Queuing Theory and Telecommunications

Transcription

1 Queuing Theory and Telecommunications

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3 Giovanni Giambene Queuing Theory and Telecommunications Networks and Applications Second Edition

4 Giovanni Giambene Department of Information Engineering and Mathematical Sciences University of Siena Siena, Italy Additional material to this book can be downloaded from ISBN ISBN (ebook) DOI / Springer New York Heidelberg Dordrecht London Library of Congress Control Number: Springer Science+Business Media New York 2005, 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 This second edition of the book is dedicated to my son Francesco, my joy. This book is in loving memory of my father Gianfranco and my uncle Ilvo. A special dedication is to the persons nearest to my heart: my mother Marisa and my wife Michela.

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7 Preface to the Second Edition From the invention of the telegraph and of the telephone networks the importance of telecommunication technologies has been clearly evident. Human beings need to interact continuously. The exchange of information of different types is today an absolute necessity. Telecommunications favor the development of countries and the diffusion of knowledge, and they are playing and will play a pivotal role in the society. Originally, telecommunication systems were simply conceived as links to transmit information between two points. At present, telecommunication systems are characterized by networks with nodes, where information is processed and correctly addressed to output links, interconnecting nodes. The first telecommunication networks for telegraphy supported the transmission of messages. Then, telephone networks were conceived to establish a physical circuit at call set up in order to connect source and destination for the whole duration of the conversation. Today s networks are digital and based on the transmission of information organized in blocks, called packets, which are either independently routed along the nodes or forwarded through a virtual path from source to destination. Transmission media are typically differentiated on the basis of the network hierarchy; in particular, twisted pairs (copper) or wireless transmissions are used for the user access, whereas, optical fibers are adopted in the core network. Telecommunication systems have reached a worldwide diffusion on the basis of the efforts of international and regional standardization bodies, which have done a significant work, allowing different pieces of hardware to interoperate on the basis of well-defined protocols and formats. Instead of having a specialized network for each traffic type, the digital representation of information has made it possible to efficiently integrate different traffic types and then services (from voice, to video to data traffic, etc.) in the same network. At present, the network of the networks, that is the Internet, has a tremendous worldwide-increasing diffusion. The outcome of this impressive process is that the Internet protocol has become the glue, unifying different network technologies, from mobile to fixed and from terrestrial to satellite. vii

8 viii Preface to the Second Edition The central issue for modern telecommunication networks is the provision of multimedia services with global-scale connectivity (also including mobile users), guaranteeing several Quality of Service (QoS) requirements, differentiated depending on the application the user is running (i.e., traffic classes). Network resources are precious and costly and must be efficiently utilized. On the other hand, digital information and data traffic worldwide are experiencing an exponential growth that represents a challenge to be addressed by the system designer and the network planners. In this scenario, wireless access will play a major role since from 2011 wireless connections have surpassed broadband wired ones. The design of modern networks requires a deep knowledge of network characteristics, transmission media types, traffic demand statistics, and so on. On the basis of these characteristics, analytical methods can be adopted to determine the appropriate transmission capacity of links, the number of links, the management strategy for sharing resources among traffic classes, and so on. The main interest of this book is in providing a basic description of important network technologies (in the first part of the book) as well as some analytical methods based on queuing theory to model the behavior of telecommunication systems (in the second part of the book). The aim and ambition is to provide the most important tools of teletraffic analysis for telecommunication networks. As for Part I of this book, the focus is on network technologies (and related protocols) according to their time evolution. In particular, this part is mainly organized according to a bottom-up approach, referring to the ISO/OSI stacked protocol model, since we start from almost-layer 2 technologies (i.e., X.25, ISDN, Frame Relay based, ATM based) in Chap. 2 and then we address layer 3 and above technologies in Chap. 3 (i.e., IP routing, MPLS, transport-layer protocols, VoIP, satellite networks). In Part II of this book, queuing systems are studied with a special interest in applying these analytical methods to the study of telecommunication systems. In particular, queuing models are adopted at different levels in telecommunication systems; they can be used to study the waiting time experienced by a given request instanced to a processor or the time spent by a message or a packet waiting to be transmitted on a given link or through a whole network. Note that the behavior of every protocol in every node of a telecommunication network can be modeled by an appropriate queuing process. Our analysis of queuing systems starts from Markov chains, such as the classical M/M/1 queuing model for message-switched networks and the M/M/S/S queue to study the call blocking probability in classical telephone networks. Then, the interest is on more advanced concepts, such as imbedded Markov chains (M/G/1 theory) with related models adopted to study the behavior of ATM switches as well as of IP routers. This second edition has been enriched and updated for what concerns both new network technologies (Part I) and mathematical tools for queuing theory (Part II). As for Part I, the main improvements are in Chaps. 2 and 3 as follows: (1) better description of policers and shapers for ATM; (2) enriched contents on QoS support in IP networks (e.g., deterministic queuing is introduced to deal with QoS guarantees with IntServ); (3) detailed analysis of TCP congestion control behavior;

9 Preface to the Second Edition ix (4) satellite IP-based networks; (5) VoIP. As for Part II, Chap. 6 on M/G/1 has been substantially improved, detailing more general cases and the relations among different imbedding options. Moreover, Chap. 7 now contains a better explanation of the potential instability of Aloha protocols, updated details on Gigabit Ethernet, and more details on three different approaches for the analysis of random access schemes. Chapter 8 now provides a better description of the conditions for the applicability of the Jackson theorem to real networks. Finally, new exercises have been added to the first part of the book as well as to all the Chapters of the second part of this book. The solution of all the exercises have been removed from the book and provided in a separated solution manual, accessible online Finally, a collection of slides has been made available for downloading and represent a support and complementary tool for teaching based on this book QoS provision is a key element for both users who are happy of the telecommunication services and network operators. The success of future telecommunication services is heavily dependent on the appropriate modeling of the networks and the application of analytical approaches for QoS support. This is the reason why the analytical teletraffic methods are of crucial importance for the design of telecommunication networks. Siena, Italy Giovanni Giambene

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11 Preface to the First Edition From the invention of the first telecommunication systems (i.e., telegraph and telephone networks) the importance of these technologies has been clearly evident. Humans need continuously to interact; the exchange of information of different types at distance is today essential. Telecommunications favor the development of countries and the diffusion of knowledge, and they are playing and will play a pivotal role in the society. Originally, telecommunications were simply conceived as links to transmit information between two points. At present, telecommunication systems are characterized by networks with nodes, where information is processed and properly addressed (i.e., switching), and links that interconnect nodes. The first telecommunication networks due to telegraphy were based on the transmission of messages. Then, telephone networks have been based on the establishment of a physical circuit at call setup in order to connect (for all the duration of the conversation) the source and the destination. Today s networks are digital and based on the transmission of information organized in blocks, called packets, that are either independently routed along the nodes or forwarded through a virtual path connecting source and destination. Transmission media are distinguished according to a hierarchy in the network typology; in particular, twisted pairs (copper) or wireless transmissions are used for the user access, whereas optic fibers are employed for core network links. Telecommunication systems have reached a worldwide diffusion on the basis of the efforts of international and regional standardization bodies that have done a significant work, allowing different pieces of hardware to interoperate on the basis of well-defined rules. Instead of having a specialized network for each traffic type, the digital representation of the information has made possible to integrate efficiently in the 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 a tremendous and ever increasing success. The outcome of this impressive process is that the Internet protocol results as the glue that can unify different network technologies, from mobile to fixed and from terrestrial to satellite. xi

12 xii Preface to the First Edition The crucial point for modern telecommunication networks is the provision of multimedia services with global-scale connectivity (also including 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 costly and must be efficiently utilized. The design of modern networks requires a deep knowledge of network characteristics, transmission media types, traffic demand statistics, and so on. On the basis of these data, analytical methods can be adopted to determine the appropriate transmission capacity of links, the number of links, the management strategy for sharing resources among traffic classes, and so on. The interest of this book is in providing the basic characteristics of current network technologies (i.e., X.25-based, ISDN, Frame Relay-based, ATM-based, IP-based, MPLS, GMPLS, and NGN) as well as some important analytical methods based on the queuing theory to be used to study the behavior of telecommunication systems. The aim is to contribute to providing the basis of teletraffic analysis for current telecommunication networks. Queuing systems are studied in this book with a special interest in applying these analytical methods to the study of telecommunication systems. In particular, queues can be applied at different levels in telecommunication systems; they can be adopted to study the waiting time experienced by a given request instanced to a processor or the time spent by a message or a packet waiting to be transmitted on a given link or through a whole network. In particular, every protocol in every node of a telecommunication network can be modeled through an appropriate queuing process. Our analysis of queuing systems will start from Markov chains, such as the typical M/M/1 queuing model to be used in message-switched networks and the M/M/S/S queue employed to characterize the call loss behavior of local offices in telephone networks. Then, the interest will be focused on more advanced concepts, such as imbedded Markov chains (M/G/1 theory) with the related models adopted to study the behavior of ATM switches. QoS provision is a key element both for the users that are happy of the telecommunication service they are adopting and for the network operators. The success of future telecommunication services and networks is heavily dependent on appropriate modeling and analysis in order to achieve an optimized network design able to guarantee suitable QoS levels for different traffic classes. This is the reason why the analytical methods of teletraffic analysis are of crucial importance for telecommunication networks. Siena, Italy Giovanni Giambene

13 Acknowledgments The author wishes to thank Prof. Giuliano Benelli of the University of Siena for his support and encouragement. xiii

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15 Contents Part I Telecommunication Networks 1 Introduction to Telecommunication Networks Milestones in the Evolution of Telecommunications Standardization Bodies in Telecommunications Telecommunication Networks: General Concepts Transmissions in Telecommunication Networks Switching Techniques in Telecommunication Networks The ISO/OSI Reference Model Traffic Engineering: General Concepts Queuing Theory in Telecommunications Transmission Media Copper Medium: The Twisted Pair Copper Medium: The Coaxial Cable Wireless Medium Optical Fibers Multiplexing Hierarchy FDM TDM The E1 Bearer Structure The Classical Telephone Network Digital Transmissions Through POTS Switching Elements in PSTN References Legacy Digital Networks Introduction to Digital Networks X.25-Based Networks ISDN Frame Relay-Based Networks xv

16 xvi Contents 2.2 B-ISDN and ATM Technology ATM Protocol Stack Cell Format ATM Protocol Stack Traffic Classes and ALL Layer Protocols ATM Switches ATM Switch Architectures Management of Traffic ATM Physical Layer Internet Access Through ATM Over ADSL References IP-Based Networks and Future Trends Introduction The Internet Introduction to the Internet Protocol Suite TCP/IP Protocol Architecture IP (Version 4) Addressing IPv4 Datagram Format IP Subnetting Public and Private IP Addresses Static and Dynamic IP Addresses An Example of Local Area Network Architecture IP Version Domain Structure and IP Routing Routing Algorithms Routing Implementation Issues QoS Provision in IP Networks IntServ DiffServ IP Traffic Over ATM Networks The LIS Method The Next Hop Routing Protocol The Integrated Approach for IP Over ATM Multi-protocol Label Switching Technology Comparison Between IP Routing and Label Switching Operations on Labels MPLS Header MPLS Nested Domains MPLS Forwarding Tables Protocols for the Creation of an LSP IP/MPLS Over ATM MPLS Traffic Management GMPLS Technology

17 Contents xvii 3.8 Transport Layer TCP UDP Port Numbers and Sockets Next-Generation Networks NGN Architecture Geographical Core/Transport Networks Current and Future Satellite Networks Future Internet Concepts References Exercises on Part I of the Book Part II Queuing Theory and Applications to Networks 4 Survey on Probability Theory The Notion of Probability and Basic Properties Random Variables: Basic Definitions and Properties Sum of Independent Random Variables Minimum and Maximum of Random Variables Comparisons of Random Variables Moments of Random Variables Random Variables in the Field of Telecommunications Transforms of Random Variables The Probability Generating Function The Characteristic Function of a pdf The Laplace Transform of a pdf Methods for the Generation of Random Variables Method of the Inverse of the Distribution Function Method of the Transform Exercises References Markov Chains and Queuing Theory Queues and Stochastic Processes Compound Arrival Processes and Implications Poisson Arrival Process Sum of Independent Poisson Processes Random Splitting of a Poisson Process Compound Poisson Processes Birth-Death Markov Chains Notations for Queuing Systems Little Theorem and Insensitivity Property Proof of the Little Theorem M/M/1 Queue Analysis

18 xviii Contents 5.7 M/M/1/K Queue Analysis PASTA Property M/M/S Queue Analysis M/M/S/S Queue Analysis The M/M/1 Queue Analysis Distribution of the Queuing Delays in the FIFO Case M/M/1 Case M/M/S Case Erlang-B Generalization for Non-Poisson Arrivals The Traffic Types in the M/M/S/S Queue Blocking Probability for Non-Poisson Arrivals Exercises References M/G/1 Queuing Theory and Applications The M/G/1 Queuing Theory The M/D/1 Case The M [comp] /G [b] /1 Queue with Bulk Arrivals or Bulk Service M/G/1 System Delay Distribution in the FIFO Case Numerical Inversion Method of the Laplace Transform Impact of the Service Time Distribution on M/G/1 Queue M/G/1 Theory with State-Dependent Arrival Process Applications of the M/G/1 Analysis to ATM A Survey of Advanced M/G/1 Cases Different Imbedding Options for the M/G/1 Theory Imbedding at Slot End of the Output Line Imbedding at Transmission End of Low-Priority Cells Imbedding at Transmission End of Low-Priority Messages Continuous-Time M/G/1 Queue with Geometric Messages Imbedding at Packet Transmission Completion Imbedding at Message Transmission Completion M/G/1 Theory with Differentiated Service Times The Differentiated Theory Applied to Compound Arrivals M/D [b] /1 Theory with Batched Service Exercises References Local Area Networks and Analysis Introduction Standards for Local Area Networks

19 Contents xix 7.2 Contention-Based MAC Protocols Aloha Protocol Slotted-Aloha Protocol The Aloha Protocol with Ideal Capture Effect Alternative Analytical Approaches for Aloha Protocols CSMA Schemes Demand-Assignment Protocols Polling Protocols Token Passing Protocols Analysis of Token and Polling Schemes Reservation-Aloha (R-Aloha) Protocol Packet Reservation Multiple Access (PRMA) Protocol Efficiency Comparison: CSMA/CD vs. Token Protocols Fixed Assignment Protocols Frequency Division Multiple Access (FDMA) Time Division Multiple Access (TDMA) Code Division Multiple Access (CDMA) Orthogonal Frequency Division Multiple Access (OFDMA) Resource Reuse in Cellular Systems Exercises References Networks of Queues Introduction Traffic Rate Equations The Little Theorem Applied to the Whole Network Tandem Queues and the Burke Theorem The Jackson Theorem Analysis of a Queue with Feedback Traffic Matrices Network Planning Issues Exercises References Index

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21 Author Biography Giovanni Giambene was born in Florence, Italy, in He received the Dr. Ing. degree in Electronics in 1993 and the Ph.D. degree in Telecommunications and Informatics in 1997, both from the University of Florence, Italy. From 1994 to 1997, he was with the Electronic Engineering Department of the University of Florence, Italy. He was Technical External Secretary of the European Community COST 227 Action ( Integrated Space/Terrestrial Mobile Networks ). From 1997 to 1998, he was with OTE of the Marconi Group, Florence, Italy, where he was involved in a GSM development program. In 1999, he joined the Department of Information Engineering and Mathematical Sciences of the University of Siena, Italy, first as a research associate and then as an assistant professor and aggregate professor. Since 2003, he teaches the master-level course on Networking at the University of Siena. From 1999 to 2003 he participated in the project Multimedialità, financed by the Italian National Research Council (CNR). From 2000 to 2003, he contributed to the Personalised Access to Local Information and services for tourists (PALIO) IST Project within the EU FP5 program. He was vice-chair of the COST 290 Action for its whole duration , entitled Traffic and QoS Management in Wireless Multimedia Networks (Wi-QoST). He participated in the SatNEx I & II Network of Excellence (EU FP6 program, ) as work package leader of two groups on radio access techniques and cross-layer air interface design for satellite communication systems. He contributed to the EU FP7 Coordination Action Road mapping technology for enhancing security to protect medical and genetic data (RADICAL) as work package leader on security challenges for e-health applications. At present, he is involved in the ESA SatNEX III research project (CoO3 on Smart Gateway Diversity ), in the COST Action IC0906 Wireless Networking for Moving Objects (WiNeMO) and in the EU FP7 Coordination Action called Responsibility. He is the author of more than 120 papers on internationally recognized journals or conferences. Further details are available on the Web page with the following URL: xxi