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.

KEYWORDS:

• M/M/1 queue
• negative customers
• single vacation
• Nash equilibrium
• threshold strategies

Acknowledgments

The authors sincerely thank the Editor-in-Chief and two anonymous referees for providing many constructive comments, which have greatly improved the quality of our paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [71871008]; National Natural Science Foundation of China [71571014]; The Emerging Interdisciplinary Project of Central University of Finance and Economics (CUFE) [grant no. 21XXJC010] .

Notes on contributors

Ke Sun

Dr. Ke Sun is an assistant professor at the School of Economics and Management, Beijing University of Chemical Technology, Beijing, China. Her research interests include queueing theory, stochastic modeling, applied probability and their applications in operations management.

Jinting Wang

Dr. Jinting Wang is a Distinguished Professor and Vice Dean at the School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China. His research interests include issues related to Operations Research/Management Science, especially on queueing theory, reliability theory, inventory control and the applications of game theory and queueing theory in operations management, service science, and wireless communication and networking. He has published over 100 papers in international journals such as Operations Research, Production and Operations Management, Manufacturing & Service Operations Management, IEEE Transactions on Vehicular Technology, IEEE Transactions on Cognitive Communications and Networking, Queueing Systems, European Journal of Operational Research, Journal of Multivariate Analysis, etc. He is a member of the Operations Research Society of China (ORSC), and now he serves as the President of Reliability Society affiliated with ORSC. He was the recipient of the Outstanding Research Award for Young Researchers from ORSC in 2004. In 2011, he was honored with the Program for New Century Excellent Talents in University by the Ministry of Education of China. Dr. Wang is currently serving as Editor for several professional journals such as International Journal of Operations Research, International Journal of Smart Grid and Green Communications and other Chinese journals.