Equilibrium joining probabilities in observable queues with general service and setup times

Abstract

This paper analyzes an M/G/1 queue with general setup times from aneconomical point of view. In such a queue whenever the systembecomes empty, the server is turned off. A new customer's arrivalwill turn the server on after a setup period. Upon arrival, thecustomers decide whether to join or balk the queue based onobservation of the queue length and the status of the server, alongwith the reward-cost structure of the system. For the observable andalmost observable cases, the equilibrium joining strategies ofcustomers who wish to maximize their expected net benefit areobtained. Two numerical examples are presented to illustrate theequilibrium joining probabilities for these cases under somespecific distribution functions of service times and setup times.

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