Quantum simulation - rare event simulation by means of cloning, thinning and distortion

Abstract

Monte Carlo, and Sequential Markov Chain simulation, is applied in this paper to rare event simulation of communication systems. The technique described in this paper generalizes importance sampling, importance splitting and the Monte Carlo method which uses a collection (population) of particles. The term quantum simulation is used for the rare-event simulation technique presented in this paper because the entire ensemble of simulations resembles the parallel universes model of quantum mechanics. By using cloning, thinning and distortion it is possible to design simulations with the speed of importance sampling and the flexibility of importance splitting. A particularly difficult system is investigated in this paper by means of quantum simulation, namely a buffer fed by a Poisson-Pareto Burst Process. The simulations are able to confirm an analytic approximation for this model to a degree not previously achievable. Furthermore, this approximation was originally developed as a consequence of the investigation of this model by means of quantum simulation. Keywords: Poisson-Pareto Burst Process, Long-range dependence, Importance Splitting, Importance Sampling, Quantum Simulation