QUEUING THEORY AND TELECOMMUNICATIONS Networks and

QUEUING THEORY ANDTELECOMMUNICATIONSNetworks and Applications

QUEUING THEORY ANDTELECOMMUNICATIONSNetworks and Applications

By

Giovanni GiambeneDipartimento di Ingegneria dell'lnformazione, Universita degli Studi di Siena,Via Roma, 56 - 53100 Siena, Italy

^y Springer

Giovanni GiambeneDipartimento di Ingegneria dell'Informazione, Universita degli Studi di Siena,Via Roma, 56-53100 Siena, Italy

Queuing Theory and TelecommunicationsNetworks and Applications

Library of Congress Cataloging-in-Publication Data

A CLP. Catalogue record for this book is availablefrom the Library of Congress.

ISBN 0-387-24065-9 e-ISBN 0-387-24066-7 Printed on acid-free paper.ISBN 978-0387-24065-7

© 2005 Springer Science+Business Media, Inc.All rights reserved. This work may not be translated or copied in whole or in part withoutthe written permission of the publisher (Springer Science+Business Media, Inc., 233 SpringStreet, New York, NY 10013, USA), except for brief excerpts in connection with reviews orscholarly analysis. Use in connection with any form of information storage and retrieval,electronic adaptation, computer software, or by similar or dissimilar methodology nowknow or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks and similar terms,even if the are not identified as such, is not to be taken as an expression of opinion as to

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Printed in the United States of America.

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Dedication

This book is in loving memoryof my father, Gianfranco. A

special dedication is to thenearest persons to my heart: my

mother Marisa, my wifeMichela, my uncle Ilvo.

Contents

DEDICATION V

AUTHOR BIOGRAPHY XIII

PREFACE XV

ACKNOWLEDGMENTS XIX

PART I: TELECOMMUNICATION NETWORKS 1

1. Introduction to Telecommunication Networks 31.1 Historic steps in the telecommunication era 31.2 Standardization bodies in telecommunications 71.3 Telecommunication networks: general concepts 9

1.3.1 Transmissions in telecommunication networks 111.3.2 Switching techniques in telecommunication networks 171.3.3 The ISO/OSI reference model 231.3.4 Traffic engineering: general concepts 321.3.5 Queuing theory in telecommunications 33

1.4 Transmission media 341.4.1 Copper medium: the twisted pair 341.4.2 Copper medium: the coaxial cable 351.4.3 Wireless medium 37

viU QUEUING THEORY AND TELECOMMUNICATIONS

1.4.4 Optic fibers1.5 Multiplexing hierarchy

1.5.1 FDM1.5.2 TDM1.5.3 The El bearer structure

1.6 The telephone network1.6.1 Digital transmissions through POTS1.6.2 Switching elements in PSTN

1.7 Bibliographic references

2. Digital Networks2.1 Digital networks introduction

2.1.1 X.25-based networks2.1.2 ISDN2.1.3 Frame Relay-based networks

2.2 B-ISDN and ATM technology2.2.1 ATM protocol stack2.2.2 Cell format2.2.3 ATM protocol stack2.2.4 Traffic classes and ALL layer protocols2.2.5 ATM switches2.2.6 ATM switch architectures2.2.7 Management of traffic2.2.8 ATM physical later2.2.9 Internet access through ATM over ADSL

2.3 Bibliographic references

3. IP-based Networks3.1 Introduction3.2 The Internet

3.2.1 Introduction to the TCP/IP protocol suite3.2.2 TCP/IP protocol architecture

3.3 IP Addressing3.3.1 IPv4 datagram format3.3.2 IP subnetting3.3.3 IP version 6

3.4 IP Routing3.4.1 Routing algorithms3.4.2 Interior routing and exterior routing

3.5 Transport layer3.5.1 TCP and UDP protocols

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QUEUING THEORY AND TELECOMMUNICATIONS

3.5.2 Port numbers and sockets 1913.6 IP traffic over ATM networks 192

3.6.1 The LIS method 1953.6.2 The Next Hop Routing Protocol 1963.6.3 The integrated approach for IP over ATM 197

3.7 Multiprotocol Label Switching technology 2003.7.1 Comparison between IP routing and label switching 2023.7.2 Operations on labels 2043.7.3 MPLS header 2053.7.4 MPLS nested domains 2073.7.5 MPLS forwarding tables 2083.7.6 Protocols for the creation of an LSP 2113.7.7 IP/MPLS over ATM 2143.7.8 MPLS traffic management 216

3.8 GMPLS technology 2203.9 Next-Generation Networks 221

3.9.1 NGN architecture 2243.9.2 DWDM technology 2263.9.3 QoS provision in IP-based networks 2263.9.4 Voice over IP 229

3.10 Bibliographic references 232

PART II: QUEUING THEORY AND APPLICATIONS 235

4. Survey on Probability Theory 2374.1 The notion of probability and basic properties 2374.2 Random variables: basic definitions and properties 241

4.2.1 Sum of independent random variables 2474.2.2 Minimum and maximum of random variables 2484.2.3 Comparisons between random variables 2504.2.4 Moments of the random variables 2504.2.5 Random variables in the field of telecommunications 254

4.3 Transformations for random variables 2734.3.1 The probability generating function 2744.3.2 The characteristic function of a pdf 2824.3.3 The Laplace transform of a pdf 288

4.4 Methods for the generation of random variables 2904.4.1 Method of the inverse of the distribution function 2914.4.2 Method of the transformation 291

4.5 Solved exercises 292


4.6 Bibliographic references 304

5. Markov Chains and Queuing Theory 3055.1 Queues and stochastic processes 3055.2 Poisson arrival process 309

5.2.1 Sum of independent Poisson processes 3115.2.2 Random splitting of a Poisson process 3125.2.3 Compound Poisson processes 313

5.3 Birth-death Markov chains 3145.4 Notations for queuing systems 3175.5 The Little theorem 3185.6 M/M/l queue analysis 3225.7 M/M/l/K queue analysis 324

5.7.1 M/M/S queue analysis 3265.8 M/M/S/S queue analysis 3285.9 The M/M/oo queue analysis 3325.10 Distribution of the queuing delays in the FIFO case 333

5.10.1 M/M/l case 3335.10.2 M/M/S case 336

5.11 Erlang-B generalization for non-Poissonian arrivals 3385.11.1 The traffic types in the M/M/S/S queue 3385.11.2 Blocking probability for non-Poissonian arrivals 340

5.12 Solved exercises 3455.13 Bibliographic references 3 82

6. M/G/l Queuing Theory and Applications 3856.1 The M/G/l queue 385

6.1.1 The M/D/l case 3926.2 M/G/l system delay distribution in the FIFO case 3936.3 Laplace transform numerical inversion method 3946.4 Generalizations of the M/G/l theory 3986.5 Applications of the M/G/l analysis to ATM 4016.6 Different imbedding instants in the M/G/l theory 405

6.6.1 Chain imbedded to the slot end instants of the output line 4076.6.2 Chain imbedded to the cell transmission completion 4086.6.3 Chain imbedded to the message transmission completion 411

6.7 M/G/l with geometrically distributed messages 4126.7.1 Chain imbedded to packet transmission completion 4136.7.2 Chain imbedded to message transmission completion 416

6.8 M/G/l and differentiated service times 4186.9 Solved exercises 4206.10 Bibliographic references 448


7. Local Area Networks Analysis 4497.1 Introduction 449

7.1.1 Standards for local area networks 4547.2 Contention-based protocols 456

7.2.1 Aloha protocol 4567.2.2 Slotted-Aloha protocol 4637.2.3 The Aloha protocol with ideal capture effect 4677.2.4 CSMA schemes 470

7.3 Demand-assignment protocols 5067.3.1 Polling protocol 5067.3.2 Token passing protocols 5077.3.3 Analysis of token and polling schemes 5107.3.4 Reservation Aloha (R-Aloha) protocol 5147.3.5 Packet Reservation Multiple Access (PRMA) protocol 5197.3.6 Comparison between CSMA/CD and token protocols 520

7.4 Fixed assignment protocols 5267.4.1 Frequency Division Multiple Access (FDMA) 5267.4.2 Time Division Multiple Access (TDMA) 5267.4.3 Resource reuse in cellular systems 5277.4.4 Code Division Multiple Access (CDMA) 528

7.5 Solved exercises 5307.6 Bibliographic references 553

8. Networks of Queues 5578.1 Introduction 557

8.1.1 Traffic rate equations 5 608.1.2 The Little theorem for the whole network 560

8.2 The Burke theorem 5618.3 The Jackson theorem 562

8.3.1 Analysis of a queue with feedback 5648.4 Traffic matrices 5668.5 Network planning aspects 5678.6 Solved exercises 5678.7 Bibliographic references 579

INDEX 581

Author biography

Giovanni Giambene was born in Florence, Italy, in 1966. He received theDr. Ing. degree in Electronics from the University of Florence, Italy, in 1993and the Ph.D. degree in Telecommunications and Informatics from theUniversity of Florence, Italy, in 1997. From 1994 to 1997, he was with theElectronic Engineering Department of the University of Florence, Italy. Hewas Technical External Secretary of the European Community COST 227Action, entitled "Integrated Space/Terrestrial Mobile Networks". He alsocontributed to the Resource Management activity of the Working Group3000 within the RACE Project, called "Satellite Integration in the FutureMobile Network" (SAINT, RACE 2117). From 1997 to 1998, he was withOTE of the Marconi Group, Florence, Italy, where he was involved in aGSM development program. In the same period he also contributed to theCOST 252 Action ("Evolution of Satellite Personal Communications fromSecond to Future Generation Systems") research activities by studying theperformance of Packet Reservation Multiple Access (PRMA) protocolssuitable for supporting voice and data transmissions in low earth orbitmobile satellite systems. In 1999 he joined the Information EngineeringDepartment of the University of Siena, Italy, first as research associate andthen as assistant professor. He teaches the advanced course ofTelecommunication Networks at the University of Siena. From 2000 to2003, he contributed to the activities of the "Personalised Access to LocalInformation and services for tOurists" (PALIO) 1ST Project within the fifthResearch Framework of the European Commission (www.palio.dii.unisi.it).At present, he is involved in the SatNEx network of excellence of the FP6programme in the satellite field, as work package responsible on radio access


techniques (www.satnex.org). He is also vice-Chair of the COST 290 Action(www.cost290.org), entitled 'Traffic and QoS Management in WirelessMultimedia Networks" (Wi-QoST). His research interests include third-generation mobile communication systems, medium access controlprotocols, traffic scheduling algorithms, and queuing theory.

Further details are available on the Web page with URL:http://marconi.ltt.dii.unisi.it/~giambene/

Preface

From the invention of the first telecommunication systems (i.e., telegraphand telephone networks) the importance of these technologies has beenclearly evident. Humans need continuously to interact; the exchange ofinformation of different types at distance is today essential.Telecommunications favor the development of countries and the diffusion ofknowledge and they are playing and will play a pivotal role in the society.

Originally, telecommunications were simply conceived as links totransmit information between two points. At present, telecommunicationsystems are characterized by networks with nodes, where information isprocessed and properly addressed (i.e., switching), and links thatinterconnect nodes.

The first telecommunication networks due to telegraphy were based onthe transmission of messages. Then, telephone networks have been based onthe establishment of a physical circuit at call set-up in order to connect (forall the duration of the conversation) the source and the destination. Today'snetworks are digital and based on the transmission of information organizedin blocks, called packets, that are either independently routed along thenodes or forwarded through a virtual path connecting source and destination.Transmission media are distinguished according to a hierarchy in thenetwork typology; in particular, twisted pairs (copper) or wirelesstransmissions are used for the user access, whereas, optic fibers areemployed for core network links.

Telecommunication systems have reached a worldwide diffusion on thebasis of the efforts of international and regional standardization bodies that

xvi QUEUING THEORY AND TELECOMMUNICATIONS

have done a significant work, allowing different pieces of hardware tointeroperate on the basis of well-defined rules.

Instead of having a specialized network for each traffic type, the digitalrepresentation of the information has made possible to integrate efficiently inthe same network different traffic types, from voice, to video to data traffic,etc.

At present, the network of the networks, that is the Internet, has atremendous and ever increasing success. The outcome of this impressiveprocess is that the Internet protocol results as the glue that can unify differentnetwork technologies, from mobile to fixed and from terrestrial to satellite.

The crucial point for modern telecommunication networks is theprovision of multimedia services with global-scale connectivity (alsoincluding mobile users) and guaranteeing several Quality of Service (QoS)requirements, differentiated depending on the application the user is running(i.e., traffic classes). Moreover, network resources are precious and costlyand must be efficiently utilized.

The design of modern networks requires a deep knowledge of networkcharacteristics, transmission media types, traffic demand statistics and so on.On the basis of these data, analytical methods can be adopted to determinethe appropriate transmission capacity of links, the number of links, themanagement strategy for sharing resources among traffic classes and so on.

The interest of this book is in providing the basic characteristics ofcurrent network technologies (i.e., X.25-based, ISDN, Frame Relay-based,ATM-based, IP-based, MPLS, GMPLS, and NGN) as well as someimportant analytical methods based on the queuing theory to be used tostudy the behavior of telecommunication systems. The aim is to contribute toprovide the basis of teletraffic analysis for current telecommunicationnetworks.

Queuing systems are studied in this book with a special interest inapplying these analytical methods to the study of telecommunicationsystems. In particular, queues can be applied at different levels intelecommunication systems; they can be adopted to study the waiting timeexperienced by a given request instanced to a processor or the time spent bya message or a packet waiting to be transmitted on a given link or through awhole network. In particular, every protocol in every node of atelecommunication network can be modeled through an appropriate queuingprocess.

Our analysis of queuing systems will start from Markov chains, such asthe typical M/M/l queuing model to be used in message-switched networksand the M/M/S/S queue employed to characterize the call loss behavior oflocal offices in telephone networks. Then, the interest will focus on more


advanced concepts, such as imbedded Markov chains (M/G/l theory) withthe related models adopted to study the behavior of ATM switches.

QoS provision is a key element both for the users that are happy of thetelecommunication service they are adopting and for the network operators.The success of future telecommunication services and networks is heavilydependent on appropriate modeling and analysis in order to achieve anoptimized network design able to guarantee suitable QoS levels for differenttraffic classes. This is the reason why the analytical methods of teletrafficanalysis are of crucial importance for telecommunication networks.

Acknowledgments

The author wishes to thank Prof. Giuliano Benelli of the University ofSiena for his support and suggestions.

PART I: TELECOMMUNICATION NETWORKS

Documents

QUEUING THEORY AND TELECOMMUNICATIONS Networks and