Let a and s denote the inter arrival times and service times in a queue. Let , be the r.v.s. with distributions as the estimated distributions of a and s from idd samples of a and s of sizes n. Let w be a r.v. with the stationary distribution of the waiting times of the queue with input (a, s). The paper considers the problem of estimating , and via simulations when are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. The paper also obtains rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robost estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process the paper obtains consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.
