An asymptotic optimality result for the multiclass queue with finite buffers in heavy traffic

TL;DR

This paper develops an asymptotically optimal control policy for a multiclass G/G/1 queue with finite buffers in heavy traffic, integrating free boundary problems and a novel c mu priority rule.

Contribution

It introduces a new control policy explicitly based on problem data and the Harrison-Taksar free boundary, extending prior infinite buffer approaches to finite buffers.

Findings

Policy achieves asymptotic optimality in heavy traffic

Incorporates a novel c mu priority rule for finite buffers

Addresses throughput time constraints as an alternative to buffer limits

Abstract

For a multiclass G/G/1 queue with finite buffers, admission and scheduling control, and holding and rejection costs, we construct a policy that is asymptotically optimal in the heavy traffic limit. The policy is specified in terms of a single parameter which constitutes the free boundary point from the Harrison-Taksar free boundary problem, but otherwise depends "explicitly" on the problem data. The c mu priority rule is also used by the policy, but in a way that is novel, and, in particular, different than that used in problems with infinite buffers. We also address an analogous problem where buffer constraints are replaced by throughput time constraints.