Abstract
We consider importance sampling simulation for estimating the probability of reaching large total number of customers in an [Formula: see text] tandem queue, during a busy cycle of the system. Our main result is a procedure for obtaining a family of asymptotically efficient changes of measure based on subsolutions. We explicitly show these families for two-node tandem queues and we find that there exist more asymptotically efficient changes of measure based on subsolutions than currently available in literature.
Highlights
In this paper, we explore possibilities for importance sampling in a Markovian tandem queue
We give sufficient conditions for an asymptotically efficient change of measure based on subsolutions for the MjMj1 tandem queue
After summarizing the subsolution method for importance sampling and stating the results from Dupuis et al.[4] and Dupuis and Wang[6] in Section 2, our first contribution is in Section 3, where we state conditions for a change of measure for the d-node MjMj1 tandem queue based on subsolutions to give an asymptotically efficient estimator, and we prove that these conditions are sufficient for d = 2
Summary
We explore possibilities for importance sampling in a Markovian tandem queue. Afterwards, in Glasserman and Kou,[2] necessary and sufficient conditions have been determined for d-node MjMj1 tandem queues in order for the same change of measure to be asymptotically efficient (which means that the relative error of the estimator grows less than exponentially fast) These conditions have been extended in the work of de Boer[3] for the case d = 2 and, in that paper, it has been shown that the change of measure from Parekh and Walrand[1] is the only state-independent change of measure that may be asymptotically efficient when d = 2. After summarizing the subsolution method for importance sampling and stating the results from Dupuis et al.[4] and Dupuis and Wang[6] in Section 2, our first contribution is, where we state conditions for a change of measure for the d-node MjMj1 tandem queue based on subsolutions to give an asymptotically efficient estimator, and we prove that these conditions are sufficient for d = 2. We both consider m2 4 m1 and m1 4 m2
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