Large Deviations for a Feed-forward Network & Importance Sampling for a Single Server Priority Queue

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Overview

Title
Large Deviations for a Feed-forward Network & Importance Sampling for a Single Server Priority Queue
Contributors
Setayeshgar, Leila (creator)
Wang, Hui (Director)
Blanchet, Jose (Reader)
Holmer, Justin (Reader)
Ramanan, Kavita (Reader)
Brown University. Applied Mathematics (sponsor)
Doi
10.7301/Z0QC01TJ
Copyright Date
2012
Abstract
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.
Keywords
Weak Convergence
Discontinuous Dynamics
Large deviations
Notes
Thesis (Ph.D. -- Brown University (2012)
Extent
viii, 85 p.

Citation

Setayeshgar, Leila, "Large Deviations for a Feed-forward Network & Importance Sampling for a Single Server Priority Queue" (2012). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.7301/Z0QC01TJ

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