Measure-Valued Differentiation for the Cycle Cost Performance in the G/G/1 Queue in the Presence of Heavy-Tailed Distributions

B. Heidergott, A. Hordijk

2009, v.15, Issue 2, 225-253


We consider the accumulate costs over a cycle of a phase-homogeneous random walk. For this model we establish sufficient conditions for the existence of the derivative of the cycle cost and we establish an unbiased gradient estimator. The main stability condition for our analysis is that the expected cycle costs are finite. We thereby improve the results known in the literature so far, where usually finiteness of higher moments of the cycle length is assumed in order to establish unbiasedness of a particular gradient estimator.

Keywords: measure-valued differentiation,perturbation analysis,Markov chains


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