An efficient importance sampling method for rare event simulation in large scale tandem networks

In this paper, we present a variance minimization (VM) procedure for rare event simulation in tandem queueing networks. We prove that the VM method can produce a zero variance. The VM method is suitable to compute optimal importance sampling (IS) parameters for small scale tandem networks. For large scale tandem networks we propose a sub-optimal IS (SOIS) method, which projects the optimal biased transition probabilities of the corresponding small scale system into those of a large scale system. In other words, we establish an efficient IS method for a large scale system by zooming into a small scale system and then projecting our findings into the large scale system. The numerical results show that our SOIS method can produce accurate results with very short CPU time, while many other methods often require much longer.