# A Renewal Theoretic Approach to Bias Reduction in Regenerative Simulations

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## Abstract

The special structure of regenerative processes is exploited to derive a new point estimate with very low bias for steady state quantities of regenerative simulations. If the simulation run length is t units of tune, the bias of the new estimate is of order 1/t 2 as opposed to the bias of order 1/t associated with more standard estimates. The bias reduction is achieved by continuing the simulation until the first regeneration after time t and then forming the ratio estimate which involves the random number of regenerative cycles observed during the simulation. Empirical results for several queueing models demonstrate that the bias reduction can be substantial for small values of t.

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