Fluid Heuristics, Lyapunov Bounds and Efficient Importance Sampling for a Heavy-tailed G/G/1 Queue (with P. Glynn and J. C. Liu)

Summary:

This can be seen as a follow up work on Blanchet and Glynn (2008) Ann. of Appl. Probab. 18, 1351-1378. In this paper we concentrate only on regularly varying distributions but make a precise connection between fluid heuristics, which are often used to guess heuristically heavy-tailed large deviations results, and the construction of suitable Lyapunov bounds for importance sampling estimators. The output is that rigorous verification of the Lyapunov bound not only validates the fluid heuristic, but also provides an efficient simulation procedure for rare-event analysis.

Bibtex:

@Article{BGL07Questa,

author = {J. Blanchet and P. Glynn, and J. C. Liu.},

title = {Fluid heuristics, Lyapunov bounds and efficient importance sampling

for a heavy-tailed G/G/1 queue.},

journal = {QUESTA},

year = {2007},

volume = {57},

pages = {99-113}

}