Importance sampling simulations of phase-type queues

Importance sampling is a variance reduction technique that is particularly well suited for simulating rare events and, more specifically, estimating rare event probabilities. Properly applied, it often results in tremendous efficiency improvements compared to direct simulation schemes, but it can also yield unbounded variance increase. Its efficiency and robustness critically rely on a suitable change of the underlying probability measure, which is highly model-dependent. In recent years, significant progress greatly broadened the classes of models successfully accessible by importance sampling, but several model classes still require further investigation. We consider importance sampling simulations of finite capacity queues where interarrival and service times are Erlang distributed. A change of measure is proposed and experimentally studied. Numerical results for loss rates due to buffer overflows indicate that the change of measure provides accurate estimates and appears promising for adaptation to other models involving phase-type distributions.