Time-Sensitive Importance Splitting

2025-06-24

AI Summary

To address the challenges of prior temporal knowledge dependency and inefficient rare-event simulation in non-Markovian models, this paper proposes a time-sensitive importance splitting method. The method integrates backward reachability analysis with timer-bound inference to construct a time-aware importance function that requires no a priori knowledge of the system’s full behavior—marking the first incorporation of timing information directly into the importance splitting framework. A prototype tool supporting input/output stochastic automata is implemented within the Modest Toolset. Evaluation on reliability engineering case studies demonstrates that, compared to conventional approaches, the method achieves a 10- to 100-fold improvement in estimation efficiency for rare-event probabilities, while reducing relative error by 30–60%. This significantly enhances the accuracy, robustness, and practicality of rare-event simulation for non-Markovian systems.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Security and Privacy: Large-scale security measurements

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.

Problem

• Simulating rare events in non-Markovian models efficiently
• Overcoming limits of prior knowledge on timed behavior
• Estimating rare event probabilities in reliability engineering

Innovation

• Time-sensitive importance function extension
• Backwards reachability search with timer bounds
• Prototype for input/output stochastic automata