Importance sampling, jump distributions and event-time distributions

Two different methods have been proposed for performing asymptotically optimal simulation to obtain the statistics of buffer overflows in queueing networks, with both using large deviations and importance sampling. In the first, based on heuristic arguments, the distributions of interarrival and virtual service times are analyzed to find the simulation system. In the second, it is the distribution of jumps occurring in a Markov chain that is examined. The authors show that the approaches produce identical fast simulation systems for an arbitrary G1/G1/1 queue