Capacity Realization in Stochastic Batch-Processing Networks Using Discrete-Review Policies

We present difficulties with realizing the capacity of queueing networks with batch servers under well known scheduling disciplines. We introduce a family of scheduling policies called discrete-review policies, which not only guarantee capacity realization for queueing network with batch servers, but also contain among them policies that allow us to realize desired behavior on “fluid” scale, including asymptotically optimal policies. In this family of policies system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed, which is them executed in open-loop fashion. We outline a proof of capacity realization for every policy in this family, and provide results of simulation studies that establish the usefulness of the proposed family of policies.