Equilibrium Balking Strategies in the Geo/Geo/1 Queues with Server Breakdowns and Repairs

Abstract

HeThis paper studies the equilibrium behavior of customers in the Geo/Geo/1 queue with server breakdowns and repairs. The reliability factor is introduced into the economic analysis and customers’ behavior analysis of the discrete-time queues. The server is subject to breakdowns and repairs when providing service to customers. Upon arrival, the customers decide for themselves whether to enter the system or balk based on a natural reward-cost structure and available information on hand. The behavior of customers is investigated with various levels of information regarding three states of server and the system queue length. By deriving and solving a set of system difference equations, we obtain the stationary distribution of the system and the mean sojourn time of an arriving customer. Equilibrium strategies for the customers under different levels of information are derived and the behaviors of the customers under these strategies are investigated. Finally we illustrate the effect of several parameters on the equilibrium behavior via numerical experiments.

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