RESTART simulation of networks of queues with Erlang service times

RESTART is an accelerated simulation technique that allows the evaluation of low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. These regions are defined by means of a function of the system state called the importance function. Guidelines for obtaining suitable importance functions and formulas for the importance function of general Jackson networks were provided in previous papers. In this paper, we study networks with Erlang service times and with the rare set defined as the number of customers in a target node exceeding a predefined threshold. The coefficients of the importance functions used here are the same as those obtained with the formula for Jackson networks but multiplied by a constant obtained heuristically. Low probabilities are accurately estimated for different network topologies within short computational time.