Optimal control of bulk queues with compound Poisson arrivals and batch service (Q801614)

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.