Linear programming relaxations and marginal productivity index policies for the buffer sharing problem

Authors:
Jianhua Cao;Christian Nyberg
Affiliations:
Department of Electrical and Information Technology, Lund University, Lund, Sweden 22100;Department of Electrical and Information Technology, Lund University, Lund, Sweden 22100
Venue:
Queueing Systems: Theory and Applications
Year:
2008

Citing 7
Cited 1

Multiservice Loss Models for Broadband Telecommunication Networks

Multiservice Loss Models for Broadband Telecommunication Networks
Restless Bandits, Linear Programming Relaxations, and a Primal-Dual Index Heuristic

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

Queueing Systems: Theory and Applications
Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues

Mathematics of Operations Research
Dynamic Programming and Optimal Control, Vol. II

Dynamic Programming and Optimal Control, Vol. II
A (2/3)n3 Fast-Pivoting Algorithm for the Gittins Index and Optimal Stopping of a Markov Chain

INFORMS Journal on Computing
Optimal buffer sharing

IEEE Journal on Selected Areas in Communications

Optimal anticipative congestion control of flows with time-varying input stream

Performance Evaluation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the dynamic admission control for a finite shared buffer with support of multiclass traffic under Markovian assumptions. The problem is often referred to as buffer sharing in the literature. From the linear programming (LP) formulation of the continuous-time Markov decision process (MDP), we construct a hierarchy of increasingly stronger LP relaxations where the hierarchy levels equal the number of job classes. Each relaxation in the hierarchy is obtained by projecting the original achievable performance region onto a polytope of simpler structure. We propose a heuristic policy for admission control, which is based on the theory of Marginal Productivity Index (MPI) and the Lagrangian decomposition of the first order LP relaxation. The dual of the relaxed buffer space constraint in the first order LP relaxation is used as a proxy to the cost of buffer space. Given that each of the decomposed queueing admission control problems satisfies the indexability condition, the proposed heuristic accepts a new arrival if there is enough buffer space left and the MPI of the current job class is greater than the incurred cost of buffer usage. Our numerical examples for the cases of two and eight job classes show the near-optimal performance of the proposed MPI heuristic.