Efficient simulation of population overflow in parallel queues

In this paper we propose a state-dependent importance sampling heuristic to estimate the probability of population overflow in networks of parallel queues. This heuristic approximates the "optimal" state-dependent change of measure without the need for difficult mathematical analysis or costly optimization involved in adaptive methodologies. Comprehensive simulations of networks with an arbitrary number of parallel queues and different traffic intensities yield asymptotically efficient estimates (with relative error increasing sub-linearly in the overflow level) where no other state-independent importance sampling techniques are known to be efficient. The efficiency of the proposed heuristic surpasses those based on adaptive importance sampling algorithms, yet it is easier to determine and implement and scales better for large networks.