Heavy Traffic Convergence of a Controlled, Multiclass Queueing System

Authors:
L. F. Martins;S. E. Shreve;H. M. Soner
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1996

Citing 0
Cited 8

Value iteration and optimization of multiclass queueing networks

Queueing Systems: Theory and Applications
A Multiclass Queue in Heavy Traffic with Throughput Time Constraints: Asymptotically Optimal Dynamic Controls

Queueing Systems: Theory and Applications
Continuous-Review Tracking Policies for Dynamic Control of Stochastic Networks

Queueing Systems: Theory and Applications
In Search of Sensitivity in Network Optimization

Queueing Systems: Theory and Applications
Two Workload Properties for Brownian Networks

Queueing Systems: Theory and Applications
Reliability by design in distributed power transmission networks

Automatica (Journal of IFAC)
A Numerical Method for Solving Singular Stochastic Control Problems

Operations Research
Approximate Dynamic Programming via a Smoothed Linear Program

Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper provides a rigorous proof of the connection between the optimal sequencing problem for a two-station, two-customer-class queueing network and the problem of control of a multidimensional diffusion process, obtained as a heavy traffic limit of the queueing problem. In particular, the diffusion problem, which is one of ``singular control'' of a Brownian motion, is used to develop policies which are shown to be asymptotically nearly optimal as the traffic intensity approaches one in the queueing network. The results are proved by a viscosity solution analysis of the related Hamilton--Jacobi--Bellman equations.