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Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 2, Pages 210–234 (Mi tvp4504)  

This article is cited in 10 scientific papers (total in 10 papers)

Multichannel queueing systems with regenerative input flow

L. G. Afanasyevaa, A. V. Tkachenkob

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b National Research University "Higher School of Economics"

Abstract: We consider the multichannel queueing system with nonidentical servers and regenerative input flow. The necessary and sufficient condition for ergodicity is established, and functional limit theorems for high and ultra-high load are proved. As a corollary, the ergodicity condition for queues with unreliable servers is obtained. Suggested approaches are used to prove the ergodic theorem for systems with limitations. We also consider the hierarchical networks of queueing systems.

Keywords: multichannel queueing system; regenerative flow; ergodicity; stochastic boundedness.

DOI: https://doi.org/10.4213/tvp4504

Full text: PDF file (251 kB)
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English version:
Theory of Probability and its Applications, 2014, 58:2, 174–192

Bibliographic databases:

MSC: 60
Received: 15.11.2012

Citation: L. G. Afanasyeva, A. V. Tkachenko, “Multichannel queueing systems with regenerative input flow”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 210–234; Theory Probab. Appl., 58:2 (2014), 174–192

Citation in format AMSBIB
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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. A. V. Tkachenko, “Multichannel queueing system in a random environment”, Moscow University Mathematics Bulletin, 69:1 (2014), 37–40  mathnet  crossref
    2. S. Zh. Aibatov, “Ergodic Theorem for a Queue with Unreliable Server”, Math. Notes, 97:6 (2015), 821–830  mathnet  crossref  crossref  mathscinet  isi  elib
    3. L. G. Afanasyeva, S. A. Grishunina, “Queueing systems with different service disciplines”, Lobachevskii J. Math., 38:5, SI (2017), 864–869  crossref  mathscinet  zmath  isi
    4. L. G. Afanas'eva, A. W. Tkachenko, “Stability conditions for queueing systems with regenerative flow of interruptions”, Theory Probab. Appl., 63:4 (2019), 507–531  mathnet  crossref  crossref  isi  elib
    5. L. G. Afanaseva, “Usloviya stabilnosti sistemy s povtornymi vyzovami pri regeneriruyuschem vkhodyaschem potoke”, Fundament. i prikl. matem., 22:3 (2018), 5–18  mathnet
    6. 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
    7. Afanaseva L.G., Tkachenko A., “Stability of Multichannel Queueing Systems With Interruptions and Regenerative Input Flow”, Markov Process. Relat. Fields, 25:4, SI (2019), 723–744  mathscinet  zmath  isi
    8. Afanasyeva L.G., “Asymptotic Analysis of Queueing Models Based on Synchronization Method”, Methodol. Comput. Appl. Probab., 22:4, SI (2020), 1417–1438  crossref  mathscinet  zmath  isi
    9. Afanaseva L., Bashtova E., Grishunina S., “Stability Analysis of a Multi-Server Model With Simultaneous Service and a Regenerative Input Flow”, Methodol. Comput. Appl. Probab., 22:4, SI (2020), 1439–1455  crossref  mathscinet  zmath  isi
    10. Afanaseva L.G. Grishunina S.A., “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
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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