Regenerative Analysis and Approximation of Queueing Systems with Superposed Input Processes

Irina Peshkova, Evsey Morozov and Michele Pagano ()
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Irina Peshkova: Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenin str. 33, 185910 Petrozavodsk, Russia
Evsey Morozov: Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenin str. 33, 185910 Petrozavodsk, Russia
Michele Pagano: Department of Information Engineering, University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy

Mathematics, 2024, vol. 12, issue 14, 1-22

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.

Keywords: superposition of arrival streams; regeneration; splitting; finite mixture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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