Large Deviations and Importance Sampling for a Feed-forward Network
Dr. Leila Setayeshgar
University of Southern California
Department of Mathematics
Friday, February 8, 2013
Shelby Center Room 218
Queuing networks arise in many application areas including, but not limited to, communications, telecommunications, and ethernet design and their analysis leads to a better understanding of such systems. In this talk, we begin by considering a d-dimensional feed-forward network with a priority service policy. We show that the family of scaled state processes satisfies the sample path large deviations principle, where we employ the weak convergence approach. We then restrict our attention to the two-dimensional network, and explicitly identify the exponential decay rate of the probability a rare event, namely, the total population overflow associated to the network. Finally, we use importance sampling – an efficient rare event simulation technique – to estimate the probability of interest. We conclude by confirming our theoretical results with numerical simulations. (This is joint work with Prof. Hui Wang).