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August 2003 A broader view of Brownian networks
J. Michael Harrison
Ann. Appl. Probab. 13(3): 1119-1150 (August 2003). DOI: 10.1214/aoap/1060202837


This paper describes a general type of stochastic system model that involves three basic elements: activities, resources, and stocks of material. A system manager chooses activity levels dynamically based on state observations, consuming some materials as inputs and producing other materials as outputs, subject to resource capacity constraints. A generalized notion of heavy traffic is described, in which exogenous input and output rates are approximately balanced with nominal activity rates derived from a static planning problem. A Brownian network model is then proposed as a formal approximation in the heavy traffic parameter regime. The current formulation is novel, relative to models analyzed in previous work, in that its definition of heavy traffic takes explicit account of the system manager's economic objective.


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J. Michael Harrison. "A broader view of Brownian networks." Ann. Appl. Probab. 13 (3) 1119 - 1150, August 2003.


Published: August 2003
First available in Project Euclid: 6 August 2003

zbMATH: 1060.90020
MathSciNet: MR1994047
Digital Object Identifier: 10.1214/aoap/1060202837

Primary: 60K25 , 90B15
Secondary: 60J70

Keywords: Brownian networks , heavy traffic , Stochastic control , Stochastic processing networks

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 3 • August 2003
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