Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates

Dmitry Efrosinin, Natalia Stepanova and Janos Sztrik ()
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Dmitry Efrosinin: Institute for Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria
Natalia Stepanova: Scientific and Production Company “INSET”, Moscow 129085, Russia
Janos Sztrik: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2023, vol. 11, issue 18, 1-14

Abstract: We study the robustness of the c μ -rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FIFO retrial discipline, when the customers at the heads of queues repeatedly try to occupy the server at a random time. It is proved that for scheduling problems in the system without arrivals, the c μ -rule minimizes the total average cost. For the system with arrivals, it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes the service for certain values of system parameters exclusively for the class- i customers if both of the queues are not empty, with the aim to minimize the average cost per unit of time. It is also shown that in a finite buffer case, the c μ -rule fails.

Keywords: queueing system; c?-rule; scheduling problem; static policy; average cost (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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