Brownian models of open processing networks: Canonical representation of workload (vol 10, pg 75, 2000)

• 成果类型: Correction
• 署名作者: Harrison, J. Michael
• 署名单位: Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000583
• 发表日期: 2006
• 页码: 1703-1732
• 关键词: heavy traffic analysis; scheduling networks; queuing-networks; closed network; queues

摘要

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.