The effect of information on the strategic behavior in a Markovian queue with catastrophes and working vacations

ABSTRACT

A stochastic clearing system is studied from a game-theoretic perspective in the paper where the server is subject to a Poisson-generated catastrophe and a follow-up repair process. Whenever a fatal shock (catastrophe) occurs, all customers are cleared from the system and the server fails. A repair is rendered immediately to fix the server with an exponential repair time. During the repair process, no customers are allowed to enter the system. Customers are strategic and they have the right to decide whether to join the system or balk based on a linear reward-cost structure with two types of rewards: A service reward for those customers that receive service and a compensation for those customers that are forced to abandon the system due to a catastrophe. During the service process, the server takes a working vacation after serving all the customers in the system. Our study is the first attempt to provide models to jointly characterize and analyse the queueing system with working vacation and catastrophes, with an emphasis on game-theoretic modeling of such a service system. The customer’s equilibrium strategy and social benefit of the system under four different information scenarios are obtained. In particular, we find that customers obey the follow-the-crowd (FTC) property in almost observable condition, which provides managerial insight on the operations management perspective. Numerical experiments are presented to show the effects of system parameters and information levels on the equilibrium joining behavior of customers.

KEYWORDS:

• Queueing-game
• catastrophe
• working vacation
• Nash equilibrium
• information disclosure

Acknowledgements

The authors would like to sincerely thank the Editor-in-Chief, Associate Editor and three anonymous referees for their valuable comments and suggestions which greatly improved the presentation and the quality of this paper.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under grant no. 71871008 and the Emerging Interdisciplinary Project of CUFE (21XXJC010).

Notes on contributors

Yilin Wang

Yilin Wang holds the BS degree in Mathematics from Chongqing University, China. Currently he is a Ph.D. candidate in the School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China. His research interests include queueing economics and platform economics.

Jinting Wang

Jinting Wang is a Distinguished Professor in the School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China. His research interests focus on stochastic operations research and management science, including queueing theory, reliability, inventory control and the applications of game theory and queueing theory in operations management, service science, and wireless communication & networking. He has published over 110 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.

George Zhang

George Zhang is a professor in the Department of Decision Sciences at Western Washington University. He received the B.Sc. degree in computer science and the M.A. degree in economics from Nankai University, the M.B.A. degree from the Schulich School of Business, York University, and the Ph.D. degree in operations research from the University of Waterloo. His research interests include queueing theory and applications, stochastic dynamic programming, probability models in reliability, and supply chain management issues in manufacturing and service organization. His studies include both theoretical work and a wide range of applications in business, engineering, economics, and applied mathematics. The main theme of his research is to bridge the gap between theory and application, obtaining unobservable and sometimes counter-intuitive but significant/practical management insights via modelling and quantitative analysis. He is one of Editor-in-Chiefs of Journal of the Operational Research Society (JORS). As one of the premier Operation Research (OR) journals, JORS is the first OR journal in the world. He is also one of the founding Editors-in-Chief of Queueing Models and Service Management. He was an Associate Editor of Information Systems and Operational Research (INFOR). He is on the editorial board of several international journals.