Importance sampling for Jackson networks with customer impatience until the end of service

Abstract

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. The standard approach, which simulates the system using an a priori fixed change of measure, has been shown to fail in even the simplest network settings. Estimating probabilities associated with rare events has been a topic of great importance in queuing theory, and in applied probability at large. In this paper, we estimate the probability of two rare events known as total population overflow and individual buffer overflow in an open Jackson network in which the customers should receive the needed service in a definite deadline. we use parallel computing in implementing the estimator. Moreover, we consider the effect of various network parameters on aforementioned overflow probabilities, and we have also shown that how these parameters affect the probability of missing the deadline.