Simulation of a Jackson tandem network using state-dependent importance sampling

This paper considers importance sampling as a tool for rareevent simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson twonode tandem queue. It is known that in this setting ‘traditional’ state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure that is provably asymptotically efficient. More specific contributions are the following. (i) We concentrate on the probability of the second queue exceeding a certain predefined threshold before the system empties. Importantly, we identify an asymptotically efficient importancesampling distribution for any initial state of the system. (ii) The choice of the importance-sampling distribution is backed up by appealing heuristics that are rooted in largedeviations theory. (iii) Our method for proving asymptotic efficiency is substantially more straightforward than some that have been used earlier.