A quick simulation method for excessive backlogs in networks of queues

The authors consider stable open Jackson networks and study the rare events of excessive backlogs. Although these events occur rarely, they can be critical, since they can impair the functioning of the network. The authors attempt to estimate the probabilities of these events by simulations. Since a direct simulation of a rare event takes a very long time, this procedure is very costly. Instead, the authors devise a method for changing the network to speed up simulations of rare events. They try to pursue this idea with the help of large deviation theory. This approach, under certain assumptions, results in a system of differential equations which may be difficult to solve. To circumvent this, the authors develop a heuristic method which gives the rule for changing the network for the purpose of simulations. They illustrate, by examples, that the present method of simulation can be several orders of magnitude faster than direct simulations.