Equilibrium balking strategies in the single-server retrial queue with constant retrial rate and catastrophes

Abstract

ABSTRACT We study an M/M/1 retrial queueing system with constant retrial rate and Poisson generated catastrophes. When a catastrophe arrives to the system that the server is working, it deletes all customers in system and breaks the server down. The failed server is repaired immediately and the repair time is exponentially distributed. We investigate a joining/balking dilemma of customers with a natural reward-cost structure under two information levels, i.e. the unobservable case where customers can only observe server’s state, and the observable case where customers know both the queue length in orbit and the status of the server. Individual equilibrium joining probabilities and socially optimal strategies are obtained in these two cases. Finally, numerical experiments are carried out to illustrate our theoretic findings and the impact of information levels on social welfare. Interestingly, by comparing the corresponding results in the standard system without catastrophes, we find that customers in our system incur a lower waiting cost, which results in the fact that customers will receive more benefit and they are more inclined to join the system with catastrophes.