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August 1997 Dynamic control of Brownian networks: state space collapse and equivalent workload formulations
J. Michael Harrison, Jan A. Van Mieghem
Ann. Appl. Probab. 7(3): 747-771 (August 1997). DOI: 10.1214/aoap/1034801252


Brownian networks are a class of linear stochastic control systems that arise as heavy traffic approximations in queueing theory. Such Brownian system models have been used to approximate problems of dynamic routing, dynamic sequencing and dynamic input control for queueing networks. A number of specific examples have been analyzed in recent years, and in each case the Brownian network has been successfully reduced to an "equivalent workload formulation" of lower dimension. In this article we explain that reduction in general terms, using an orthogonal decomposition that distinguishes between reversible and irreversible controls.


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J. Michael Harrison. Jan A. Van Mieghem. "Dynamic control of Brownian networks: state space collapse and equivalent workload formulations." Ann. Appl. Probab. 7 (3) 747 - 771, August 1997.


Published: August 1997
First available in Project Euclid: 16 October 2002

zbMATH: 0885.60080
MathSciNet: MR1459269
Digital Object Identifier: 10.1214/aoap/1034801252

Primary: 60J70 , 60K25 , 90B15

Keywords: Brownian networks , dynamic scheduling , Queueing networks , state space collapse

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 3 • August 1997
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