Teletraffic
Theory and Applications
Published on 6. December 2012
XI, 225 pages
978-1-4471-3362-9 (ISBN)
Description
Telecommunications systems have been evolving from the conventional telephone network that mainly deals with voice, to the ISDN (integrated services digital net work) integrating voice, data and image. Moreover, the ATM (asynchronous trans fer mode) and optical switching technologies are being developed for the broadband ISDN which can handle the high speed video communications as well. Computer networks are also progressing from centralized TSS (time-sharing system) to dis tributed LAN (local area network) and VAN (value added network). In the research, development, design and operation of such telecommunications and computer networks, the important problems are determining the optimum con figuration and dimensions of the systems for providing a given performance or GOS (grade of service). The teletraflic theory, the basis for the performance evaluation and the dimensioning, has been studied along with the switching technology, and has developed rapidly by incorporating the recent advances in OR (operations research) and queueing theory. However, it is sometimes difficult for non-experts of teletraffic to understand and apply these theories, because they require a deep mathematical background.
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Content
1 Introduction.- 1.1 Features of Teletraffic Systems.- 1.2 Modeling of Teletraffic Systems.- 1.3 Fundamental Relations.- Exercises.- 2 Markovian Models.- 2.1 Markovian Loss Systems.- 2.2 Markovian Delay Systems.- 2.3 Extended Markovian Models.- Exercises.- 3 Non-Markovian Models.- 3.1 Renewal Process.- 3.2 Poisson Input General Service Time Models.- 3.3 Poisson Input Constant Service Time Model.- 3.4 Renewal Input Exponential Server Models.- 3.5 Renewal Input Single Server Models.- Exercises.- 4 Multi-Class Input Models.- 4.1 Batch Arrival Models.- 4.2 Priority Models.- 4.3 Multi-Dimensional Traffic Models.- 4.4 Mixed Loss and Delay Systems.- 4.5 Multi-Queue Models.- Exercises.- 5 Alternative Routing Systems.- 5.1 Overflow System.- 5.2 Approximate Methods for Overflow Systems.- 5.3 Optimum Design of Alternative Routing.- 5.4 Numerical Analysis of State Equations.- Exercises.- 6 Advanced Teletraffic Models.- 6.1 Renewal Input Multi-Server Model.- 6.2 PH-MRP Input Models.- 6.3 MMPP Input Model.- 6.4 Statistical Packet Multiplexer.- 6.5 Local Area Networks.- Exercises.- 7 Traffic Simulation.- 7.1 Introduction.- 7.2 Methods of Simulation.- 7.3 Generation of Random Numbers.- 7.4 Analysis of Output Result.- Exercises.- Appendices.- A Basic Teletraffic Formulas.- A.1 Notation.- A.2 Markovian Models.- A.3 Poisson Input Non-Markovian Models.- A.4 Renewal Input Non-Markovian Models.- A.5 Non-Renewal Input Models.- B Programs for Erlang B Formula.- B.1 Integer Number of Servers.- B.2 Real Number of Servers.- B.3 Derivatives of Erlang B Formula.- B.4 BASIC Program Lists.- C Basis of Probability Theory.- C.1 Events and Probability.- C.1.1 Events.- C.1.2 Probability.- C.1.3 Conditional Probability.- C.2 Distribution Functions.- C.2.1 Random Variables.- C.2.2 Joint Distribution Function.- C.2.3 Convolution.- C.3 Expectation and Transforms.- C.3.1 Expectation.- C.3.2 Laplace-Stieltjes Transform.- C.3.3 Probability Generating Function.- C.4 Examples of Probability Distributions.- C.4.1 Probability Distribution.- C.4.2 Discrete Distributions.- C.4.3 Continuous Distributions.- C.5 Stochastic Processes.- C.5.1 Markov Process.- C.5.2 Discrete-Time Markov Chain.- C.5.3 Continuous-Time Markov Chain.- C.5.4 Birth-Death Process.- D Solutions to Exercises.
