Time-Sensitive Importance Splitting

TL;DR

This paper introduces a novel time-sensitive importance splitting method that enhances rare event simulation for non-Markovian models by using backwards reachability and timer bounds, improving estimation accuracy.

Contribution

It extends importance splitting with a time-sensitive importance function and a backwards reachability search, addressing limitations of prior methods for non-Markovian models.

Findings

Prototype implementation developed within the Modest Toolset.

Preliminary experiments demonstrate improved rare event probability estimation.

Potential applicability in reliability engineering contexts.

Abstract

State-of-the-art methods for rare event simulation of non-Markovian models face practical or theoretical limits if observing the event of interest requires prior knowledge or information on the timed behavior of the system. In this paper, we attack both limits by extending importance splitting with a time-sensitive importance function. To this end, we perform backwards reachability search from the target states, considering information about the lower and upper bounds of the active timers in order to steer the generation of paths towards the rare event. We have developed a prototype implementation of the approach for input/output stochastic automata within the Modest Toolset. Preliminary experiments show the potential of the approach in estimating rare event probabilities for an example from reliability engineering.