Shumska A. Fast Simulation of Rare Events in Different Load Conditions of a Queueing System.

The thesis is devoted to the developing of new efficient fast simulation methods for the evaluation of nonstationary and stationary probability characteristics of queueing systems in case when system behaviour can't be described by Markov or semi-Markov process with a countable state space. A fast simulation method for the evaluation of the unavailability of a repairable system consisting of components with significantly different reliabilities is proposed. Application of importance sampling and stratified sampling enables to decrease the variance of the estimate two orders of magnitude and more. The unbiasedness of estimate and the boundedness of coefficient of variation are proved both for exponential distributed failure-free operation times of components and for distributions of a general form. A multiserver queueing system with recurrent input flows is considered. A fast simulation method for the evaluation of the steady-state loss probability is proposed. Estimates are asymptotically unbiased. A queueing system with infinite number of servers and batch arrival process controlled by a semi-Markov process is investigated. A fast simulation method for the evaluation of the steady-state distribution of the number of customers is proposed. The asymptotic unbiasedness of estimates is proved. Key words: queueing system, unavailability, importance sampling, stratified sampling, variance, unbiased estimate, coefficient of variation, recurrent flow, steady-state distribution.