Title: Service pricing and customer behaviour strategies of Stackelberg's equilibrium in an unobservable Markovian queue with unreliable server and delayed repairs

Authors: Kamel Meziani; Fazia Rahmoune; Mohammed Said Radjef

Addresses: Research Unit LaMOS (Modelling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia 06000, Algeria ' Research Unit LaMOS (Modelling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia 06000, Algeria ' Research Unit LaMOS (Modelling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, Bejaia 06000, Algeria

Abstract: In this paper, we model as a Stackelberg game with the service pricing of server and the strategic behaviour of customers in a totally unobservable M/M/1 queueing system subject to random breakdowns and delayed repairs, under a reward-cost structure. For this, we first use the partial generating functions to determine the steady-state condition and the sojourn time of a customer in the considered queueing system. The analytical forms of the service price and the customer entrance strategies of the Stackelberg equilibrium of the game are given. Through numerical examples, we illustrate the effect of the price and the reliability parameters on the entrance probability of customers and the server profit. Finally, we define and solve the corresponding social welfare problem. This study has not only a theoretical aspect, but also a practical one, and it can be adapted to several real-life situations.

Keywords: unreliable queue; delayed repairs; pricing; strategic behaviour; Stackelberg game; equilibrium.

DOI: 10.1504/IJMOR.2022.122216

International Journal of Mathematics in Operational Research, 2022 Vol.21 No.3, pp.281 - 304

Received: 30 Jul 2020
Accepted: 04 Jan 2021
Published online: 12 Apr 2022 *

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