The Annals of Applied Probability

Correction: Brownian models of open processing networks: canonical representation of workload

J. Michael Harrison

Full-text: Open access

Abstract

Due to a printing error the above mentioned article had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error.

A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an “equivalent workload formulation” of a Brownian network model. Denoting by Z(t) the state vector of the original Brownian network, one has a lower dimensional state descriptor W(t)=MZ(t) in the equivalent workload formulation, where M can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing networks, and in that context develops a more extensive interpretation of the equivalent workload formulation, thus extending earlier work by Laws on alternate routing problems. A linear program called the static planning problem is introduced to articulate the notion of “heavy traffic” for a general open network, and the dual of that linear program is used to define a canonical choice of the basis matrix M. To be specific, rows of the canonical M are alternative basic optimal solutions of the dual linear program. If the network data satisfy a natural monotonicity condition, the canonical matrix M is shown to be nonnegative, and another natural condition is identified which ensures that M admits a factorization related to the notion of resource pooling.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 3 (2006), 1703-1732.

Dates
First available in Project Euclid: 2 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1159804997

Digital Object Identifier
doi:10.1214/105051606000000583

Mathematical Reviews number (MathSciNet)
MR2260079

Zentralblatt MATH identifier
1121.60095

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60J7 90B15: Network models, stochastic

Keywords
Queueing theory heavy traffic dynamic control Brownian approximation equivalent workload formulation

Citation

Harrison, J. Michael. Correction: Brownian models of open processing networks: canonical representation of workload. Ann. Appl. Probab. 16 (2006), no. 3, 1703--1732. doi:10.1214/105051606000000583. https://projecteuclid.org/euclid.aoap/1159804997


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