Abstract
We consider a two-stage service system with batch processing. More specifically, customers arrive according to a Poisson process at the first stage of the system, where they do not receive any service, but wait until a number K of them are accumulated. Then, these K customers form a batch which is instantaneously transferred to the second stage where the batches are served sequentially, as single units, by a single server. We derive customer equilibrium strategies, regarding the joining/balking dilemma, for the (partially) observable case where the customers are informed upon arrival about the number of present customers at the first stage. We prove the existence and study the uniqueness of equilibrium strategies and give a simple procedure for their computation. Moreover, we juxtapose the customer strategic behavior in this system with the corresponding behavior in the unobservable system and study the effect of information on the resulting social welfare per time unit under equilibrium.
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