Abstract:
Queueing systems of type G|G|∞ are analyzed by the author's method proposed in [2] and [3] for studying stability of systems of type G|G|1. General quantitative estimates for the continuity property of such systems are obtained. In a number of particular cases, these estimates can be expressed in an explicit form.
Citation:
V. M. Zolotarev, “Quantitative estimates for the continuity property of queueing systems of type G|G|∞”, Teor. Veroyatnost. i Primenen., 22:4 (1977), 700–711; Theory Probab. Appl., 22:4 (1978), 679–691
\Bibitem{Zol77}
\by V.~M.~Zolotarev
\paper Quantitative estimates for the continuity property of queueing systems of type $G|G|\infty$
\jour Teor. Veroyatnost. i Primenen.
\yr 1977
\vol 22
\issue 4
\pages 700--711
\mathnet{http://mi.mathnet.ru/tvp3621}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=652297}
\zmath{https://zbmath.org/?q=an:0403.60086}
\transl
\jour Theory Probab. Appl.
\yr 1978
\vol 22
\issue 4
\pages 679--691
\crossref{https://doi.org/10.1137/1122083}
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https://www.mathnet.ru/eng/tvp3621
https://www.mathnet.ru/eng/tvp/v22/i4/p700
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Zeifman A. Korolev V. Satin Ya., “Two Approaches to the Construction of Perturbation Bounds For Continuous-Time Markov Chains”, Mathematics, 8:2 (2020), 253
Evsey Morozov, Michele Pagano, Irina Peshkova, Alexander Rumyantsev, “Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution”, Mathematics, 8:8 (2020), 1277
A. I. Zeifman, V. Yu. Korolev, A. V. Korotysheva, S. Ya. Shorgin, “Obschie otsenki ustoichivosti dlya nestatsionarnykh markovskikh tsepei s nepreryvnym vremenem”, Inform. i ee primen., 8:1 (2014), 106–117
Vyacheslav M. Abramov, “Continuity theorems for the M/M/1/n queueing system”, Queueing Syst, 59:1 (2008), 63
S. T. Rachev, “The problem of stability in queueing theory”, Queueing Syst, 4:4 (1989), 287
Heinz W. Engl, Anton Wakolbinger, “Continuity properties of the extension of a locally Lipschitz continuous map to the space of probability measures”, Monatshefte f�r Mathematik, 100:2 (1985), 85
L. Seidl, “Quantitative estimates of the continuity of many-channel queueing systems”, Theory Probab. Appl., 26:4 (1982), 732–744
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