Equilibrium Mixed Strategies in a Discrete-Time Markovian Queue Under Multiple and Single Vacation Policies

Abstract

We study the Nash equilibrium behavior of customers in a discrete-time single-server queue under multiple vacation policy or single vacation policy. Every arriving customer either joins the queue or balks based on his or her service utility. Using a Quasi-Birth-Death Processes (QBD) model, we obtain the stationary distribution of the queue length via the Matrix-Geometric Solution method. We analyze the equilibrium mixed threshold strategies under two different vacation policies. By presenting numerical examples, we examine the impacts of system parameters on the equilibrium customer behavior and compare the single and multiple vacation policies in terms of the social welfare.

Key Words:

• Economics of queues
• Matrix-Geometric solution
• multiple vacations
• Nash equilibrium strategy
• single vacation.

Additional information

Notes on contributors

Zaiming Liu

Zaiming Liu is a Professor in Central South University (CSU). He is also the dean of the School of Mathematics and Statistics at CSU. His research interests are in issues related to queueing theory and network applications, insurance risk theory, Markov process and its applications. He has published more than 60 papers in international journals such as Applied Mathematics and Computation, Nonlinear Analysis, Economic Model, etc.

Yan Ma

Yan Ma is a Ph.D. student in the School of Mathematics and Statistics at Central South University. She is currently studying in Beedie School of Business at Simon Fraser University as a joint Ph.D. student under the support of China Scholarship Council. Her research interests include vacation queueing systems and economics of queues.

Zhe George Zhang

Zhe George Zhang is a Professor in Management Science at Western Washington University in the USA and a Professor in Operations Research at Simon Fraser University in Canada. He obtained his Ph.D. in Operations Research from the University of Waterloo, Canada. The focus of his current research is on theory and application of queueing and other stochastic models.