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Maximum Remaining Service Time in Infinite-Server Queues

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Abstract

We study the maximum remaining service time in infinite-server queues of type M|G|∞ (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 MX|G|∞, including those with dependent service times within a batch.

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Authors and Affiliations

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

    A. V. Lebedev

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  1. A. V. Lebedev
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Correspondence to A. V. Lebedev.

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Original Russian Text © A.V. Lebedev, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 2, pp. 86–102.

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Lebedev, A.V. Maximum Remaining Service Time in Infinite-Server Queues. Probl Inf Transm 54, 176–190 (2018). https://doi.org/10.1134/S0032946018020060

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  • DOI: https://doi.org/10.1134/S0032946018020060

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