Strategic Behavior and Social Optimization in Markovian Vacation Queues

Abstract

We consider a single server queueing system in which service shuts down when there are no customers present and is resumed only when the queue length reaches a given critical length. We analyze the strategic response of customers to this mechanism and compare it to the overall optimal behavior, with and without information on delay. The results are significantly different from those obtained when the server is continuously available. We show that there may exist multiple equilibria in such a system and the optimal arrival rate may be greater or smaller than that of the decentralized equilibrium. Finally, the critical length is taken as a decision variable, and the optimal operations policy is discussed by taking strategic customers into consideration.