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Optimal control of bulk queues with compound Poisson arrivals and batch service. (English) Zbl 0552.60092
The problem of optimal control of batch service in a queue with compound Poisson arrivals is studied. The process is controlled at points in time when the server is idle and a new group of customers arrives or when a service has just been completed.
One of the following procedures is taken: no customers is served; a batch consisting of all or a portion of the waiting customer is served. Costs are charged for serving the customers and for holding them in the system. It is proved that optimal policy has the form: if x customers are waiting, they all are served iff \(x>M\), where M is a constant.
Reviewer: J.Morozov

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research