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Teoriya Veroyatnostei i ee Primeneniya, 2018, Volume 63, Issue 4, Pages 623–653
DOI: https://doi.org/10.4213/tvp5227 (Mi tvp5227) 		 
This article is cited in 4 scientific papers (total in 5 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
Full-text PDF (588 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp5227
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).
Received: 13.06.2018
Accepted: 21.06.2018
English version:
Theory of Probability and its Applications, 2019, Volume 63, Issue 4, Pages 507–531
DOI: https://doi.org/10.1137/S0040585X97T989349
Bibliographic databases:
Document Type: Article
Language: Russian
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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  • https://doi.org/10.4213/tvp5227
  • https://www.mathnet.ru/eng/tvp/v63/i4/p623
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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