Permuted derivative and importance-sampling estimators for regenerative simulations

Abstract

In a previous paper we introduced a new variance-reduction technique for regenerative simulations based on permuting regeneration cycles. In this paper we apply this idea to new classes of estimators. In particular, we derive permuted versions of likelihood-ratio derivative estimators for steady-state performance measures, importance-sampling estimators of the mean cumulative reward until hitting a set of states, and Tin estimators for steady-state ratio formulas. Empirical results are presented showing that modest to significant variance reductions can be obtained.