Marginal Productivity Index Policies for Scheduling Multiclass Delay-/Loss-Sensitive Traffic with Delayed State Observation

This paper addresses the problem of dynamic bandwidth allocation in a channel to multiclass packet traffic, where each traffic class has a finite dedicated buffer. Class-dependent linear holding and rejection cost rates are used to model differing levels of tolerance to delay and loss. Time is slotted, and the controller´s backlog information is delayed by one slot. The goal is to design well-grounded and tractable scheduling policies that nearly minimize expected total discounted or long-run average cost. New dynamic index policies are introduced, awarding higher priority to classes with larger index values, where a class´ index measures the marginal productivity of work at its current state. The results are obtained by deploying the work-cost analysis approach to marginal productivity indices (MPIs) for restless bandits developed by the author. The results of a computational study on two-class instances are reported, shedding light on how the MPI policy´s relative performance varies with each parameter. Across the range of instances explored, the MPI policy is shown to be nearly optimal, and to substantially outperform conventional benchmark policies.