Session TB3 (Invited) - Queues and Rare Events Chair and organizer: Ad Ridder in A002 Analysis of a state-independent change of measure for the G/G/1 tandem queue

In 1989, Parekh and Walrand introduced a method to efficiently estimate the probability of a rare event in a single queue or network of queueus. The event they consider is that the total number of customers in the system reaches some level N in a busy cycle. Parekh and Walrand introduce a simple change of measure, which is stateindependent, in order to estimate this probability efficiently using simulation. However, they do not provide any proofs of some kind of efficiency of their method. For the single queue (with mutiple servers) it has been shown by Sadowsky, in 1991, that the change of measure as proposed by Parekh and Walrand is asymptotically efficient under some mild conditions. In this work we study the state-independent change of measure of the G|G|1 tandem queue, along the lines of Parekh and Walrand, and we provide necessary conditions for asymptotic efficiency. To the best of our knowledge, no results on asymptotic effciency for the G|G|1 tandem queue had been obtained previously. Looking at the results for the M |M |1 tandem queue, it is expected that this state-independent change of measure is the only stateindependent change of measure for the G|G|1 tandem queue that can possibly be asymptotically effcient. We show that, under some conditions, it is indeed the only exponential state-independent change of measure that can be asymptotically effcient. However, we have also identified conditions for the two node G|G|1 tandem queue under which the Parekh and Walrand change of measure is still not asymptotically effcient.