Bounds and Maxima for the Workload in a Multiclass Orbit Queue

Evsey V. Morozov, Irina V. Peshkova () and Alexander S. Rumyantsev
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Evsey V. Morozov: Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
Irina V. Peshkova: Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
Alexander S. Rumyantsev: Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia

Mathematics, 2023, vol. 11, issue 3, 1-15

Abstract: In this research, a single-server M -class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical M / G / 1 systems where the service time has M -component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes.

Keywords: finite mixture distribution; retrial system; extremal index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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