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This article is cited in 5 scientific papers (total in 5 papers)
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.
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
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https://www.mathnet.ru/eng/ppi2313 https://www.mathnet.ru/eng/ppi/v56/i1/p80
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Abstract page: | 209 | Full-text PDF : | 18 | References: | 19 | First page: | 8 |
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