Fast simulation of buffer overflows in tandem networks of GI/GI/1 queues

Simply because of their rarity, the estimation of the statistics of buffer overflows in well-dimensioned queueing networks via direct simulation is extremely costly. One technique that can be used to reduce this cost is importance sampling, and it has been shown previously that large deviations theory can be used in conjunction with importance sampling to minimize the required simulation time. In this paper, we obtain results on the fast simulation of tandem networks of queues, and derive an analytic solution to the problem of finding an optimal simulation system for a class of tandem networks of GI/GI/1 queues.