The effect of information on the strategic behavior in a Markovian queue with catastrophes and working vacations

Abstract

A stochastic clearing system is studied from a game-theoretic perspective in the paper where the server is subject to a Poisson-generated catastrophe and a follow-up repair process. Whenever a fatal shock (catastrophe) occurs, all customers are cleared from the system and the server fails. A repair is rendered immediately to fix the server with an exponential repair time. During the repair process, no customers are allowed to enter the system. Customers are strategic and they have the right to decide whether to join the system or balk based on a linear reward-cost structure with two types of rewards: A service reward for those customers that receive service and a compensation for those customers that are forced to abandon the system due to a catastrophe. During the service process, the server takes a working vacation after serving all the customers in the system. Our study is the first attempt to provide models to jointly characterize and analyse the queueing system with working vacation and catastrophes, with an emphasis on game-theoretic modeling of such a service system. The customer’s equilibrium strategy and social benefit of the system under four different information scenarios are obtained. In particular, we find that customers obey the follow-the-crowd (FTC) property in almost observable condition, which provides managerial insight on the operations management perspective. Numerical experiments are presented to show the effects of system parameters and information levels on the equilibrium joining behavior of customers.

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