Fast Simulation of Rare Events Using Reverse-Time Models

W e consider the estimation by simulation of probabilities of rare but potentially damaging events i n Markovian systems. The problem is that the rarity of the event mitigates against its frequent occurence in simulation. Here we show how a reverse-time model m a y be simulated in place of the fonuard-time system in order to provide significantly faster estimates of the rare probabilities. A n example of an ALOHA system will be used and simulation speed up compared with alternative methods based on Large Deviations theory.