Equilibrium customers strategies in the Markovian working vacation queue with setup times

Abstract

In this paper, we research the customers' equilibrium behaviour in the single server Markovian queue with setup times and working vacation. In such an M/M/1 queueing system, the arriving customers' decision is whether to enter the system or balk based on the reward-cost structure, which includes their desire for service and their unwillingness to wait. We separately discuss the fully observable and fully unobservable cases. For each of case, we acquire the related equilibrium balking strategies of customers and the expected social benefits per time unit. Finally, we obtain some numerical examples to illustrate the effect of several parameters on the equilibrium and optimal strategy.