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On Waiting Time for Many-Server Queueing Systems

1965; Society for Industrial and Applied Mathematics; Volume: 10; Issue: 1 Linguagem: Inglês

10.1137/1110006

1095-7219

Ė. L. Presman,

Advanced Data Processing Techniques

Previous article Next article On Waiting Time for Many-Server Queueing SystemsE. L. PresmanE. L. Presmanhttps://doi.org/10.1137/1110006PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] D. V. Lindley, The theory of queues with a single server, Proc. Cambridge Philos Soc., 48 (1952), 277–289 MR0046597 0046.35501 CrossrefGoogle Scholar[2] J. Kiefer and , J. Wolfowitz, On the theory of queues with many servers, Trans. Amer. Math. Soc., 78 (1955), 1–18 MR0066587 0064.13303 CrossrefGoogle Scholar[3] Walter L. Smith, On the distribution of queueing times, Proc. Cambridge Philos. Soc., 49 (1953), 449–461 MR0054870 0053.10002 CrossrefGoogle Scholar[4] David G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain, Ann. Math. Statistics, 24 (1953), 338–354 MR0056231 0051.10505 CrossrefGoogle Scholar[5] Ju. V. Prokhorov, Transition phenomena in queueing processes. I, Litovsk. Mat. Sb., 3 (1963), 199–205, (In Russian.) MR0168043 0144.40501 Google Scholar[6] E. G. Samandarov, Service systems in heavy traffic, Theory Prob. Applications, 8 (1963), 307–309, (English translation.) 10.1137/1108036 0121.35405 LinkGoogle Scholar[7] B. V. Gnedenko and , I. N. Kovalenko, Lectures in the Theory of Queues, Kiev, 1963, (In Russian.) Google Scholar[8] J. F. C. Kingman, On queues in heavy traffic, J. Roy. Statist. Soc. Ser. B, 24 (1962), 383–392 MR0148146 0127.10003 Google Scholar[9] J. G. Wendel, Spitzer's formula: a short proof, Proc. Amer. Math. Soc., 9 (1958), 905–908 MR0103531 Google Scholar[10] Glen Baxter, A two-dimensional operator identity with application to the change of sign in sums of random variables, Trans. Amer. Math. Soc., 96 (1960), 210–221 MR0119231 0118.33603 CrossrefGoogle Scholar[11] A. A. Borovkov, New limit theorems in boundary-value problems for sums of independent terms, Sibirsk. Mat. Ž., 3 (1962), 645–694, (In Russian.) MR0145568 Google Scholar[12] I. C. Gokhberg, The factorization problem in normed rings, functions of isometric and symmetric operators, and singular integral equations, Uspehi Mat. Nauk, 19 (1964), 71–124, (In Russian.) MR0163184 0124.07103 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Waiting time distribution for the M∕M∕m queueIEE Proceedings - Communications, Vol. 150, No. 3 | 1 Jan 2003 Cross Ref Heavy Traffic Limit Theorems for Queues: A SurveyMathematical Methods in Queueing Theory | 1 Jan 1974 Cross Ref Multiple channel queues in heavy traffic. IAdvances in Applied Probability, Vol. 2, No. 01 | 1 July 2016 Cross Ref Multiple channel queues in heavy traffic. IAdvances in Applied Probability, Vol. 2, No. 1 | 1 July 2016 Cross Ref Transient behavior of multi-server queues with recurrent input and exponential service timesJournal of Applied Probability, Vol. 5, No. 01 | 14 July 2016 Cross Ref Transient behavior of multi-server queues with recurrent input and exponential service timesJournal of Applied Probability, Vol. 5, No. 1 | 14 July 2016 Cross Ref Boundary Problems for Sums of Lattice Random Variables, Defined on a Finite Regular Markov ChainE. L. PresmanTheory of Probability & Its Applications, Vol. 12, No. 2 | 17 July 2006AbstractPDF (702 KB) Volume 10, Issue 1| 1965Theory of Probability & Its Applications1-192 History Submitted:22 September 1964Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110006Article page range:pp. 63-73ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics