On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals

Alexandra Borodina () and Vladimir Mazalov
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Alexandra Borodina: Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
Vladimir Mazalov: Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia

Mathematics, 2023, vol. 11, issue 16, 1-15

Abstract: This paper considers a callback single-server system with an orbit and a First-Come First-Served (FCFS) service discipline. Customers (users, clients) that encounter a busy server are sent into orbit and then have the option to retry service after an exponential period of time. In addition, each customer entering the system uses a strategy and must independently decide when to arrive in the system within a fixed admission period of time so that the expected sojourn time is minimal. We interpret the arrival process as a Nash equilibrium solution of a noncooperative game when the arrival intensity is completely described by an unknown distribution function, and then we propose a way to find an equilibrium for the case when the client’s waiting time for service is obviously limited. The analytical solution for the equilibrium is illustrated numerically for two-person and three-person games.

Keywords: callback one-server queuing system; orbit; retrials; strategic behavior; equilibrium arrivals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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