Article1997

Dynamic control of Brownian networks: state space collapse and\n\t\t equivalent workload formulations

J. Michael Harrison · Jan Albert Van Mieghem

148 citations0/0 files storedProject Euclid (Cornell University)

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Advanced Queuing Theory Analysis Stochastic processes and financial applications Stochastic processes and statistical mechanics

Abstract

Brownian networks are a class of linear stochastic control systems\nthat arise as heavy traffic approximations in queueing theory. Such Brownian\nsystem models have been used to approximate problems of dynamic routing,\ndynamic sequencing and dynamic input control for queueing networks. A number of\nspecific examples have been analyzed in recent years, and in each case the\nBrownian network has been successfully reduced to an "equivalent workload\nformulation" of lower dimension. In this article we explain that reduction in\ngeneral terms, using an orthogonal decomposition that distinguishes between\nreversible and irreversible controls.

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References

1984Open Queueing Networks in Heavy Traffic 1988Brownian Models of Queueing Networks with Heterogeneous Customer Populations 1995Dynamic Scheduling with Convex Delay Costs: The Generalized $c|mu$ Rule 1990Scheduling Networks of Queues: Heavy Traffic Analysis of a Two-Station Closed Network 1989Scheduling networks of queues: Heavy traffic analysis of a simple open network 2006Some diffusion approximations with state space collapse 1993Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling 1992Dynamic Scheduling of a Multiclass Make-to-Stock Queue

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