Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks

In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies

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.\u

Efficient Heuristics for Simulating Population Overflow in Parallel Networks

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 costly optimization involved in other recently proposed adaptive algorithms. Preliminary results from simulations of networks with up to 4 parallel queues and different traffic intensities yield asymptotically efficient estimates (with relative error increasing sublinearly in the overflow level) where state-independent importance sampling is ineffective.\u

Efficient Importance Sampling Heuristics for the Simulation of Population Overflow in Feed-Forward Queueing Networks

In this paper we propose a state-dependent importance sampling heuristic to estimate the probability of population overflow in feed-forward networks. This heuristic attempts to approximate the “optimal” state-dependent change of measure without the need for difficult analysis or costly optimization involved in other recently proposed adaptive importance sampling algorithms. Preliminary simulation experiments with a 4-node feed-forward network yield asymptotically efficient estimates, with relative error increasing at most linearly in the overflow level, where state-independent importance sampling is demonstrably ineffective.\u