Robust bounds and optimization at the large deviations scale for queueing models via Rényi divergence

Large Deviations and Queueing Networks : Methods for

Queueing Models for Large Scale Call Centers

To my parents and grandparents... iii ACKNOWLEDGEMENTS I am indebted to many people for their help and support during my graduate studies. This thesis would not have been possible without them. First and foremost, I would like to thank my advisors Jim Dai and Amy Ward. I would like to thank Dr. Ward for serving as my principal advisor for the first half of my Ph.D. studies. Dr. Ward provided me...

Large deviations in queueing networks

In this paper we describe how the joint large deviation properties of traac streams are altered when the traac passes through a shared buuer according to a FCFS service policy with stochastic service capacity. We also consider the stationary case, proving large deviation principles for the state of the system in equilibrium and for departures from an equilibrium system.

Sharper Bounds in Lattice-Based Cryptography Using the Rényi Divergence

The Rényi divergence is a measure of divergence between distributions. It has recently found several applications in lattice-based cryptography. The contribution of this paper is twofold. First, we give theoretic results which renders it more efficient and easier to use. This is done by providing two lemmas, which give tight bounds in very common situations – for distributions that are tailcut ...

Large deviations bounds for estimating conditional value-at-risk

In this paper, we prove an exponential rate of convergence result for a common estimator of conditional value-at-risk for bounded random variables. The bound on optimistic deviations is tighter while the bound on pessimistic deviations is more general and applies to a broader class of convex risk measures. © 2007 Elsevier B.V. All rights reserved.