Workload Reduction of a Generalized Brownian Network

J. M. Harrison and R. J. Williams
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. Consequently, 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.
This paper appears in the Annals of Applied Probability, Vol. 15 (2005), 2255-2295, published by the Institute of Mathematical Statistics. For a copy of a reprint for personal scientific non-commercial use only, click here for pdf.

Last updated: December 2, 2005