Strategic joining in an M/M/K queue with asynchronous and synchronous multiple vacations

We study customers’ equilibrium joining strategies in an M/M/K queue with asynchronous and synchronous multiple vacations. Arriving customers face four different information levels, that is, fully observable, almost observable, almost unobservable and fully unobservable cases, and they decide whether to join or balk the system based on their service utility. In this study, we analyse customers’ equilibrium strategies in terms of the social welfare. It is found that the equilibrium social welfare under an asynchronous vacation policy is higher than that under a synchronous vacation policy when the traffic density is low, the opposite relation exists when the traffic density is high. Furthermore, when the traffic density is high enough, the difference between the two vacation policies in terms of social welfare can be negligible. Finally, if all customers follow the equilibrium strategies, compared to the situation with no information provided for customers, the social planner would prefer to reveal the queue length. Such a finding has the managerial implication for waiting line managers who want to maximise the social welfare of customers.