A tutorial on queuing and trunking with applications to communications Tranter, William H. creator MacKenzie, Allen Brantley 1977- text abstract or summary cau San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) Morgan & Claypool c2012 2012 monographic eng
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The motivation for developing this synthesis lecture was to provide a tutorial on queuing and trunking, with extensions to networks of queues, suitable for supplementing courses in communications, stochastic processes, and networking. An essential component of this lecture are the MATLAB-based demonstrations and exercises, which can be easily modified to enable the student to observe and evaluate the impact of changing parameters, arrival and departure statistics, queuing disciplines, the number of servers, and other important aspects of the underlying system model. Much of the work in this lecture is based on Poisson statistics, since Poisson models are useful due to the fact that Poisson models are analytically tractable and provide a useful approximation for many applications. We recognize that the validity of Poisson statistics is questionable for a number of networking applications and therefore we briefly discuss self-similar models and the Hurst parameter, long-term dependent models, the Pareto distribution, and other related topics. Appropriate references are given for continued study on these topics. 1. Introduction -- 1.1 The Poisson process - strengths and weaknesses -- 1.2 Outline -- 1.3 MATLAB -- 2. Poisson, Erlang, and Pareto distributions -- 2.1 The Poisson distribution -- 2.1.1 Development of the Poisson distribution -- 2.1.2 Interevent times -- 2.2 The Erlang distribution -- 2.2.1 Derivation of the Erlang distribution -- 2.2.2 Mean and variance of the Erlang-m random variable -- 2.2.3 Plots of the Erlang distribution -- 2.2.4 Erlang and gamma random variables -- 2.3 The Pareto distribution -- 2.4 Problems -- 2.5 Appendix A. Generating samples with an exponential distribution -- 2.6 Appendix B. The gamma function -- 3. A brief introduction to queueing theory -- 3.1 Birth-death processes -- 3.2 Examples of simple queues -- 3.2.1 The single-server queue -- 3.2.2 Multiple-server queues -- 3.3 Three example simulations -- 3.3.1 The simulation of a pure birth process -- 3.3.2 Simulation of a birth-death process -- 3.4 Problems -- 3.5 Appendix A. The moment-generating function -- 3.6 Appendix B. MATLAB code for examples 3.2 and 3.3 -- 3.6.1 MATLAB code for example 3.2 -- 3.6.2 MATLAB code for example 3.3 -- 4. Blocking and delay -- 4.1 Erlang-B results (M/M/C/C) -- 4.2 Erlang-C results (M/M/C/[infinity]) -- 4.3 Delay time, Little's theorem -- 4.3.1 Little's theorem -- 4.3.2 Average queue length for M/M/C/[infinity] system -- 4.3.3 Result for delay -- 4.4 Problems -- 4.5 Appendix A. MATLAB code for the Erlang-B chart -- 4.6 Appendix B. MATLAB code for the Erlang-C chart -- 5. Networks of queues -- 5.1 Burke's theorem -- 5.2 Basic model -- 5.3 Jackson's theorem -- 5.3.1 Statement of Jackson's theorem -- 5.3.2 Proof of Jackson's theorem -- 5.4 Extensions to Jackson's theorem -- 5.4.1 Dependent service rate networks -- 5.4.2 Jackson's theorem for dependent service rate network -- 5.4.3 Closed networks -- 5.4.4 Jackson's theorem for closed networks -- 5.5 BCMP theorem -- 5.5.1 Statement of the BCMP theorem -- 5.6 Kleinrock's formula -- 5.7 Problems -- 5.8 Appendix A. MATLAB code for example 5.3 -- 5.9 Appendix B. MATLAB code for example 5.3 -- Bibliography -- Authors' biographies. specialized William H. Tranter and Allen B. MacKenzie. Part of: Synthesis digital library of engineering and computer science. Series from website. Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader. Includes bibliographical references (p. 89-90). Abstract freely available; full-text restricted to subscribers or individual document purchasers. Also available in print. MATLAB Queuing networks (Data transmission) Mathematical models Queuing theory queuing trunking Poisson process Erlang distribution Erlang-A and Erlang-B characteristics blocking probability delay probability Little's theorem networks of queues Jackson's theorem BCMP theorem Kleinrock's formula T57.9 .T727 2012 519.82 Compendex INSPEC Google scholar Google book search Synthesis digital library of engineering and computer science Synthesis lectures on communications ; # 8 9781598292695 (electronic bk.) http://ieeexplore.ieee.org/servlet/opac?bknumber=6813292 http://ieeexplore.ieee.org/servlet/opac?bknumber=6813292 Abstract freely available; full-text restricted to subscribers or individual document purchasers. CaBNVSL 121210 20220822104830.0 6813292