Equilibrium and social optimality in queues with service rate and customers’ joining decisions

ABSTRACT

This paper treats a single server Markovian queueing system with changeable service rates and customer choice. When a customer arrives at an empty system, he is served by the server at a low service rate. This low service rate continues until the queue length reaches a threshold. Then the server switches to a high service rate to serve customers who join the system. The high service rate continues until the system becomes empty and a low service rate starts again. Under a service reward and waiting cost structure, customers decide to join or to balk based on their net utility of joining the system. The customers’ equilibrium and socially optimal joining strategies are studied under two information scenarios which are observable and unobservable queues, respectively. Such a model fits a stochastic service system where the server can make his service rate decision and customers can make their joining or baking decisions and thus has wide applications in service industries. Our focus is on examining the equilibrium performance of the queue under the interaction between the server’s service rate and customers’ joining decisions. We develop the steady-state distribution and performance measures of the system by formulating two-dimensional continuous-time Markov chains.

KEYWORDS:

• Applied probability
• equilibrium strategy
• social welfare
• threshold policy
• service rate policy

Disclosure statement

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

Additional information

Notes on contributors

Ruiling Tian

Dr. Ruiling Tian is an associate professor in the College of Science at Yanshan University in China. Her research interests are stochastic modeling and queueing theory.

Siping Su

Ms. Siping Su is a senior lecturer in the Department of Decision Sciences at Western Washngton University and a PhD candidate at Department of Business Administration at Asia University in Taiwan. Her research interests include operations management and statistical models in business.

Zhe George Zhang

Dr. Zhe George Zhang is a professor in the Department of Decision Sciences at Western Washington University. His research interests are queueing models and business analytics.