Efficient heuristics for the simulation of population overflow in series and parallel queues

In this paper we propose state-dependent importance sampling heuristics to estimate the probability of population overflow in Markovian networks of series and parallel queues. These heuristics capture state-dependence along the boundaries (when one or more queues are empty) which is critical for the asymptotic optimality of the change of measure. The approach does not require difficult (and often intractable) mathematical analysis or costly optimization involved in adaptive importance sampling methodologies. Experimental results on tandem and parallel networks with a moderate number of nodes yield asymptotically efficient estimates (often with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient. Insight drawn from simulating basic networks in this paper promises the applicability of the proposed methodology to larger networks with more general topologies.