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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 4, Pages 623–653 (Mi tvp5227)  
This article is cited in 4 scientific papers (total in 4 papers)

Stability conditions for queueing systems with regenerative flow of interruptions

L. G. Afanas'eva, A. W. Tkachenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input flow, and a regenerative process of interruptions. Two service disciplines are studied: preemptive-repeat-different service discipline and preemptive resume service discipline. We consider discrete as well as continuous-time cases. We introduce an auxiliary service flow, which does not depend on the input flow, and construct the common points of regeneration for these two flows. Using such a synchronization method, we establish necessary and sufficient conditions for stability of the system under some additional assumptions. Additionally, under weaker assumptions, we also find the conditions needed for the queue length process to be stochastically bounded.

Keywords: multichannel queueing system, stability, interruption, priority, regeneration, synchronization.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00468
This work was supported by the Russian Foundation for Basic Research (grant 17-01-00468).


DOI: https://doi.org/10.4213/tvp5227

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English version:
Theory of Probability and its Applications, 2019, 63:4, 507–531

Bibliographic databases:

Received: 13.06.2018
Accepted:21.06.2018

Citation: L. G. Afanas'eva, A. W. Tkachenko, “Stability conditions for queueing systems with regenerative flow of interruptions”, Teor. Veroyatnost. i Primenen., 63:4 (2018), 623–653; Theory Probab. Appl., 63:4 (2019), 507–531

Citation in format AMSBIB
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\paper Stability conditions for queueing systems with regenerative flow of interruptions
\jour Teor. Veroyatnost. i Primenen.
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\pages 623--653
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\pages 507--531
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Grishunina, “Multiserver queueing system with constant service time and simultaneous service of a customer by random number of servers”, Theory Probab. Appl., 64:3 (2019), 456–460  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. L. A. Meikhanadzhyan, R. V. Razumchik, “Sistema massovogo obsluzhivaniya $\mathrm{Geo}/G/1/\infty$ s inversionnym poryadkom obsluzhivaniya i resamplingom v diskretnom vremeni”, Inform. i ee primen., 13:4 (2019), 60–67  mathnet  crossref
    3. L. G. Afanaseva, S. A. Grishunina, “Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers”, Queueing Syst., 94:3-4, SI (2020), 213–241  crossref  mathscinet  zmath  isi
    4. G. A. Afanasev, “Sistema $\mathrm{M}|\mathrm{G}|1$ s pereryvami v rabote pribora i ikh zaderzhkami”, Teoriya veroyatn. i ee primen., 66:1 (2021), 3–19  mathnet  crossref
    		• Теория вероятностей и ее применения Theory of Probability and its Applications
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