Rate-tilting for fast simulation of level/phase processes Original Research Article

This paper study the efficient simulation methods for estimating some metrics that depend heavily on a certain rarely occurring event. The process considered is the so-called level/phase process, a Markov process in which the “level” and the “phase” are two state variables. Furthermore, changes of level and phase are induced by events, which have rates that are independent of the level except at a “boundary”. If a system typically stays at lower levels, then reaching a high level n is a rare event, thus direct simulation for the related metrics is very inefficient. We change the events rates in a level/phase process to accelerate simulation, and find from simulation the so-called hitting probability: the probability of entering a rare event set. This method is called “rate-tilting”, and in our approach, a proper construct of rate-tilting relates to a generalized eigenvalue problem involving the infinitesimal generator matrix of the process being considered. We can show that the relative estimation error of the hitting probability resulting from the proposed simulation remains bounded as the level increases, provided that the boundary set of the state space satisfies certain conditions. If these conditions are met, rate-tilting will be advantageous.