Quick Simulation of Excessive Backlogs in Networks of Queues

Abstract

We 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. We attempt to estimate the probability of these events by simulations. Since, the direct simulation of rare events takes a very long time, this procedure is very costly. Instead, we devise a method for changing the network to speed up the simulation of rare events. We 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, we develop a heuristic method which gives the rule for changing the network for the purpose of simulations. We illustrate, by examples, that our method of simulations can be several orders of magnitude faster than direct simulations.

This research was supposed in pan by NSF Grant No. ECS. 8421128 and by Pacific Bell and a MICRO Grant from the state of California.