Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue

We address the problem of scheduling a multiclass M/M/1 queue with a finite dedicated buffer for each class. Some classes are delay-sensitive, modeling real-time traffic (e.g. voice, video), whereas others are loss-sensitive, modeling nonreal-time traffic (e.g. data). Different levels of tolerance to delay and loss are modeled by appropriate linear holding cost and rejection cost rates. The goal is to design well-grounded and tractable scheduling policies which nearly minimize the discounted or long-run average expected cost objective. We develop new dynamic index policies, prescribing to give higher service priority to classes with larger index values, where the priority index of a class measures the marginal productivity of work at its current state. To construct the indices, we deploy the theory of marginal productivity indices (MPIs) and PCL-indexability we have introduced in recent work, and further introduce significant extensions to such theory motivated by phenomena observed in the model of concern. The MPI policies are shown to furnish new, insightful structural results, and to exhibit a nearly optimal performance in a computational study.