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Probl. Peredachi Inf., 2018, Volume 54, Issue 2, Pages 86–102 (Mi ppi2268)  

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

Communication Network Theory

Maximum remaining service time in infinite-server queues

A. V. Lebedev

Department of Probability Theory, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We study the maximum remaining service time in infinite-server queues of type $M|G|\infty$ (at a given time and in a stationary regime). The following cases for the arrival flow rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a random process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In the case of a constant rate, we study effects that arise when the average service time is infinite (for power-law distribution tails). We find the extremal index of the sequence of maximum remaining service times. The results are extended to queues of type $M^X|G|\infty$, including those with dependent service times within a batch.

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English version:
Problems of Information Transmission, 2018, 54:2, 176–190

Bibliographic databases:

UDC: 621.391.1+519.21
Received: 13.04.2017
Revised: 21.07.2017

Citation: A. V. Lebedev, “Maximum remaining service time in infinite-server queues”, Probl. Peredachi Inf., 54:2 (2018), 86–102; Problems Inform. Transmission, 54:2 (2018), 176–190

Citation in format AMSBIB
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\paper Maximum remaining service time in infinite-server queues
\jour Probl. Peredachi Inf.
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\issue 2
\pages 86--102
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\transl
\jour Problems Inform. Transmission
\yr 2018
\vol 54
\issue 2
\pages 176--190
\crossref{https://doi.org/10.1134/S0032946018020060}
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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. Lebedev, “Upper bound for the expected minimum of dependent random variables with known Kendall's tau”, Theory Probab. Appl., 64:3 (2019), 465–473  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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