Variance reduction for likelihood-ratio method

The likelihood-ratio (LR) method is a powerful method for sensitivity analysis of stochastic system performance because of its wide applicability. However, the variance of the estimate from the LR increases linearly with the length of the segment path, which makes the steady-state performance sensitivity estimation difficult. To overcome this difficulty, regenerative simulation is used. However, the mean length of regenerative cycles for a queuing network usually grows combinatorially with the size of the network. Thus, the LR method in its current stage is impractical for queuing networks. The authors propose using segments defined by an embedded ergodic Markov chain to cut the regenerative segments into shorter segments to reduce the variance. Applications are illustrated by examples