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Splitting-Based Regenerations for Accelerated Simulation of Queues

Author

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  • Irina Peshkova

    (Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenin Str. 33, 185910 Petrozavodsk, Russia
    Institute of Applied Mathematical Research, Karelian Research Centre of Russian Academy of Sciences, Pushkinskaja Str. 11, 185910 Petrozavodsk, Russia
    These authors contributed equally to this work.)

  • Evsey Morozov

    (Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenin Str. 33, 185910 Petrozavodsk, Russia
    Institute of Applied Mathematical Research, Karelian Research Centre of Russian Academy of Sciences, Pushkinskaja Str. 11, 185910 Petrozavodsk, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia
    These authors contributed equally to this work.)

  • Michele Pagano

    (Department of Information Engineering, University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, we address the problem of increasing the number of regenerations in the simulation of the workload process in a single-server queueing system. To this end, we extend the splitting technique developed for the Markov workload process in the M/M/1 queue to the more general GI/M/1 queueing systems. This approach is based on a minorization condition for the transition kernel of the workload process, which is a Markov chain defined by the Lindley recursion. The proposed method increases the number of regenerations during the simulation and potentially reduces the time required to estimate stationary performance metrics with a given level of precision.

Suggested Citation

  • Irina Peshkova & Evsey Morozov & Michele Pagano, 2025. "Splitting-Based Regenerations for Accelerated Simulation of Queues," Mathematics, MDPI, vol. 13(17), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2883-:d:1743607
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