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A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing, and the cost is a cumulative discounted functional of the system’s state. We examine two versions of the problem:(More)
We study the a.s. exponential stability of the optimal lter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the lter) for a general setting both in discrete and in continuous time, in terms of Birkhoo's contraction coeecient. Criteria for exponential stability and explicit bounds on the rate(More)
This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers working in parallel, grouped in several stations. Servers in different stations offer service to customers of each class at(More)
Let be a nonnegative random variable and let the conditional distribution of a random variable , given , be Poisson , for a parameter . We identify a natural loss function such that: (1) the derivative of the mutual information between and with respect to is equal to the minimum mean loss in estimating based on , regardless of the distribution of ; (2) when(More)
By Rami Atar, Amarjit Budhiraja and Paul Dupuis Technion-Israel Institute of Technology, University of North Carolina at Chapel Hill and Brown University Let G ⊂ IRk be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {Gi, i = 1, · · · , N}, where ni and di denote the inward normal and direction of constraint(More)
We extend the duality between exponential integrals and relative entropy to a variational formula for exponential integrals involving the Rényi divergence. This formula characterizes the dependence of risk-sensitive functionals to perturbations in the underlying distribution. It also shows that perturbations of related quantities determined by tail(More)
We propose to study the sensitivity of the optimal lter to its initialization, by looking at the distance between two di erently initialized ltering processes in terms of the ratio between two simple FeynmanKac integrals in the product space. We illustrate, by considering two simple examples, how this approach may be employed to study the asymptotic decay(More)
In this appendix to “A diffusion regime with non-degenerate slowdown”, Op. Res. (2012), we provide the proofs of the main results. Theorem 2.1 is proved in Subsection A.1 and Theorem 2.2 in Subsection A.2. For the notation used in this appendix, see the end of Section 1 of the main body of the paper. Equation and theorem numbers, such as (1), (2),...,(More)