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.