Rare events and reverse-time models

Consideration is given to the estimation by simulation of probabilities of rare but potentially damaging events in Markovian systems. The problem is that the rarity of an event prevents its regular occurrence in simulation, and hence very long, time-consuming simulation runs are needed. It is shown how significantly faster estimates of the probabilities of rare events can be found by simulating a reverse-time model in place of the forward-time system. The simulation speedup afforded by simulating with the reverse-time model is compared with that obtained with alternative methods based on large deviations theory, using an uncontrolled Aloha system as an example