The Stochastic Machine Replenishment Problem

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The Stochastic Machine Replenishment Problem
We study the stochastic machine replenishment problem, which is a canonical special case of closed multiclass queuing systems in Markov decision theory. The problem models the scheduling of processor repairs in a multiprocessor system in which one repair can be made at a time and the goal is to maximize system utilization. We analyze the performance of a natural greedy index policy for this problem. We first show that this policy is a 2 approximation by exploring linear queuing structure in the index policy. We then try to exploit more complex queuing structures, but this necessitates solving an infinite-size, non-linear, non-convex, and non-separable function-maximization program. We develop a general technique to solve such programs to arbitrary degree of accuracy, which involves solving a discretized program on the computer and rigorously bounding the error. This proves that the index policy is
Kamesh Munagala, Peng Shi
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where IPCO
Authors Kamesh Munagala, Peng Shi
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