The Bigstep approach to flow management in stochastic processing networks

Abstract

Abstract Flow management in stochastic networks may involve dynamic routing, dynamic input control, dynamic resource allocation, or combinations thereof. This paper describes a new and very general approach to flow management in which system status is reviewed at discrete points in time, a linear programming problem is solved at each such point, and the processing plan obtained from that linear program is implemented in open-loop fashion over the ensuing period. Discrete-review policies of the proposed type are motivated by heavy traffic theory for network control problems, in which the loads imposed on at least some processing resources are assumed to approach the capacities of those resources. Striving to construct a discrete-review policy that is asymptotically optimal in the heavy traffic limit, one must first formulate and analyze an approximating Brownian control problem, which typically is much simpler than the original processing network.

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