Large Deviations for a Feed-forward Network & Importance Sampling for a Single Server Priority Queue Setayeshgar, Leila creator 2012 viii, 85 p. born digital Thesis (Ph.D. -- Brown University (2012) Wang, Hui Director Blanchet, Jose Reader Holmer, Justin Reader Ramanan, Kavita Reader Brown University. Applied Mathematics sponsor theses This thesis considers a feed-forward network with a single server station serving jobs with multiple levels of priority. The service discipline is preemptive in that the server always serves a job with the current highest priority level. For this system with discontinuous dynamics, we show that the family of scaled state processes satisfy the sample path large deviations principle using a weak convergence argument. In the special case where the jobs have two different levels of priority, we explicitly identify the exponential decay rate of the probability a rare event, namely, the “total population overflow” associated to the feed-forward network. We then use importance sampling -- a variance reduction technique -- efficient for rare event probabilities to simulate the exact probability of interest. The thesis concludes by numerical simulations which confirm our theory. Weak Convergence Discontinuous Dynamics Large deviations RPB 20121023 engEnglish10.7301/Z0QC01TJIn CopyrightCollection is open for research.dissertations