A dynamic importance sampling methodology for the efficient estimation of rare event probabilities in regenerative simulations of queueing systems

Importance sampling (IS) is recognized as a potentially powerful method for reducing simulation runtimes when estimating the probabilities of rare events in communication systems using Monte Carlo simulation. When simulating networks of queues, regenerative techniques must be used to make the application of IS feasible and efficient. The application of regenerative techniques is also crucial in obtaining correct confidence intervals for the estimates involved. The authors present a methodology that uses IS dynamically, within each regeneration cycle, to drive the system back to the regeneration state, after an accurate estimate has been obtained. They also extend a technique developed earlier for finding near-optimal biasing parameters for link simulations to discrete-event simulations of queuing systems. The combination of these techniques was demonstrated by estimating blocking probabilities for the M/M/1/K, M/D/1/K, and GI/D/1/K queues. Improvement factors of thirteen to fourteen orders of magnitude were obtained for these examples