the required QoS and used by RAMON algorithms in their decisional tasks.

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Performance Issues

The most meaningful simulated situations are: 1) Forced inter-RE Handover. 2) User-driven inter-RE Handover; These scenarios are relevant in the RAMON context because they easily show how a Common Control Plane (RE-independent) can react to variations in the REs it handles, perceived by means of Control Parameters, for optimization purposes. In the first scenario the VMS loses connectivity and is forced to attach to another RE to maintain session continuity. In the second one the VMS is in the coverage area of two different REs (UMTS and 802.11) at the same time and chooses the best RE evaluating a cost function as described in Section 3.1. 5.1

Forced Handover

In this Section some simulation results relevant to an inter-RE forced handover are presented. The scenario involves a UMTS BS, which is the MIP (HA), and a Bluetooth BS, which has the role of (FA). A Forced Handover between the former and the latter is simulated. Figure 5 shows the temporal behaviour of the TCP sender when TCP NewReno is used and when the modified TCP-RAMON is used. When TCP NewReno is used, multiple RTOs expire during the handover and lead to the ssthresh to its minimum value. Thus, when the handover ends, the TCP enters in the phase and thus its cwnd increases slowly. When TCP-RAMON is used, as soon as the CC-plane detects a loss of connectivity, a start handover notification() primitive is issued to the TCP layer. This freezes the value of ssthresh to the one determined by the last congestion event occured. Accordingly, timeouts expiring during the handover do not impact the value of ssthresh. Once the end handover notification() is received the value of sstresh is set equal to the one determined by the last congestion event. Thus, TCP enters the slow start phase (it does not enter the congestion avoidance phase until cwnd reaches the ssthresh value). In these simulations, buffers are considered to be infinite and the initial ssthresh value has been set to 20 which is a typical value in several TCP implementations. 5.2

Handover Customization

In this Section we present some simulation results relevant to user-driven handovers. Our purpose is to demonstrate how user profile specifications affect handover trigger and detection phases. In fact, the optimization of different performance figures requires different choices in terms of RE attachment/detachment policy. For example, if user main goal is cost saving, connections to low-price access points have to be maintained as long as possible, even if better transmission

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Fig. 5. UMTS-Bluetooth Forced Handover.

conditions (in terms of bandwidth or channel quality) towards other stations are available. In our simulations we consider an area in which heterogeneous radio access technologies (namely UMTS and 802.11), experiencing different traffic conditions, overlap. In particular, we have considered a simple network topology: four 802.11 BSs (referred to as BS2 , BS3 , BS4 , BS5 ) are placed at the vertices of a square and a UMTS BS (BS1 ) is placed in the centre. The side of the square is set to 600m, while the coverage areas of the 802.11 and UMTS BSs are set respectively to 200m and 1000m. Channel rate in 802.11 cells is set to 2 Mb/s. 802.11 BSs have a different number of attached users: four mobile nodes are connected to BS2 and BS4 , while nine mobile users are connected to BS3 and BS5 . In the simulation run, a RAMON mobile node, involved in a 6 Mbytes file transfer from the fixed network, moves clock-wise at 6m/s along the square starting from a vertex, for example from BS2 . Although during the simulation time RAMON node is covered by BS1 , handover to 802.11 BSs can be performed in order to save power or reduce cost. Nevertheless, an handover towards 802.11 BSs implies a lower amount of available bandwidth because of their load conditions. The required user trade-off is expressed by the decision metric (Section 3.1) settings. We compute such a metric considering distance, price and bandwidth offered by each BS. In order to make different system parameteres comparable, we normalize each parameter as follows: distance is expressed as the ratio between actual distance and maximum coverage radius, price and bandwidth are

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normalized with respect to the maximum inter-RE values. In particular, we assume that the cost to transfer 1 kbyte of data is 1 for UMTS, 0.5 for 802.11. In our simulations, we set the metric distance weight to 0.5 and we observe

Fig. 6. Selected BS vs simulation time.

performance results varying the cost and bandwidth weights according to the relation: wb = 0.5 − wc . Consider preliminarly the extreme situations in which we want to minimize the file transfer-cost regardless of the transfer-time (wb = 0) or, conversely, we want to minimize the transfer-time regardless of the cost (wc = 0). Figure 6 shows the handover trigger and decision policies adopted in the cosidered extreme cases. We report the identifier of the selected BS versus the simulation time. In the wb situation, connection to WLAN is kept as long as possible, since this access technology is the cheapest (handovers are triggered only when the RAMON node moves outside the coverage area of an 802.11 BS). In the wc case, the RAMON node remains connected to UMTS for a greater time (switch to WLAN occurs only when the distance from the relevant BS is very small). Note that, since our metric accounts for both distance and load, the permanence time in 802.11 BSs is not constant and depends on the BS considered. The time and the cost resulting for the considered 6 Mbytes file transfer is reported in Figure 7 versus the wc setting. This figure shows that, by changing the weights of the cost function, the RAMON user can effectively configure its optimal cost/performance trade-off.

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Fig. 7. Time and Cost Trade Off.

6

Conclusions

In this paper the guidelines adopted for the design of a module able to reconfigure different mobile communication environments for computing applications are introduced. The paper mostly concentrates on architectural issues and on control information flows. In particular, the Algorithms that constitute the processing core of the module are briefly described. The integrated RAMON simulator is described and some performance results are finally shown.

7

Acknowledgments

The authors would like to thank all the researchers of the Polytechnic of Turin and of the Universities of Catania, Ferrara, Palermo, Perugia and Rome “La Sapienza” who participated to the RAMON project and, notwithstanding their important contribution, do not appear as authors of this work.

References 1. Z.J. Haas, “Design Methodologies for Adaptive and Multimedia Networks,” IEEE Communications Magazine., Vol. 39, no. 11, November 2001, pp 106-07. 2. T.S. Rappaport, A. Annamalai, R.M. Buehrer, W.H. Tranter, “Wireless Communications: Past Events and a future Perspective,” IEEE Commun. Mag., Vol 39, no. 11, May 2002, pp 106-07.

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3. Network Simulator http://www.isi.edu/nsnam/ns/. 4. M. Stemm, R. H. Katz, “Vertical Handoffs in Wireless Overlay Networks,” ACM Mobile Networking (MONET) Vol 3, n 4, 1998, pp 335-350. 5. M.E. Kounavis, A. T. Campbell, G. Ito, G. Bianchi, “Design, Implementation and Evaluation of Programmable Handoff in Mobile networks,” ACM Mobile Networking (MONET), Vol. 6, Sept. 2001, pp. 443-461. 6. G. Morabito, S. Palazzo, M. Rossi, M. Zorzi, “Improving End-To-End Performance in Reconfigurable Networks through Dynamic Setting of TCP Parameters,” published in these Proceedings. 7. G. Bianchi, N. Blefari-Melazzi, M. Femminella, F. Pugini, “Joint support of QoS and mobility in a stateless IP environment,” IEEE GLOBECOM 2001, San Antonio, USA, November 2001. 8. A.T. Campbell et al., “Comparison of IP micromobility protocols,” IEEE Wireless Communications, February 2002. 9. M. Femminella, L. Piacentini, “Mobility Management in a Reconfigurable Environment: the RAMON Approach,” published in these Proceedings. 10. C. F. Chiasserini and M. Meo, “A Re-configurable Protocol Setting to Improve TCP over Wireless,” IEEE Transactions on Vehicular Technology (to appear). 11. A. Baiocchi, F. Cuomo, T. Melodia, A. Todini, F. Vacirca, “Reconfigurable packet scheduling for radio access jointly adaptive to traffic and channel,” published in these Proceedings. 12. Bluehoc Simulator http://www-124.ibm.com/developerworks/opensource/bluehoc/. 13. J Widmer, “Network Simulations for a Mobile Network Architecture for Vehicles,” http://www.icsi.berkeley.edu/˜widmer/mnav/ns-extension/. 14. M. Zorzi, R.R. Rao, “Perspectives on the Impact of Error Statistics on Protocols for Wireless Networks,” IEEE Personal Communications, vol. 6, Oct. 1999.

R econ fi g u r a b le P a ck et S ch ed u li n g f or R a d i o Acces s J oi n tly Ad a p ti v e to T r a f fi c a n d C h a n n el Andrea Baiocchi, Francesca Cuomo, Tommaso Melodia, Alfredo Todini, and Francesco Vacirca University of Roma “La Sapienza”, INFOCOM Dept., Via Eudossiana 18, 00184, Rome, Italy

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Ab s tr a ct. Adaptive packet scheduling for wireless data access systems, including channel state information based algorithms, is a quite well established topic. We develop here an original framework to define such an algorithm in a reconfigurable context, i.e. with the ability to exploit heterogeneous communication environments. The focus is to define platform independent algorithms that can be “adapted”, by a specific software, to different environments, so that the core communication functions can be defined, modified and improved once for all. The specific communication function addressed in this work is packet scheduling. For better performance the packet scheduling design exploits the cross-layering approach, i.e. information and functions from different communication layers are used. The concept is proved with reference to the UMTS and Bluetooth technologies, as representatives of a cellular system and a local access one respectively.

I n tr od u cti on The importance of reconfigurability in wireless access interfaces (at least at the physical layer, e.g. software radio) is due to existence of various technologies spanning from personal area networks and wireless local area networks (e.g. IEEE 802.11, Bluetooth, Hiperlan/2) to cellular systems (e.g. GSM, GPRS, CDMA2000, UMTS, etc.). The common meaning of reconfigurability [1] is the capability to provide a network element with different sets of communication functions and with the ability to switch among them so as to exploit any of a number of different wireless access environments that might be available at a given time and place. In the following we adopt a somewhat broader point of view: a system is reconfigurable if some communication functions and relevant algorithms are defined and implemented by abstracting from a specific wireless access. The specific wireless access is represented by models able to express the traffic load, the channel conditions and other communication parameters from a high level point of view. It becomes possible to design algorithms (e.g. packet scheduling) according to some general criteria independent of the specific technology. A strictly related approach to high performance wireless access system is crosslayering [2] [3]. Optimization of data transfer and quality of service is best achieved by jointly considering functions and parameters traditionally belonging to different architectural layers (e.g. error control by means of hybrid ARQ/FEC techniques, power control, packet scheduling and radio resource sharing) M. Ajmone Marsan et al. (Eds.): QoS-IP 2003, LNCS 2601, pp. 485–498, 2003. c Springer-Verlag Berlin Heidelberg 2003 

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The conception of communication algorithms and specifically of radio resource management algorithms is therefore “generalized” along two directions: reconfigurability, in order to exploit different wireless communication systems, and cross-layer design, to achieve a better efficiency and exploitation of the time-varying communication environment. This work fits in a comprehensive effort to specify a reconfigurable wireless communication architecture for mobile computing applications, named R e - c o n fi g u r a b l e A c c e s s m o d u l e f o r M O b i l e c o m p u t i N g a p p l i c a t i o n s (RAMON in the sequel [1]). The framework of RAMON is a mobile computing environment adopting the TCP/IP protocol suite. Different communication environments (R e f e r e n c e E n v i r o n m e n t , RE) are provided to the mobile host; in the following, we consider as example network environments UMTS-TDD [4] and Bluetooth [5]. This paper focuses on the radio resource management functions, specifically on packet scheduling and resource sharing. There are some works on these subjects with specific reference to the wireless access. Papers [6]-[8] address wireless packet scheduling with emphasis on the fairness issue arising primarily from reuse of channel state information and the short term variability of channel condition that bring about unfairness at least in the short term if a high efficiency is targeted. Adaptation of the classic Weighted Fair Queuing schemes are investigated in [6] and [7]. Papers [9]-[12] deal with radio resource sharing for wireless packet access in a CDMA based air interface with mutual interference. Finally, papers [13] and [14] consider using channel state information for resource sharing in wireless packet access. Some of these works take what can be viewed as a cross-layer approach, in that radio resource assignment is based on radio channel state for the competing links. This is also the approach considered in our research [15]. The novel points with respect to previous works are the reconfigurability framework and the specific scheduling algorithm with its adaptation to the considered REs (UMTS and Bluetooth). The first point has a conceptual value: from a large number of studies developed with reference to specific technologies, we abstract the major common ideas to define a general framework for wireless access thus simplify the design of efficient algorithms. The second point is the development of a packet scheduling scheme that is jointly adaptive to channel and traffic conditions. This scheme, named C H a n n e l A d a p t i v e O p e n S c h e d u l i n g (CHAOS) fully exploits the abstract and general model available in the RAMON platform. The rest of the work contains a brief description of the overall RAMON architecture (Section 2), aimed at stating our original context for the radio resource management algorithms. Section 3 defines the general, platform independent radio resource assignment algorithm, by exploiting RLC, MAC and physical layer information (cross-layer design). Section 4 describes in detail the adaptation modules to fit the general algorithm onto two specific REs, UMTS and Bluetooth. Section 5 shows some performance results. Final remarks and further work are addressed in Section 6.

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F u n cti on a l Ar ch i tectu r e RAMON allows the deployment of control algorithms independent of the considered RE. A M o b i l e S t a t i o n (MS) or a B a s e S t a t i o n (BS), equipped with the RAMON software module, supports abstract functionalities common to all the REs. Such functionalities are obtained from the specific operations of each RE, by means of translation entities, as described below.

F i g . 1 . Overall system architecture.

Figure 1 shows the RAMON functional architecture. It includes a C o m m o n C o n t r o l p l a n e (CC-plane) and an A d a p t a t i o n p l a n e (A-plane). N a t i v e C o n t r o l functionalities (NC-plane) for each RE (denoted as NC/RE-i for the i -th RE) are located below the A-plane. A service development RE-independent API (A p p l i c a t i o n P r o g r a m m i n g I n t e r f a c e ) is offered to the overlying A p p l i c a t i o n L a y e r . CC-plane functions, which are defined independently of the underlying RE, are grouped in three functional sets, according to the classical model adopted for wireless communications: i) R a d i o R e s o u r c e C o n t r o l (RRC-c); ii) S e s s i o n C o n t r o l (SC-c); iii) M o b i l i t y M a n a g e m e n t (MM-c) 1 ; The A-plane, which is divided into as many parts (A/RE-i ) as the number of different REs involved, translates: 1) Primitives exchanged between the CC-plane and the NC-plane for each RE; 2) C o n t r o l P a r a m e t e r s (CP) data passed from the N a t i v e U s e r p l a n e (NU-plane) and the CC-plane. Two different types of interfaces can be identified: i) the α interface, between the CC-plane and the A-plane; ii) the β interface, between the A-plane and the NC-plane of each RE. Figure 2 completes Figure 1. The CC-plane and the A-plane with the relevant α and β interfaces are depicted on the right. The NCplanes and NU-planes are shown on the left. Figure 2 clarifies how the SC-c, MM-c and RRC-c functionalities interact with the corresponding SC-i , MM-i and RRC-i (i =1,2) of the two REs through the translation performed by the A planes (A/RE-1, A/RE-2). The relations between the NC-planes and NU-planes are highlighted and particularly how the SC-i , MM-i and RRC-i functionalities are related with Physical (PHY-i ), M e d i u m A c c e s s C o n t r o l (MAC-i ) and R a d i o L i n k C o n t r o l (RLC-i ) functions is shown. Finally, Applications, TCP/UDP and IP layers, which are part of the NU-plane, directly interact with the CC-plane. The main idea is to dynamically adapt the whole stack to the perceived link quality by means of adequate control actions. Quality measurements are passed to the RAMON entity by means of CP data. 1

-c means in the common control plane.

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F i g . 2 . Basic interactions among Control and User planes.

Cross-layer interaction requires control information sharing among all layers of the protocol stack in order to achieve dynamic resource management. It may be performed in two directions: i) u p w a r d i n f o r m a t i o n s h a r i n g : upper layers parameters may be configured to adapt to the variable RE characteristics; ii) d o w n w a r d i n f o r m a t i o n s h a r i n g : MAC, RLC and PHY layer parameters can adapt to the state of Transport and Application layer parameters.

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C om m on C on tr ol P la n e a n d R econ fi g u r a b le Alg or i th m This Section is dedicated to describe the general CHAOS scheme in the framework of the RAMON architecture. CHAOS is part of the RRC functional set of the CC-plane of the RAMON architecture. Thus it is defined independently of the underlying REs. The scheme sets a framework for designing scheduling strategies for efficient resource sharing control in a scenario constituted by a single cell served by a BS, based on an “abstract” representation of i) physical channel state; ii) traffic condition for each MS involved in the communication process. This representation is expressed by means of abstract quantized parameters, C H A N N E L S T A T E and T R A F F I C C O N D I T I O N respectively. The system state can be described by four vectors of length N (where N is the number of MSs in the scenario): 1. 2. 3. 4.

CHANNEL STATE for each MS (downlink); CHANNEL STATE for each MS (uplink); TRAFFIC CONDITION for each MS (downlink); TRAFFIC CONDITION for each MS (uplink).

Figure 3 shows the basic information flow, i.e., how the CHAOS entity running in the CC-plane gathers information about system state. For every MS, in both directions, the RRC-i (relative to the i -th RE) entity in the NC-plane of the BS collects information that will be used for the evaluation of the abstract parameters by the A-plane. The RRC-i

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F i g . 3 . Description of Information Flow from U-plane to CC-plane.

entity on the BS gets the BS-related information directly from the different layers of the NU-plane (i.e. the RLC-i , MAC-i and PHY-i layers). Information lying in the MS has to be exchanged between the two RRC peer entities (MS RRC-i and BS RRC-i ) by means of the transport facilities offered by lower layers. As soon as new information describing the system state is acquired by the BS RRC-i , a C P U P D A T E i n d i c a t i o n p r i m i t i v e (1), which is RE-dependent, is issued to the A-plane. The mapping of these RE-dependent parameters into abstract parameters (CHANNEL STATE and TRAFFIC CONDITION), that can be used by the CHAOS algorithm, is up to the A-plane, which asynchronously communicates the abstract parameters to the CC-plane entity as soon as they are available, by means of an RE-independent C P U P D A T E p r i m i t i v e (2). The A/RE-i entity asynchronously issues RE-independent C A P A C I T Y A S S I G N M E N T R E Q U E S T p r i m i t i v e s (4) to the CHAOS entity in the CC-plane. These abstract requests are formulated by the A/RE-i plane on the basis of the RE-dependent explicit request coming from the RRC-i (RE-Dependent C A P A C I T Y R E Q U E S T p r i m i t i v e (3)) or on the basis of the CPs gathered when no explicit requests are issued by native system control mechanisms. These primitives contain the overall amount of capacity to be assigned. The CHAOS entity processes this request and returns an ordered vector of length NT (NT ≤ N ) whose element contains the MS i d and the amount of capacity assigned to it through the RE-independent C A P A C I T Y A S S I G N M E N T p r i m i t i v e (5). The last step (6) consists in the A/RE-i entity translating the assignment into an RE-dependent C A P A C I T Y A S S I G N M E N T p r i m i t i v e command that can be issued to the BS NC-plane. This will result in the actual assignment with NC-plane specific mechanisms. As a matter of example, the channel state could be a normalized measure of the distance between the target S i g n a l t o N o i s e R a t i o (SNR) of the link and its actual SNR; or it could be derived from B i t E r r o r R a t e measurements. For instance, we could have

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three channel states (good, fair, bad). Analogously, traffic condition could be a normalized measure of the age of the packets or backlog.

F i g . 4 . The CHAOS matrix. Examples of matrix scanning methods We will finish this section by describing how the CHAOS entity uses system state information to assign capacity to the different MSs. As soon as C A P A C I T Y R E Q U E S T p r i m i t i v e s arrive from the A/RE-i plane, this information is arranged in a matrix. In Figure 4 the CHAOS matrix is shown with three different scanning methods. The horizontal dimension represents the channel state, and thus requests with a different value of CHANNEL STATE occupy different positions in the matrix. The vertical dimension is associated with traffic condition, thus requests with different values of TRAFFIC CONDITION are put in different vertical positions in the matrix. What the CHAOS entity obtains is thus a two-dimensionally ordered description of the requests coming from different MSs. User requests are served in the order defined by a predefined rule (scanning method). Each different rule results in a different scheduling discipline. In Figure 4(a) the matrix is scanned by column by giving priority to traffic state conditions; in Figure 4(b) it is scanned by row by giving priority to channel state conditions; a combination of the first two methods is shown in Figure 4(c). Thus, CHAOS can be better understood as a class of algorithms, each qualified by a different service discipline, which is somehow computed on the basis of the matrix.

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Ad a p ta ti on P la n es a n d R ef er en ce E n v i r on m en ts In this Section the RE-dependent A-planes for the UMTS and Bluetooth systems are described. Native mechanisms and procedures are introduced and some design choices are explained. After a brief description of the capacity allocation procedures of the two REs (Subsections 4.1 and 4.3), we illustrate how to adapt these mechanisms to uniform them to the CHAOS paradigm (Subsections 4.2 and 4.4)). 4 .1

U MT S - T D D

In UMTS-TDD air interface the time axis is slotted into T i m e S l o t s (TSs) and 15 TSs are grouped into a 10 ms frame. Within each time slot a set of variable spreading factor

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orthogonal codes are defined to spread QPSK modulated data symbols of up to 16 different users. The overall capacity of the radio interface is shared by common channels and data channels. In our study the R a n d o m A c c e s s C H a n n e l (RACH) is allocated to the first TS of every frame and the F o r w a r d A c c e s s C H a n n e l (FACH) and B r o a d c a s t C H a n n e l (BCH) are allocated to the last one. We assume that transport blocks are 320 bit long, (including MAC/RLC overhead); a T r a n s m i s s i o n T i m e I n t e r v a l (TTI) of 10 ms and a convolutional coding with rate 1/2 are used. This implies that four codes with spreading factor 16 are required to carry the coded transport block; the choice of this transport format implies that the minimum assignable capacity is 32 kbit/s which will be referenced to in the sequel as R e s o u r c e U n i t (RU). From a modeling point of view, the entire transport resource of the radio interface (i.e. 60 RUs) is divided into common channels (8 RUs) and shared channels (52 RUs) for data transfer. Each slot can carry up to four data (plus associated signaling) transport blocks in each frame, if we require that the four RUs used by a transport block be all in the same time slot. Different kind of logical channels are available for data transfer. The choice depends on the traffic type and on traffic volume. D e d i c a t e d C H a n n e l s (DCH) are well suited for R e a l T i m e services (RT), whereas common channels (RACH and FACH) or shared channels (U p l i n k S h a r e d C H a n n e l (USCH) and D o w n l i n k S h a r e d C H a n n e l (DSCH)) are suited for N o n R e a l T i m e services (NRT). For mobile computing purposes (weblike and file transfer applications) the DSCH and the USCH are the most appropriate choices. These channels are allocated for a limited time and are released automatically. Figure 5 shows the data transfer procedure on USCH [16]. After scanning the RLC buffer, the MS sends a C a p a c i t y R e q u e s t message to the UTRAN; this message contains a traffic measure (the RLC buffer length) and it is sent on the SHCCH (S H a r e d C o n t r o l C H a n n e l ), mapped on the RACH channel or on a USCH (if there is one already allocated to the MS). When the UTRAN RRC layer runs the S c h e d u l i n g A l g o r i t h m , a resource allocation message (P h y s i c a l S h a r e d C h a n n e l A l l o c a t i o n ) is sent to the MS on the SHCCH, which is mapped on the FACH or on the DSCH. At this point the MS can start data transfer. The allocation message allocates a number of RUs for a number t of frames (with 1 ≤ t ≤ tmax ). For this reason, it is not necessary to acknowledge the message. A similar procedure is employed for DSCH allocation. 4 .2

U MT S - T D D Ad a p ta ti on P la n e

In this Section the interactions of the A/UMTS-plane with the UMTS-RRC entity and with RRC-c entity are described. On the one hand the UMTS-TDD Adaptation plane reads informations about channel and traffic conditions of MSs from the RRC-UMTS layer, processes these informations and informs the RRC-c plane about these updates, on the other hand it requests RRC-c plane for the resource allocation, maps it in a UMTS native language and passes it to the RRC-UMTS. To perform all these operations the plane must be aware of the UMTS resource allocation procedures (exchanged messages, parameters, etc.) and must interact with the RRC-UMTS entity to get all needed informations and to replace the RRC allocation algorithm. There are two basic procedures which can be better explained with two examples. – C P - U P D A T E . When the RRC-UMTS layer receives a new allocation request from a MS (see Figure 3 (3)), or when it receives new packets directed to a MS, it sends a

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F i g . 5 . USCH channel allocation procedure.

CP-UPDATE command to the RRC-c plane with the direction link (UL or DL), the mobile identity and the channel quality. The queue length indicated in the request is sent in a CAPACITY REQUEST (see Figure 3(4)). The RRC-c functional entity updates the matrix. – C A P A C I T Y R E Q U E S T . Every 10 ms the A-plane sends a CAPACITY ASSIGNMENT REQUEST to the RRC-c entity indicating the unallocated capacity of the frame; the RRC-c scans the matrix and creates a vector with the MS identities, the capacity to allocate in one frame and the duration of the allocation. The A-plane translates it into the UMTS-TDD language (i.e. TSs, codes to assign and number of frames) and sends new allocations to the RRC-UMTS that will inform the involved MSs. As seen in the second example, the CAPACITY ASSIGNMENT REQUEST indication primitive is sent one time per frame and lets the RAMON module synchronize with the UMTS frame. The UPDATE messages, instead, are totally asynchronous and can be transmitted at every instant. From the RAMON point of view the whole UMTS-TDD system can be seen as shared capacity that varies in time but remains fixed in the frame. 4 .3

B lu etooth MAC

In this paragraph the basic issues related to the MAC technique adopted in the Bluetooth (BT) technology are presented. Devices are organized into piconets, i.e., small networks which include up to 8 nodes. Different piconets share the same channel (2.4 GHz ISM band) by exploiting the FHSS (Frequency Hopping Spread Spectrum) technique, i.e., by following different hopping sequences. In a piconet, one device has the role of master, all the other devices are slave. Time is slotted (625μs), the master controls the traffic and takes care of the centralized access control. Only master-slave communications are allowed. Odd slots in the TDD slotted structure are reserved for master transmission. The slave that receives a packet from the master is implicitly polled for the following even slot. Thus, the master controls the

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medium access by sending data to different slaves in even slots and implicitly authorizing the slave to transmit starting from the following slot. If the master has no data to send, it can authorize slaves transmission with an explicit POLL packet. Three data packet sizes are allowed: one slot, three slot, and five slot length. 4 .4

B lu etooth Ad a p ta ti on L a y er

While the RRC-UMTS provides much information that can be easily adapted for the CHAOS scheduling, Bluetooth lacks mechanisms to retrieve physical layer (both in the UL and DL directions) and traffic state informations (for the UL direction). A great effort has been done to define a suitable A-plane2 that would make up for the lack of native system informations. Moreover, due to the particular polling mechanism adopted in Bluetooth, master-slave pairs have to be jointly represented in a CHAOS matrix, since a slot assigned in the downlink direction implies at least a slot being assigned in the uplink. For every Master-Slave pair, the master keeps memory of the average Packet Error Rate (PER) on the link, by mediating on the last Ntx transmissions. This information is passed to the A-Plane which classifies the slaves into different classes of CHANNEL STATE according to their PER values. Traffic condition for each link can be expressed by the amount of data to be transmitted in the L2CAP queue [17]. However, although the master node exactly knows queue-length for any of its slaves in the downlink direction (DLQi ), uplink queue state must be somehow signaled by the slaves. We propose, as in [17], to use the flow bit in the Baseband packet header, which was intended in the Bluetooth Specifications [5] to convey flow information at the L2CAP level. In a way similar to [17], we use this bit to estimate the queue length of the slaves for the uplink direction, (U LQi ). The masterslave pair, in the scheduling process, will be then represented by its V i r t u a l Q u e u e , defined as V Qi = U LQi + DLQi . This parameter is then quantized by the A-plane and passed as TRAFFIC CONDITION parameter to the CHAOS RRC-c entity. Due to the particular polling mechanism adopted in Bluetooth, the resource to be shared among the different M-S couples can not be easily described as capacity. The scheduler only decides which M-S couple has the right to transmit on the next available slot, but the amount of capacity assigned to each couple strongly depends also on other factors, such as the SAR (Segmentation & Reassembly), since choosing different packet sizes leads to different capacities being assigned. An additional variable is defined in the A/BT-plane for each M-S couple, namely V i r t u a l T i m e , to adapt the CHAOS framework to the polling mechanism. The Virtual Time assigned to the i-th M-S couple at step t is defined as: i + Vti = Vt−1

lt−1 rti

(1)

where rti represents the abstract capacity assigned by CHAOS to the i-th couple at step t and lt−1 is the duration of the last transmission of the M-S couple (which ranges from 625 · 2μs if a 1 slot packets is used in both directions to 625 · 10μs if both transmitters 2

The authors would like to thank M. D. Marini for his precious work in adapting CHAOS to Bluetooth and for the simulation results presented in Section 5.2.

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use a 5 slot packet). Thus, when CHAOS assigns high values of capacity, the V i r t u a l T i m e increases slowly after each transmission, where as when it assigns high values of capacity it increases in a faster way. After one couple’s transmission, the scheduler gives the right to transmit to the M-S couple with the minimum value of Virtual Time. This results in a higher number of chances to transmit being given to M-S couples CHAOS has assigned high capacity. CHAOS assigns capacity on the basis of functions that can be computed on the matrix representing the system state, which somehow represent the scheduling discipline chosen. For the simulations presented in the following paragraph, a 5x5 matrix has been used to describe the system state. CHANNEL STATE (CS ) and TRAFFIC CONDITION (TC ) assume discrete values ranging from 1 to 5. The capacity assigned to the i-th couple is then calculated as: rti =

TC2 CS3

(2)

which results in high capacity being assigned to couples with low values of CHANNEL STATE (good channel) and high values of TRAFFIC CONDITION (high traffic). However, channel state is given a higher exponent because the main target is avoiding potentially power-wasting transmissions when the state of the channel is bad.

5

R es u lts In this Section results about improvements that can be achieved with the CHAOS strategies are shown for the UMTS and for Bluetooth. Results have been obtained using an UMTS module for the n s network simulator [18] and extending the B l u e h o c [19] functionalities. As said before it is important to notice that CHAOS constitutes a large class of algorithms and by modifying the matrix scanning methods different service disciplines (with different targets) can be easily achieved. This can be simply obtained by different scanning methods. 5 .1

U MT S

In the simulated scenario N mobiles in a single cell send data through a gateway to N wired nodes. The entire data traffic is in the uplink direction. In the UMTS frame 9 time-slots have been statically allocated to the uplink (1 for the RACH and 8 for the USCHs), and the remaining 6 have been allocated to the downlink (1 for the FACH and BCH and 5 for the DSCH); thus, the maximum attainable throughput in the uplink direction is 1024 kbit/s. The traffic is generated by FTP traffic sources (one FTP agent per node) on a TCP transport layer. Three matrix scanning methods have been used in simulations; the first one, named Random, scans the matrix randomly; the second one, named CHAOS1 , scans the matrix by giving priority to the oldest requests (see Figure 4(b)), and the last one, CHAOS2 , gives priority to the requests from users with better channel quality (see Figure 4(a)). In Figure 6 we can see that throughput is maximized by giving priority to

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1 1 0 0 1 0 0 0 9 0 0 8 0 0

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1 0 0 0 0

5

1 0

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3 0

F i g . 6 . FTP throughput vs. number of MSs varying matrix scanning methods.

“best channel” requests. This throughput gain is due to more efficient use of the radio interface: the adoption of a channel adaptive scheduling decreases the RLC-PDU error probability, leading to a better exploitation of the radio resource. This in turn reduces the need for packet retransmissions, as can be seen from Table 1. Figure 7 illustrates

R etr a n s m i s s i on s 0 1 2 3 4 5 ≥6

Alg or R a n d om 95.676 2.765 0.98 0.363 0.128 0.05 0.068

i th m C H AO S 99.888 0.1 0.011 0.00099 0.00013 0 0

T a b le 1 . Percentual distribution of RLC PDU retransmissions

the gain in energy efficiency brought about by the use of a channel-adaptive packet scheduling algorithm. This result can be explained by observing that, with the CHAOS algorithm, mobiles tend to transmit more during the intervals in which they experience a high channel quality, when the transmitted power is reduced by the power control algorithm. Moreover, the decrease in the number of retransmissions also contributes to the increase in efficiency.

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5 .2

B lu etooth

6

The simulation scenario involves a piconet with one master and two slaves. Two different CBR connections are supported in the downlink direction (from master to slave), and transport and network layer protocols are respectively UDP and IP. The channel is modeled as a two-state Markov Chain: in the BAD state the P a c k e t E r r o r R a t e PER is very high (90%) where as in the GOOD state no errors occur on the channel. Residence time in each state is exponentially distributed with mean residence time equal to 5 seconds in the BAD state and 20 seconds in the GOOD state. This model tries to account for interference from co-located 802.11b devices. Figure 8 shows the throughput of the piconet with respect to the load offered to the piconet, normalized to the capacity of the piconet itself. CHAOS is shown to reach a better throughput with respect to a Deficit Round Robin (DDR) scheduler, especially as the load increases. Figure 9 shows the number of information bits received with respect to information bits transmitted obtained by varying the offered load to the piconet. This value can be interpreted as a measure of power efficiency since for low power devices (CLASS 2) no power control is used. It can be observed that while CHAOS constantly outperforms the DRR scheduler, higher values of power efficiency are obtained when offered load increases. This mainly happens because when much free capacity is available (which happens for lower values of offered load) useless retransmissions occur, which fail because the channel is in the BAD state.

F i n a l R em a r k s a n d F u r th er W or k In this paper a scheme for developing reconfigurable scheduling disciplines was presented. A modular architectural paradigm was introduced, which allows the deployment

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F i g . 8 . Throughput vs Offered Load with different scheduling disciplines.

of general algorithms based on simple modules that abstract functionalities common to the wireless systems in use today. We exploited this architecture to develop scheduling algorithms adaptive to both traffic and channel quality; these algorithms are then applied to two different Reference Environments (Bluetooth and UMTS), and they are shown to achieve an efficient utilization of the radio interface. This occurs because the adoption of a cross layered architecture enhances native system functionalities. The adaptation plane algorithms for the two reference environments have been specified in detail. Results for each RE show how scheduling algorithms manage to reap the best from different REs.

R ef er en ces 1. Roveri A., Chiasserini C.F., Femminella M., Melodia T., Morabito G., Rossi M., Tinnirello I.: “The RAMON module: architecture framework and performance results,“ published in these Proceedings. 2. Haas Z.J.: “Design Methodologies for Adaptive and Multimedia Networks,” IEEE Communications Magazine., Vol. 39, no. 11, November 2001. 3. Rappaport T.S., Annamalai A., Buehrer R.M., Tranter W.H.: “Wireless Communications: Past Events and a future Perspective,” IEEE Commun. Mag., Vol 39, no. 11, May 2002. 4. Haardt M., Klein A., Kohen R., Oestreich S., Purat M., Sommer V., Ulrich T.: “The TDCDMA Based UTRA TDD Mode,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 8, August 2000. 5. Bluetooth Special Interest Group: “Specifications of the Bluetooth System, Volume 1, Core. Version 1.1, February 22 2001. 6. Bharghavan V., Lu S., Nandagopal T.: “Fair Queuing in Wireless Networks: Issues and Approaches,” IEEE Personal Communications, vol. 6, no. 1, February 1999. 7. Lu S., Bharghavan V., Srikant R.: “Fair Scheduling in Wireless Packet Networks,” IEEE/ACM Trans. on Networking, vol. 7, no. 4, August 1999.

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F i g . 9 . Received Bits/Transmitted Bits vs Offered Load with different scheduling disciplines.

8. Nandagopal T., Kim T. E., Gao X., Bharghavan V.: “Achieving MAC Layer Fairness in Wireless Packet Networks,” Proc. of ACM MOBICOM 2000, August 6-11 2000, Boston, Massachussets. 9. Liu Z., Karol M.J., El Zarki M., Eng K.Y.: “Channel access and interference issues in multicode DS-CDMA wireless packet (ATM) networks,” ACM Wireless Networks, 2, 1996. 10. Alonso L., Agust R., Sallent O.: “A Near-Optimum MAC Protocol Based on the Distributed Queueing Random Access Protocol (DQRAP) for a CDMA Mobile Communication System,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 9, September 2000. 11. Elaoud M., Ramanathan P.: “Adaptive Allocation of CDMA Resources for Network-level QoS Assurances,” Proc. of ACM MOBICOM 2000, August 6-11 2000, Boston, Massachussets. 12. Lee S. J., Lee H. W., Sung D. K.: “Capacity of Single-Code and Multicode DS-CDMA System Accommodating Multiclass Services,” IEEE Transactions on Vehicular Technology, vol. 48, no. 7, March 1999. 13. Bhagwat P., Bhattacharya P., Krishna A., Tripathi S.K.: “Enhancing throughput over wireless LANs using channel state dependent packet scheduling,” Proc. of IEEE INFOCOM 96, April 2-6 1996, San Francisco, California. 14. Fragouli C., Sivaraman V., Srivastava M.B.: “Controlled multimedia wireless link sharing via enhanced class-based queuing with channel state dependent packet scheduling,” Proc. INFOCOM 98, April 1998, San Francisco, California. 15. Baiocchi A., Cuomo F., Martello C.: “Optimizing the radio resource utilization of multiaccess systems with a traffic-transmission quality adaptive packet scheduling,” Computer Networks (Elsevier), Vol. 38, n. 2, February 2002. 16. 3GPP Technical Specification TS 25.331, V3.8.0 Release 99, “RRC Protocol Specification,” September 2001. 17. Das A., Ghose A., Razdan A., Saran H., and Shorey R.: “Enhancing Performance of Asynchronous Data Traffic over the Bluetooth Wireless Ad-hoc Network,”IEEE INFOCOM 2001, Alaska, USA, April 2001. 18. n s - Network Simulator, UC Berkeley. Internet Site: http://www.isi.edu/nsnam/ns. 19. Bluehoc Simulator Site: http://www-124.ibm.com/developerworks/opensource/bluehoc/.



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