Variance reduction in simulations of loss models

We propose a new estimator of steady-state blocking probabilities for simul ations of stochastic loss models that can be much more efficient than the n atural estimator (ratio of losses to arrivals). The proposed estimator is a convex combination of the natural estimator and an indirect estimator base d on the average number of customers in service, obtained from Little's law (L = lambda W). It exploits the known offered load (product of the arrival rate and the mean service time). The variance reduction is dramatic when t he blocking probability is high and the service times are highly variable. The advantage of the combination estimator in this regime is partly due to the indirect estimator, which itself is much more efficient than the natura l estimator in this regime, and partly due to strong correlation (most ofte n negative) between the natural and indirect estimators. In general, when t he variances of two component estimators are very different, the variance r eduction from the optimal convex combination is about 1 - rho(2), where rho is the correlation between the component estimators. For loss models, the variances of the natural and indirect estimators are very different under b oth light and heavy loads. The combination estimator is effective for estim ating multiple blocking probabilities in loss networks with multiple traffi c classes, some of which are in normal loading while others are in light an d heavy loading, because the combination estimator does at least as well as either component estimator, and it provides improvement as well.