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

Abstract

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.

Keywords:

• M/M/K queue
• equilibrium strategies
• asynchronous vacations
• synchronous vacations
• social welfare

Acknowledgements

The authors would like to thank the Editor, an Associate Editor, and the anonymous referees for their valuable comments and suggestions which have improved the presentation and the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant nos. 71871008 and 71571014).