Equilibrium and optimal balking strategies of customers in unobservable queues with double adaptive working vacations

Abstract

This paper studies the customers’ equilibrium and socially optimal balking behaviour in some single-server Markovian queues with double adaptive working vacations. Once the system becomes empty, the server takes a working vacation with a low service rate. If there are customer arrivals during this period, a regular busy period begins as soon as he finishes the vacation. Otherwise, he takes another working vacation with a much lower service rate than that in the first working vacation. After completing the second vacation, the server either stays idle or begins a busy period. We discuss two types of unobservable queues: the almost unobservable queues and the fully unobservable queues, respectively, and arriving customers can’t observe system occupancy in both cases. For each type of queues, we get both the customers’ equilibrium and socially optimal balking strategies and make numerical comparisons between them. We observe that their positive and stable equilibrium strategy and optimal strategy are unique, and especially, the customers’ actual arrival rates in equilibrium in vacation states are not necessarily smaller than that in busy state in the almost unobservable queues. Moreover, we also find that whether the system information should be revealed to customers depends on the potential demand arrivals.

Keywords:

• Unobservable queues
• double adaptive working vacations
• balking strategy
• social welfare

Acknowledgements

The authors would like to thank the anonymous reviewers for the useful comments and suggestions on this work, and the support from the National Natural Science Foundation of China (No.71101124, No.71301139), the Natural Science Foundation of Hebei Province (No.G2016203236), the Humanity and Social Science Foundation for Colleges of Hebei Province (No.BJ2016063), and the Program for Outstanding Young Scholars of Hebei Province.

Notes

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 [number 71101124], [number 71301139]; the Natural Science Foundation of Hebei Province [number G2016203236]; the Humanity and Social Science Foundation for Colleges of Hebei Province [number BJ2016063]; the Program for Outstanding Young Scholars of Hebei Province.