Optimal control of batch service queues with finite service capacity and linear holding costs

We consider the optimal control problem of certain batch service queueing s ystems with compound Poisson arrivals and linear holding costs. The control problem involves the determination of the epochs at which the service is i nitiated as well as the sizes of the batches served. The service times are assumed to be independent and identically distributed, however, with a gene ral distribution. A quite natural operating policy is to start the service as soon as the number of customers reaches some threshold and serve always as many customers as possible. Assuming infinite service capacity Deb [4] p roved that under some mild conditions the optimal operating policy is of th is type. In this paper we show that a similar result is valid even if the s ervice capacity is finite. In this case the threshold is never greater than Q, the service capacity (the maximum number of customers that can be serve d at the same time).