## The Annals of Applied Probability

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

### A broader view of Brownian networks

#### 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