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Workload Reduction of a Generalized Brownian Network
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J. M. Harrison and R. J. Williams
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Abstract
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*