Dynamic control of Brownian networks: state space collapse and equivalent workload formulations
Open Access
- 1 August 1997
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 7 (3) , 747-771
- https://doi.org/10.1214/aoap/1034801252
Abstract
Brownian networks are a class of linear stochastic control systems that arise as heavy traffic approximations in queueing theory. Such Brownian system models have been used to approximate problems of dynamic routing, dynamic sequencing and dynamic input control for queueing networks. A number of specific examples have been analyzed in recent years, and in each case the Brownian network has been successfully reduced to an "equivalent workload formulation" of lower dimension. In this article we explain that reduction in general terms, using an orthogonal decomposition that distinguishes between reversible and irreversible controls.Keywords
This publication has 15 references indexed in Scilit:
- Some diffusion approximations with state space collapsePublished by Springer Nature ,2005
- Dynamic Scheduling with Convex Delay Costs: The Generalized $c|mu$ RuleThe Annals of Applied Probability, 1995
- Dynamic routing in open queueing networks: Brownian models, cut constraints and resource poolingQueueing Systems, 1993
- Resource pooling in queueing networks with dynamic routingAdvances in Applied Probability, 1992
- Routing and Singular Control for Queueing Networks in Heavy TrafficSIAM Journal on Control and Optimization, 1990
- Dynamic Scheduling of a Four-Station Queueing NetworkProbability in the Engineering and Informational Sciences, 1990
- Scheduling networks of queues: Heavy traffic analysis of a simple open networkQueueing Systems, 1989
- Brownian Models of Queueing Networks with Heterogeneous Customer PopulationsPublished by Springer Nature ,1988
- Open Queueing Networks in Heavy TrafficMathematics of Operations Research, 1984
- The Heavy Traffic Diffusion Approximation for Sojourn Times in Jackson NetworksPublished by Springer Nature ,1982