Strategic Behavior in the Single-Server Constant Retrial Queue with Individual Removal

Abstract

We consider the system with no waiting space in which primary customers arrive according to a Poisson process. The arriving customer receives service immediately as the server is idle, otherwise, he will enter a retrial orbit asking for repeated requests. When a negative customer comes, the customer being served is deleted immediately and it also causes the server’s breakdown. Whenever the server breaks down, it is sent for repair immediately. If no customer arrives after every service completion, the server selects the first customer of the orbit to serve. The time required to find the first customer is assumed exponentially distributed with a constant rate referred as constant retrial rate. Based on a natural reward-cost structure, we study the equilibrium behavior of the customers and derive the corresponding Nash equilibrium joining strategies and social net benefit maximization problem with respect to the levels of information available to customers upon arrival.

Key Words:

• Constant retrial rate
• equilibrium strategies
• individual removal
• reward-cost structure
• social optimization.

Additional information

Notes on contributors

Fang Wang

Fang Wang is a Ph.D candidate at the Department of Mathematics, School of Science at Beijing Jiaotong University in Beijing, China. Her research interest is queueing theory.

Jinting Wang

Jinting Wang is a Professor of Operations Research at Beijing Jiaotong University. He received his PhD in Operational Research from the Institute of Applied Mathematics, Chinese Academy of Sciences (CAS) in 2000. His research interests include issues related to queueing theory, reliability and applied probability. He has published over 40 papers in international journals such as Queueing Systems: Theory and Applications, Journal of Multivariate Analysis, European Journal of Operational Research, etc. He is a member of the Operations Research Society of China (ORSC), and now he serves as a Vice-Presidents of the Queueing Chapter and the Reliability Chapter associated with ORSC. He received the Outstanding Research Award for Young Researchers from ORSC in 2004. In 2011, he was honored with “Program for New Century Excellent Talents in University” by the Ministry of Education of China.

Feng Zhang

Feng Zhang is a Ph.D. candidate the Department of Mathematics, School of Science at Beijing Jiaotong University in Beijing, China. He has published several papers in international journals and his research interests include queueing theory and reliability.