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Regenerative Analysis and Approximation of Queueing Systems with Superposed Input Processes

Author

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  • Irina Peshkova

    (Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenin str. 33, 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, Lomonosov Moscow State University, GSP-1, Leninskie Gory, 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

A single-server queueing system with n classes of customers, stationary superposed input processes, and general class-dependent service times is considered. An exponential splitting is proposed to construct classical regeneration in this (originally non-regenerative) system, provided that the component processes have heavy-tailed interarrival times. In particular, we focus on input processes with Pareto interarrival times. Moreover, an approximating G I / G / 1 -type system is considered, in which the independent identically distributed interarrival times follow the stationary Palm distribution corresponding to the stationary superposed input process. Finally, Monte Carlo and regenerative simulation techniques are applied to estimate and compare the stationary waiting time of a customer in the original and in the approximating systems, as well as to derive additional information on the regeneration cycles’ structure.

Suggested Citation

  • Irina Peshkova & Evsey Morozov & Michele Pagano, 2024. "Regenerative Analysis and Approximation of Queueing Systems with Superposed Input Processes," Mathematics, MDPI, vol. 12(14), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2202-:d:1434504
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    References listed on IDEAS

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    4. Whitt, Ward, 1985. "Queues with superposition arrival processes in heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 81-91, December.
    5. G. F. Newell, 1984. "Approximations for Superposition Arrival Processes in Queues," Management Science, INFORMS, vol. 30(5), pages 623-632, May.
    6. Karl Sigman, 1990. "One-Dependent Regenerative Processes and Queues in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 175-189, February.
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