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
access
1 electronic text (xii, 92 p.) : ill., digital file.
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
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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