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Probl. Peredachi Inf., 2020, Volume 56, Issue 1, Pages 80–98 (Mi ppi2313)  

This article is cited in 1 scientific paper (total in 1 paper)

Communication Network Theory

Bivariate distributions of maximum remaining service times in fork-join infinite-server queues

A. V. Gorbunovaa, A. V. Lebedevb

a Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
b Department of Probability Theory, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We study the maximum remaining service time in $M^{(2)}|G_2|\infty$ fork -join queueing systems where an incoming task forks on arrival for service into two subtasks, each of them being served in one of two infinite-sever subsystems. The following cases for the arrival rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a stochastic process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In a number of cases we find copula functions and the Blomqvist coefficient. We prove asymptotic independence of maximum remaining service times under high load conditions.

Keywords: infinite-server queue, fork-join queue, maximum remaining service time, copula, Blomqvist's coefficient, distributed computing, cloud technologies.

DOI: https://doi.org/10.31857/S0555292320010076

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English version:
Problems of Information Transmission, 2020, 56:1, 73–90

Bibliographic databases:

UDC: 621.391.1 : 519.21, 519.872
Received: 15.11.2019
Revised: 15.01.2020
Accepted:28.01.2020

Citation: A. V. Gorbunova, A. V. Lebedev, “Bivariate distributions of maximum remaining service times in fork-join infinite-server queues”, Probl. Peredachi Inf., 56:1 (2020), 80–98; Problems Inform. Transmission, 56:1 (2020), 73–90

Citation in format AMSBIB
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\paper Bivariate distributions of maximum remaining service times in fork-join infinite-server queues
\jour Probl. Peredachi Inf.
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\vol 56
\issue 1
\pages 80--98
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\crossref{https://doi.org/10.31857/S0555292320010076}
\elib{https://elibrary.ru/item.asp?id=43270103}
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\jour Problems Inform. Transmission
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\vol 56
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\pages 73--90
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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. Gorbunova, A. V. Lebedev, “Effekty stokhasticheskoi netranzitivnosti v sistemakh massovogo obsluzhivaniya”, UBS, 85 (2020), 23–50  mathnet  crossref
  • Проблемы передачи информации Problems of Information Transmission
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