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Limit Theorems for Queueing Networks. I

1987; Society for Industrial and Applied Mathematics; Volume: 31; Issue: 3 Linguagem: Inglês

10.1137/1131056

1095-7219

А. А. Боровков,

Probability and Risk Models

Previous article Next article Limit Theorems for Queueing Networks. IA. A. BorovkovA. A. Borovkovhttps://doi.org/10.1137/1131056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] James R. Jackson, Networks of waiting lines, Operations Res., 5 (1957), 518–521 19,1203c CrossrefGoogle Scholar[2] J. R. Jackson, Job shop-like queueing systems, Management Sci., 10 (1963), 131–142 CrossrefGoogle Scholar[3] W. J. Gordon and , J. F. Newell, Closed queueing systems with exponential servers, Oper. Res., 15 (1967), 254–265 CrossrefGoogle Scholar[4] Forest Basket, , M. Chandy, , R. Muntz and , J. Palacios, Open, closed, and mixed networks of queues with different classes of customers, J. Assoc. Comput. Mach., 22 (1975), 248–260 51:2001 0313.68055 CrossrefGoogle Scholar[5] Frank P. Kelly, Reversibility and stochastic networks, John Wiley & Sons Ltd., Chichester, 1979viii+230 81j:60105 0422.60001 Google Scholar[6] L. 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Nummelin, Uniform and Ratio Limit Theorems for Markov Renewal and Semi-regenerative Processes on a General State Space, Report, HTKK-MAT-A98, Inst. Math., Helsinki Univ. Tech., Espoo, 1977 Google Scholar[21] Kai Lai Chung, Markov chains with stationary transition probabilities, Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 104, Springer-Verlag New York, Inc., New York, 1967xi+301, Heidelberg–Berlin 36:961 0146.38401 Google Scholar[22] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 15,445b 0053.26802 Google Scholar[23] Ralph L. Disney and , Dieter König, Queueing networks: a survey of their random processes, SIAM Rev., 27 (1985), 335–403 10.1137/1027109 86j:60205 0581.60075 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On Little's Formula in Multiphase Queues16 September 2021 | Mathematics, Vol. 9, No. 18 Cross Ref On the law of iterated logarithm for extreme queue length in an open queueing network6 September 2021 | International Journal of Computer Mathematics: Computer Systems Theory, Vol. 6, No. 3 Cross Ref Heavy-traffic limits for stationary network flows7 January 2020 | Queueing Systems, Vol. 95, No. 1-2 Cross Ref A Review of Decomposition Methods for Open Queueing Networks Cross Ref Stability of queueing networksProbability Surveys, Vol. 5, No. none Cross Ref Convergence rates in monotone separable stochastic networksQueueing Systems, Vol. 52, No. 2 Cross Ref Taking Account of Correlations Between Streams in Queueing Network ApproximationsQueueing Systems, 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independence of states of units in an open stationary Markov queueing network with one class of customers17 July 2006 | Theory of Probability & Its Applications, Vol. 35, No. 4AbstractPDF (649 KB)Some Methods of Investigating Regeneration Times in Queueing Networks17 July 2006 | Theory of Probability & Its Applications, Vol. 35, No. 2AbstractPDF (483 KB)Asymptotically exact decomposition approximations for open queueing networksOperations Research Letters, Vol. 9, No. 6 Cross Ref The stability of open queueing networksStochastic Processes and their Applications, Vol. 35, No. 1 Cross Ref On the ergodicity of networks of ·/GI/1/N queues1 July 2016 | Advances in Applied Probability, Vol. 22, No. 01 Cross Ref On the ergodicity of networks of ·/ GI /1/ N queues1 July 2016 | Advances in Applied Probability, Vol. 22, No. 1 Cross Ref Notes on the stability of closed queueing networks14 July 2016 | Journal of Applied Probability, Vol. 26, No. 3 Cross Ref On the Ergodicity of an Open Queueing Network17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 4AbstractPDF (613 KB)Stability of generalized Jackson networks with permanent customers Cross Ref Ergodicity of networks with blocking Cross Ref A survey of Markovian methods for stability of networks Cross Ref Volume 31, Issue 3| 1987Theory of Probability & Its Applications History Submitted:26 February 1986Published online:28 July 2006 InformationCopyright © 1987 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131056Article page range:pp. 413-427ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics