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Published in:
Computational Probability Read chapter Read first chapter

2017 | OriginalPaper | Chapter

13. Transient Queueing Analysis

Authors : John H. Drew, Diane L. Evans, Andrew G. Glen, Lawrence M. Leemis

Published in: Computational Probability

Publisher: Springer International Publishing

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Abstract

An APPL extension that computes the exact distribution of the nth customer’s sojourn time in an M∕M∕s queue with k customers initially present is derived in this chapter. Algorithms for computing the covariance between sojourn times for an M∕M∕1 queue with k customers present at time zero are also developed. Maple computer code is developed to implement the transient queue analysis for many system measures of performance without regard to traffic intensity (i.e., the system may be unstable with traffic intensity greater than one).

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previous chapter Stochastic Simulation
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Literature
1.
Abate J, Whitt W (1988) Transient behavior of the M∕M∕1 queue via Laplace transforms. Adv Appl Probab 20:145–178CrossRef
25.
e Silva ES, Gail HR, Campos RV (1995) Calculating transient distributions of cumulative reward. In: Proceedings of the 1995 ACM SIGMETRICS joint international conference on measurement and modeling of computer systems, pp 231–240
34.
Gafarian AV, Ancker CJ Jr, Morisaku T (1976) The problem of the initial transient in digital computer simulation. In: Proceedings of the 76 bicentennial conference on winter simulation, pp 49–51
40.
Grassmann WK (1977) Transient solutions in Markovian queueing systems. Comput Oper Res 4:47–53CrossRef
41.
Grassmann WK (2008) Warm-up periods in simulation can be detrimental. Probab Eng Inform Sci 22:415–429CrossRef
43.
Hagwood C (2009) An application of the residue calculus: the distribution of the sum of nonhomogeneous gamma variates. Am Stat 63:37–39CrossRef
49.
Hillier FS, Lieberman GJ (2010) Introduction to operations research, 9th edn. McGraw–Hill, New York
52.
Hogg RV, McKean JW, Craig AT (2005) Introduction to the mathematical statistics, 6th edn. Prentice-Hall, Upper Saddle River, New Jersey
59.
Kelton WD (1985) Transient exponential-Erlang queues and steady-state simulation. Commun ACM 28:741–749CrossRef
60.
Kelton WD, Law AM (1985) The transient behavior of the M∕M∕s queue, with implications for steady-state simulation. Oper Res 33:378–396CrossRef
62.
Kleinrock L (1975) Queueing systems. Wiley, New York
66.
Law AM (1975) A comparison of two techniques for determining the accuracy of simulation output. Technical Report 75–11, University of Wisconsin at Madison
76.
Leguesdron P, Pellaumail J, Rubino G, Sericola B (1993) Transient analysis of the M∕M∕1 queue. Adv Appl Probab 25:702–713CrossRef
90.
Morisaku T (1976) Techniques for data-truncation in digital computer simulation. Ph.D. thesis, University of Southern California, Los Angeles
94.
Odoni AR, Roth E (1983) Empirical investigation of the transient behavior of stationary queueing systems. Oper Res 31:432–455CrossRef
99.
Parthasarathy PR (1987) A transient solution to an M∕M∕1 queue: a simple approach. Adv Appl Probab 19:997–998CrossRef
101.
Pegden CD, Rosenshine M (1982) Some new results for the M∕M∕1 queue. Manage Sci 28:821–828CrossRef
107.
Ruskey F, Williams A (2008) Generating balanced parentheses and binary trees by prefix shifts. In: Proceedings of the 12th computing: the Australasian theory symposium (CATS2008), CRPIT, vol 77, pp 107–115
111.
Stanley RP (1999) Enumerative combinatorics. Volume 62 of Cambridge studies in advanced mathematics. Cambridge University Press, Cambridge
118.
Winston WL (2004) Operations research: applications and algorithms, 4th edn. Thompson, Belmont, California
Metadata
Title
Transient Queueing Analysis
Authors
John H. Drew
Diane L. Evans
Andrew G. Glen
Lawrence M. Leemis
Copyright Year
2017
Book
Computational Probability

Print ISBN: 978-3-319-43321-9

Electronic ISBN: 978-3-319-43323-3

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-43323-3_13

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