Convergence of perturbation analysis based optimization algorithm with fixed number of customers period

In this paper we show that an optimization algorithm using infinitesimal perturbation analysis converges to the minimum of the performance measure. The algorithm is updated every fixed number of customers period rather than every one or two busy periods. The key step of the proof is to verify that the observation noises satisfy the strong law of large numbers. Then applying a stochastic approximation theorem leads to the desired results.

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