Splitting-Based Regenerations for Accelerated Simulation of Queues

Peshkova, Irina; Morozov, Evsey; Pagano, Michele

doi:10.3390/math13172883

Open AccessArticle

Splitting-Based Regenerations for Accelerated Simulation of Queues

by

Irina Peshkova

^1,2,†

,

Evsey Morozov

^1,2,3,†

and

Michele Pagano

^4,*,†

¹

Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenin Str. 33, 185910 Petrozavodsk, Russia

²

Institute of Applied Mathematical Research, Karelian Research Centre of Russian Academy of Sciences, Pushkinskaja Str. 11, 185910 Petrozavodsk, Russia

³

Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia

⁴

Department of Information Engineering, University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2025, 13(17), 2883; https://doi.org/10.3390/math13172883

Submission received: 13 August 2025 / Revised: 1 September 2025 / Accepted: 3 September 2025 / Published: 6 September 2025

(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)

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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.

Keywords: queueing system; artificial regeneration; splitting

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MDPI and ACS Style

Peshkova, I.; Morozov, E.; Pagano, M. Splitting-Based Regenerations for Accelerated Simulation of Queues. Mathematics 2025, 13, 2883. https://doi.org/10.3390/math13172883

AMA Style

Peshkova I, Morozov E, Pagano M. Splitting-Based Regenerations for Accelerated Simulation of Queues. Mathematics. 2025; 13(17):2883. https://doi.org/10.3390/math13172883

Chicago/Turabian Style

Peshkova, Irina, Evsey Morozov, and Michele Pagano. 2025. "Splitting-Based Regenerations for Accelerated Simulation of Queues" Mathematics 13, no. 17: 2883. https://doi.org/10.3390/math13172883

APA Style

Peshkova, I., Morozov, E., & Pagano, M. (2025). Splitting-Based Regenerations for Accelerated Simulation of Queues. Mathematics, 13(17), 2883. https://doi.org/10.3390/math13172883

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Splitting-Based Regenerations for Accelerated Simulation of Queues

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