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Asymptotic Analysis of Queueing Models Based on Synchronization Method

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Abstract

This paper is focused on the stability conditions for a multiserver queueing system with heterogeneous servers and a regenerative input flow X. The main idea is constructing an auxiliary service process Y which is also a regenerative flow and definition of the common points of regeneration for both processes X and Y. Then the traffic rate is defined in terms of the mean of the increments of these processes on a common regeneration period. It allows to use well-known results from the renewal theory to find the instability and stability conditions. The possibilities of the proposed approach are demonstrated by examples. We also present the applications to transport system capacity analysis.

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Acknowledgements

Work is partially supported by RFBR grant 17-01-00468.

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  1. Department of Probability Theory, Lomonosov Moscow State University, GSP-1, 1 Leninskiye Gory, Main Building, 119991, Moscow, Russia

    L. G. Afanasyeva

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  1. L. G. Afanasyeva
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Correspondence to L. G. Afanasyeva.

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Afanasyeva, L.G. Asymptotic Analysis of Queueing Models Based on Synchronization Method. Methodol Comput Appl Probab 22, 1417–1438 (2020). https://doi.org/10.1007/s11009-019-09694-9

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