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

Rami Atar,Mark Shifrin

doi:10.1214/13-ssy124

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.

Highlights

In this work we consider the problem of finding asymptotically optimal (AO) controls for the multiclass G/G/1 queue with finite buffers, in heavy traffic
Using this result we can show that the policy we develop for the finite buffer problem satisfies the throughput time constraints and that its limit performance is dominated by the Brownian control problem (BCP) value (Theorem 5.1)
The workload process X = θ · X is given as a reflected BM (RBM) on [0, x∗], where the free boundary point x∗ is dictated by the Bellman equation

Summary

Stochastic Systems

Publication details, including instructions for authors and subscription information: http://pubsonline.informs.org. An Asymptotic Optimality Result for the Multiclass Queue with Finite Buffers in Heavy Traffic. To cite this article: Rami Atar, Mark Shifrin (2014) An Asymptotic Optimality Result for the Multiclass Queue with Finite Buffers in Heavy Traffic. Full terms and conditions of use: https://pubsonline.informs.org/Publications/Librarians-Portal/PubsOnLine-Terms-andConditions. With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org. AN ASYMPTOTIC OPTIMALITY RESULT FOR THE MULTICLASS QUEUE WITH FINITE BUFFERS IN HEAVY TRAFFIC∗

By Rami Atar and Mark Shifrin

Introduction

Denote by I the operator

Hence and therefore