The Annals of Applied Probability

A broader view of Brownian networks

J. Michael Harrison

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 3 (2003), 1119-1150.

Dates
First available in Project Euclid: 6 August 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1060202837

Digital Object Identifier
doi:10.1214/aoap/1060202837

Mathematical Reviews number (MathSciNet)
MR1994047

Zentralblatt MATH identifier
1060.90020

Subjects
Primary: 90B15: Network models, stochastic 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

Keywords
Stochastic processing networks Brownian networks heavy traffic stochastic control

Citation

Harrison, J. Michael. A broader view of Brownian networks. Ann. Appl. Probab. 13 (2003), no. 3, 1119--1150. doi:10.1214/aoap/1060202837. https://projecteuclid.org/euclid.aoap/1060202837


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References

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