Importance sampling in systems simulation: a practical failure?

A network of servers, known as a grading in telecommunication engineering, is simulated in order to estimate the probability of a customer being “blocked”: all servers busy. Since blocking is a very rare event (1‰ to 5% chance), importance sampling was considered for reduction of the simulation variance. The basic idea of importance sampling is first explained by means of a non-dynamic system. For dynamic systems a method was proposed by Bayes in 1970, which is related to the “virtual measures” published by Carter and Ignall in 1975. For simple queuing systems, we derive the resulting variance, using the renewal or regenerative property of such systems. For our practical “grading” system several alternative importance regions are investigated. For practical reasons we choose to start an importance region immediately after a call gets blocked (not a renewal state). The analysis and simulation experiments for the resulting estimator yielded the estimated optimal length of the importance region and the optimal number of replications of the region. Unfortunately, a net increase in variance resulted.