Analysis of strategic customer behavior in observable M/G/ 1 queues with impatience

ABSTRACTIn this paper, we propose a queueing-game-theoretic model and analyze the strategic behavior of customers and social optimization in an observable M/G/1 queue, in which arriving customers decide whether to join the system or balk based on a new binary and random reward-cost structure. Each incoming customer to the queue has a relative tolerance time. If the customer’s service does not begin (or end) within his or her relative tolerance time, the customer will incur a cost for his or her waiting. We first derive closed-form solutions for customers’ equilibrium and socially optimal joining strategies using the technique of the Laplace-Stieltjes transform. Furthermore, some representative numerical experiments are performed to visualize the theoretical results. The numerical scenarios illustrate the influence of the relative tolerance time on equilibrium strategy and socially optimal strategy. Finally, we compare the effect of relative tolerance time on social welfare in observable and unobservable queues. The numerical results show that observable queues lead to higher social welfare. This study provides guidance for system providers in designing more economical and sustainable public service systems.KEYWORDS: Observable M/G/1 queueimpatienceequilibrium strategiessocial welfare AcknowledgementsThe authors would like to thank the editor and two reviewers for their constructive and insightful comments and suggestions, which significantly improved the presentation and quality of this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is partially supported by the National Natural Science Foundation of China (72201072, 12071487), Guangdong Provincial Philosophy and Social Science Planning Project (GD23XGL072), Scientific Research Fund of Zhejiang Provincial Education Department and Guangdong Basic and Applied Basic Research Foundation (2022B1515120060).Notes on contributorsJingchuan ZhangJingchuan Zhang is currently an assistant professor in Alibaba Business School, Hangzhou Normal University, Hangzhou, China. She received the Ph.D. degree in Mathematics from Central South University, Changsha, China, in 2022. She studied as a visiting Ph.D. candidate in McDonough School of Business, Georgetown University, Washington DC, the United States, from September 2019 to September 2020. Her main scientific interests include operations research, stochastic process, queueing theory, queueing games, and mathematical modeling. She has published several papers in international professional journals such as RAIRO-Operations Research, Operations Research Letters, Journal of Industrial & Management Optimization, etc.Zaiming LiuZaiming Liu is a professor in the School of Mathematics and Statistics, Central South University, Changsha, China. He received the Ph.D. degree in Mathematics from Central South University, Changsha, China, in 1988. He has published three books as a co-author and over 100 research papers in a variety of journals, such as Applied Mathematics Letters, Applied Mathematics and Computation, Applied Mathematical Modelling, Computers & Operations Research, Computers & Mathematics with Applications, Annals of Operations Research, and Journal of Mathematical Analysis and Applications. His main research interests focus on Markovian processes and their application, queueing theory, and stochastic models.Gang ChenGang Chen is an associate professor in the School of Management, Guangzhou University, Guangzhou, China. He worked as a postdoctoral in the School of Business, Sun Yat-Sen University during 2019–2022, He received the Master degree and the Ph.D. degree in Mathematics both from Central South University, Changsha, China, in 2016 and 2019, respectively. His current research interests focus on stochastic models, sensitivity-based optimization, Markov decision processes, and queueing games. He has published several papers in a variety of journals, such as Operations Research, Journal of the Operational Research Society, Operations Research Letters, etc.