The Optimal Policy for a Controlled Brownian Motion Process

Abstract

This paper studies a controlled reflected Brownian motion process where there is a choice between two sets of drift and diffusion parameters. Operating, switching, and linear holding costs are imposed. The process arises naturally as an approximation for a controlled queuing problem. When the objective is to minimize the expected average cost per unit time over an infinite horizon it is shown that the optimal policy can be characterized by two switching points. The result is proved by showing the corresponding result for a random walk, and then using a sequence of random walks to obtain the final result.

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