Rare Events in a Network

WB26.1 Asymptotically Optimal Importance Sampling & Stratification for Gaussian Intergrals, with Applications to Option Pricing Paul Glasserman, Philip Heidelberger, Perwez Shahabuddin --- Columbia Univ., Bus. Sch., 403 Uris Hall, New York, NY 10027 , (pglasser@research.gsb.columbia.edu)

We use a Laplace principle to identify the asymptotically optimal change of drift for importance sampling applied to functions of Gaussian vectors. The change of drift eliminates the linear part of the log of the integrand. Stratification reduces variance from the quadratic part. We identify the optimal direction for stratification and a surprising connection with the optimal drift. We apply the method to pricing path-dependent options.

WB26.2 Join the Shortest Queue Systems: Stability & Exact Asymptotics Robert D. Foley, David R. McDonald --- GA Inst. of Tech., Sch. of ISyE, 765 Ferst Dr., Atlanta, GA 30332-0205, (rfoley@isye.gatech.edu)

WB26.3 A Unified Approach to Fast Teller Queues an ATM David R. McDonald, Beno Beck, Andre Dabrowski --- Univ. of Ottawa, Dept. of Math. & Stats., 585 King Edward Ave., Ottawa, Ontario, , Canada K1N 6N5 (dmdsg@omid.mathstat.uottawa.ca)

We consider a model with $A$ independent sources of customers where each source is modeled by a Markov renewal point process with batch arrivals. We do not assume the sources are necessarily identically distributed. These arrivals join a queue served by multiple independent servers with service times modeled also as a Markov renewal process...