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Workload reduction of a generalized Brownian network. (English) Zbl 1096.60036

Summary: 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.

MSC:

60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60J60 Diffusion processes
90B15 Stochastic network models in operations research
90B36 Stochastic scheduling theory in operations research
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