Analysis of Equilibrium Strategies in Markovian Queues with Negative Customers and Working Breakdowns

Abstract

We consider the customers' strategic behavior in Markovian queues with negative customers and working breakdowns. when a negative customer arrives, the customer being served is forced to leave the system. At the same time, the server breaks down and the service rate decreases. Arriving customers decide whether to enter the system or balk based on a natural reward-cost structure and the information of the system. By using the probability generating functions, we analyze the steady-state distribution and obtain the mean sojourn time of the arriving customers. We investigate the customers' behavior under different information levels of the system and derive equilibrium strategy for the customers in the fully observable, almost observable, almost unobservable and fully unobservable cases. Finally, some numerical results are provided to illustrate the effect of the system parameters on equilibrium strategies of the observable case and customers' sojourn time for unobservable cases.