Equilibrium balking strategies in the single-server retrial queue with constant retrial rate and catastrophes

ABSTRACT

We study an M/M/1 retrial queueing system with constant retrial rate and Poisson generated catastrophes. When a catastrophe arrives to the system that the server is working, it deletes all customers in system and breaks the server down. The failed server is repaired immediately and the repair time is exponentially distributed. We investigate a joining/balking dilemma of customers with a natural reward-cost structure under two information levels, i.e. the unobservable case where customers can only observe server’s state, and the observable case where customers know both the queue length in orbit and the status of the server. Individual equilibrium joining probabilities and socially optimal strategies are obtained in these two cases. Finally, numerical experiments are carried out to illustrate our theoretic findings and the impact of information levels on social welfare. Interestingly, by comparing the corresponding results in the standard system without catastrophes, we find that customers in our system incur a lower waiting cost, which results in the fact that customers will receive more benefit and they are more inclined to join the system with catastrophes.

KEYWORDS:

• Strategic queueing
• constant retrials
• equilibrium strategies
• catastrophes quality of experience (QoE)

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was in part supported by the National Natural Science Foundation of China [71871008]; National Natural Science Foundation of China [71571014]; the Fundamental Research Funds for the Central Universities [2017YJS206]. This work was in part supported by the National Natural Science Foundation of China [71871008]; National Natural Science Foundation of China [71571014]; the Fundamental Research Funds for the Central Universities [2017YJS206].

Notes on contributors

Kaili Li

Kaili Li received the B.Sc. Degree from Beijing Jiaotong University, Beijing, China, in 2015, and now is a Ph.D. candidate in Beijing Jiaotong University, Beijing, China. She is a member of the Operations Research Society of China (ORSC). Her research interests include queueing game  theory, the applications of game theory and queueing theory in operations management. She has published several papers in the proceedings of international conferences and international professional journals such as RAIRO-OR, etc.

Jinting Wang

Jinting Wang is currently a professor and  the associate dean in the School of Management Science and Engineering, at the Central University of Finance and Economics, Beijing, China. He received the B.Sc. degree from Hebei Normal College, Shijiazhuang, China, in 1994, the M.Sc. degree from Hebei University of Technology, Tianjin, China, in 1997, and the Ph.D. degree from the Chinese Academy of Sciences, Beijing, China, in 2000. His research interests include issues related to Operations Research and Management Science, especially in the area of queueing theory, inventory management, reliability and the applications of game theory in these areas. He has published over 100 papers in international journals such as Operations Research, Production and 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 an Editor for several professional journals such as International Journal of Operations Research, International Journal of Smart Grid and Green Communications and other two Chinese journals.