Efficient Estimation of the Mean Hitting Time to a Set of a Regenerative System

Marvin K Nakayama (1) , Bruno Tuffin (2)

1 NJIT - New Jersey Institute of Technology [Newark]
2 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS

We consider using simulation to estimate the mean hitting time to a set of states in a regenerative process. A classical simulation estimator is based on a ratio representation of the mean hitting time, using crude simulation to estimate the numerator and importance sampling to handle the denominator , which corresponds to a rare event. But the estimator of the numerator can be inefficient when paths to the set are very long. We thus introduce a new estimator that expresses the numerator as a sum of two terms to be estimated separately. We provide theoretical analysis of a simple example showing that the new estimator can have much better behavior than the classical estimator. Numerical results further illustrate this.

Domaines: Recherche opérationnelle [math.OC]

Marvin K Nakayama, Bruno Tuffin. Efficient Estimation of the Mean Hitting Time to a Set of a Regenerative System. WSC 2019 - Winter Simulation Conference, Dec 2019, National Harbor, United States. pp.1-14. ⟨hal-02155409⟩