The Annals of Applied Probability

Workload reduction of a generalized Brownian network

J. M. Harrison and R. J. Williams

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We consider a dynamic control problem associated with a generalized Brownian network, the objective being to minimize expected discounted cost over an infinite planning horizon. In this Brownian control problem (BCP), both the system manager’s control and the associated cumulative cost process may be locally of unbounded variation. Due to this aspect of the cost process, both the precise statement of the problem and its analysis involve delicate technical issues. We show that the BCP is equivalent, in a certain sense, to a reduced Brownian control problem (RBCP) of lower dimension. The RBCP is a singular stochastic control problem, in which both the controls and the cumulative cost process are locally of bounded variation.

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Ann. Appl. Probab., Volume 15, Number 4 (2005), 2255-2295.

First available in Project Euclid: 7 December 2005

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Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65] 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 90B15: Network models, stochastic 90B36: Scheduling theory, stochastic [See also 68M20]

Stochastic control singular control Brownian network model reflected Brownian motion workload no-arbitrage state space collapse continuous selection


Harrison, J. M.; Williams, R. J. Workload reduction of a generalized Brownian network. Ann. Appl. Probab. 15 (2005), no. 4, 2255--2295. doi:10.1214/105051605000000458.

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