An importance sampling method studied by Siegmund and Asmussen in the case of waiting time probabilities is extended to the mean and other functionals. The ideas involve exponential families of queues and control variates (regression), and it is found both from theory and practice that the method is dramatically better than standard tools like regenerative simulation or sample-mean estimation, not least under heavy traffic conditions.
"Exponential Families and Regression in the Monte Carlo Study of Queues and Random Walks." Ann. Statist. 18 (4) 1851 - 1867, December, 1990. https://doi.org/10.1214/aos/1176347883