Game-theoretic analysis of the single vacation queue with negative customers

ABSTRACT We present a game-theoretic analysis of an M/M/1 queueing system with negative customers and single server vacation. Both positive and negative customers arrive according to a Poisson process and the server stars a vacation when the system is empty. Whenever a negative customer arrives, the positive customer being served (if any) is forced to abandon the system and the server suffers a breakdown, immediately after, a repair is required. During the repair process, positive customers are not allowed to join the system. Besides, they decide whether to join or to balk the system based on a reward-cost structure under four cases of different levels of information. We derive the equilibrium joining strategies of positive customers in each case. Specifically, we obtain the equilibrium threshold in the observable queue and mixed joining probability in the unobservable queue. Finally, the effects of different information levels and several parameters on the equilibrium threshold and mixed joining probabilities are illustrated by numerical examples.