Optimal control of batch service queues with compound Poisson arrivals and finite service capacity

We consider the optimal control problem of an M^X/G(Q)/1 batch service queueing system with Q<∞. So, we assume that customers arrive according to a compound Poisson process and are served in batches not greater than the finite service capacity Q. The control problem involves the determination of the epochs at which the service is initiated as well as the sizes of the batches served. We introduce a new class of operating policies and prove that, under some additional assumptions, there is an optimal operating policy belonging to this new class.