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.