The Annals of Applied Probability

Dynamic control of Brownian networks: state space collapse and equivalent workload formulations

J. Michael Harrison and Jan A. Van Mieghem

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 7, Number 3 (1997), 747-771.

Dates
First available in Project Euclid: 16 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034801252

Digital Object Identifier
doi:10.1214/aoap/1034801252

Mathematical Reviews number (MathSciNet)
MR1459269

Zentralblatt MATH identifier
0885.60080

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

Keywords
Brownian networks queueing networks state space collapse dynamic scheduling

Citation

Harrison, J. Michael; Van Mieghem, Jan A. Dynamic control of Brownian networks: state space collapse and equivalent workload formulations. Ann. Appl. Probab. 7 (1997), no. 3, 747--771. doi:10.1214/aoap/1034801252. https://projecteuclid.org/euclid.aoap/1034801252


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References

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