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.

中文翻译：

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两阶段批处理系统中的战略客户行为

我们考虑一个带有批处理的两阶段服务系统。更具体地说，客户在系统的第一阶段根据泊松过程到达，在那里他们不接受任何服务，而是等到他们的数量 K 累积。然后，这 K 个客户形成一个批次，该批次立即转移到第二阶段，其中批次作为单个单元由单个服务器顺序提供。对于（部分）可观察的情况，即在第一阶段客户到达时被告知现有客户的数量，我们推导出关于加入/阻止困境的客户均衡策略。我们证明了均衡策略的存在性和唯一性，并给出了一个简单的计算过程。而且，