Séminaire Mathématique de Béjaia
Volume 16, Numéro 1, Pages 96-96
2018-12-31
Monopoly Pricing In An M/m/1 Queue With Breakdowns And Repairs
Authors : Meziani Kamel . Rahmoune-aoudia Fazia . Radjef Mohammed Said .
Abstract
In this work, we study the service pricing and the customers strategic behavior in a totally unobservable M/M/1 queue with server breakdowns and repairs, under a rewardcost structure. We model the system using the two-stage dynamic game theory tools, in order to analyze the decision process and determine the equilibrium strategies for the server and the customers, according to their objectives. At the first stage of the game, the server imposes a service price in order to maximize its revenue. Then, at the second stage, a customer arriving at the system must make a decision to join the system or to choose an outside opportunity, knowing the service price imposed by the server and the information on the system state. Thus, we show that the constructed game admits Nash equilibrium and we provide the server equilibrium strategies and those of customers. Finally, we illustrate, by numerical examples, the effect of the system parameters on the customer's entrance probability, the equilibrium service price and the revenue of the server.
Keywords
Strategic customers; Pricing; M/M/1 Queue with server breakdowns and repairs; Two-stage dynamic game; Nash Equilibrium.
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