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This paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution. This uncertainty description is a natural extension to the case of stochastic uncertain systems, of the sum quadratic(More)
Generalized processor sharing has been proposed as a policy for distributing processing in a fair manner between diierent data classes in high-speed networks. In this paper we show how recent results on the Skorokhod Problem can be used to construct and analyze the mapping that takes the input processes into the buuer content. More precisely, we show how to(More)
The solution to the Skorokhod Problem de nes a deterministic mapping, referred to as the Skorokhod Map, that takes unconstrained paths to paths that are con ned to live within a given domainG IRn. Given a set of allowed constraint directions for each point of @G, the solution to the Skorokhod Problem de nes the constrained version of , where the(More)
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. For random variables with heavy tails there is little consensus on how to choose the change of measure used in importance sampling. In this article we study dynamic importance sampling schemes for sums of independent and identically(More)