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

Authors:
D. I. Miretskiy;W. R. W. Scheinhardt;M. R. H. Mandjes
Affiliations:
University of Twente, The Netherlands;University of Twente, The Netherlands;The University of Amsterdam, The Netherlands
Venue:
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Year:
2008

Citing 8
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Abstract

This paper considers importance sampling as a tool for rare-event simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson two-node 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 importance-sampling 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 large-deviations theory. (iii) Our method for proving asymptotic efficiency is substantially more straightforward than some that have been used earlier.