Abstract:

We consider the single-server Markovian queue with infinite waiting space and assume that there exists a certain reward-cost structure that reflects the customers’ desire for service and their dislike for waiting. The system is unobservable for the customers at their arrival instants, but the administrator provides them with periodic announcements of their current positions at rate (Formula presented.), so that they may renege if it is preferable for them to do so. The customers are strategic, and their decision problem is whether to join or not the system upon arrival and whether to stay or renege later. Their strategies are specified by a join probability q and a reneging threshold n. We determine the equilibrium strategies (Formula presented.) and study the socially optimal strategies (Formula presented.). Extensive numerical experiments provide interesting qualitative insight about the model. In particular, the equilibrium throughput of the system is a unimodal function of (Formula presented.). Moreover, despite the fact that we have an avoid-the-crowd situation, it is possible that (Formula presented.), in contrast to the classical unobservable model. © 2017 Springer Science+Business Media New York

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