Analysis of the equilibrium strategies in the GeoGeo1 queue with multiple working vacations

Abstract

In this paper, we deal with the customers’ equilibrium strategies in a Geo / Geo / 1 queuing system with multiple working vacations. The arriving customers decide whether to join or balk the queuing system depended on the information of the server’s states and the queue length. Based on the reward-cost structure, we obtain the equilibrium balking strategies and socially optimal strategies in three cases of the fully observable queue, the partially observable queue and the unobservable queue. In addition, we provide some numerical experiments to illustrate the influence of the information level on the equilibrium behavior and to compare the customers’ equilibrium and socially optimal strategies.

Keywords:

• Geo Geo1 queue
• multiple working vacations
• equilibrium balking strategies
• socially optimal strategies

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is partially supported by the National Natural Science Foundation of China [grant number 11201489], [grant number 11271373], [grant number 11371374], the project of Mathematics and Interdisciplinary Science and Innovation-Driven of Central South University and the Yu Ying project of Central South University. Helpful comments by two anonymous referees are gratefully acknowledged.