Simulation of Rare Event in Queueing Systems

Abstract The paper is devoted on computer simulation of rare event probability, which is a critical issue in areas such as reliabilities, telecommunications, aircraft management, etc. This means that it is necessary to evaluate probabilityties less than 10-9, which is unreasonable to be simulated with standard Monte Carlo approach. M/M/1/N queuing system and tandem queuing system are under investigation where the overflow probabilities are estimated with rare event simulation. For queuing systems performance were used discrete-time Markov chains models. An algorithm with RESTART approach and Limited Relative Error was developed to speed-up the rare event simulation. This algorithm has been successfully applied to M/M/1/N queuing system and tandem queuing system. Simulation results for two servers tandem queuing system with Poisson arrival and service rates are shown