Two-parameter Sample Path Large Deviations for Infinite Server Queues (with X. Chen and H. Lam).

Summary:

Several authors have written papers on heavy-traffic approximations for the infinite server queue (Glynn and Whitt, Pang and Whitt, Reed and Talreja, Decreusefond and Moyal, etc.). In its more general form the measure-valued process converges to an infinite dimensional Gaussian Ornstein-Uhlenbeck and the strongest weak convergence topologies are the ones considered in the paper of Pang and Whitt. Our result extends the paper by Pang and Whitt by providing a sample-path large deviations result (so the optimal “paths” are described in terms of a PDE). We are able to actually strengthen the topology a tiny bit, and illustrate the use of these results in the context of large deviations for large life insurance portfolios. I believe that there is a more to do on the insurance application side of this result.

Bibtex:

@Article{BlaCheLam_14,

author = { J. Blanchet and X. Chen and H. Lam},

title = {Two-parameter Sample Path Large Deviations for Infinite Server Queues},

journal = {Stochastic Systems},

year = {2014},

volume = {4},

pages = {206-249}

}