A Study of Equilibrium Joining and Socially Optimal Strategic Behavior in Discrete-Time Queue with Multiple Working Vacations

Abstract

We analyze equilibrium balking strategies and the social benefits in a discrete-time batch arrival renewal input queue with multiple working vacations. The arriving batch customers decide whether to join or balk the queue on the basis of a natural reward-cost structure, which integrates their wish for service as well as their reluctance to wait. We study customers' behavior and estimate the net benefit of the batch customers that prefer to take part in the system. The fully observable and unobservable cases with respect to various levels of information availability from the system are examined. We analyze the fully observable case by applying embedded Markov chain and the fully unobservable case by using the roots of the characteristic equations of the probability generating function of system length distribution at pre-arrival epochs. The significance of the information levels along with various parameters on the equilibrium behavior and social benefits is illustrated by numerical results.