Rare-event Simulation for a Slotted Time M/G/s model (with P. Glynn and H. Lam)

Summary:

This paper develops ideas for the rare-event analysis of many server systems. It concentrates on a slotted time model with Poisson arrivals in order to illustrate the main conceptual strategy which should work in a large class of many server queues. The strategy contains three elements: I) The ability of finding a ``distinguished set A’’ that contains difficult boundary behavior and that is NOT a rare set, II) Having access to a free process (free in the sense of not being sensitive to boundary behavior typical of queueing systems) that is coupled with the underlying system under consideration OUTSIDE the set A, III) Being able to do efficient rare-event simulation for such a free process. We apply this strategy to estimating loss probabilities and we can also sample the state of the whole system (which is discrete measured-valued) given the occurrence of loss event within a fixed time horizon. The extension to fully continuous measured-valued processes is the main chapter of the PhD dissertation of my student Henry Lam. The paper can be found in this website as well.

Bibtex:

@Article{BlaGlyLam2009,

author = { J. Blanchet and P. Glynn and H. Lam},

title = {Rare-event simulation for a slotted time M/G/s model},

journal = {QUESTA},

year = {2009},

volume = {63},

pages = {33-57}

}