Optimal splitting for rare-event simulation

Efficient simulation of blackout probabilities using splitting

“…Although the method is not technically optimal, it performs better than the equal-allocation rule for the examples in this paper (Sections 4 and 5). For other technical conditions and implementation issues, see Shortle et al [22]. One slight modification here is that, as a warmup period, an equalallocation scheme is used until at least one occurrence of the rare-event is observed, then the modified-allocation scheme is used.…”

“…Our implementation is an iterative variation of fixedeffort splitting. It works as follows (see also [22]). Let A 0 denote a set of possible starting states.…”

“…The rule in (6) is an iterative implementation of an optimal allocation rule given in Shortle et al [22]. The optimality of the rule was derived under the assumption that the probability of advancing from level j À 1 to j does not depend on the starting state in A jÀ1 .…”

“…Modified allocation [22]. Following the completion of each stage run, determine the index j that maximizes:…”

“…The choice of the level function may be less critical than the locations of the levels. In most cases, a modified-allocation splitting scheme [22] gives an improvement over a standard equal-allocation splitting scheme.…”