This paper presents models, algorithms and analysis for measurement-based admission control in network applications in which there is high uncertainty concerning source statistics. In the process it extends and unifies several recent approaches to admission control. A new class of algorithms is introduced based on results concerning Markov's canonical distributions. In addition, a new model is developed for the evolution of the number of flows in the admission control system. Performance evaluation is done through both analysis and simulation. Results show that the proposed algorithms minimize buffer-overflow probability among the class of all moment-consistent algorithms

A robust hypothesis testing framework is introduced in which candidate hypotheses are characterized by moment classes. It is shown that there exists a test sequence that is asymptotically optimal in the min-max sense, and that it is expressed as a comparison of a log-linear combination of the constraint functions to a predetermined threshold.

Many problems in information theory can be distilled to an optimization problem over a space of probability distributions. The most important examples are in communication theory, where it is necessary to maximize mutual information in order to compute channel capacity, and the classical hypothesis testing problem in which an optimal test is based on the maximization of divergence. Two general classes of optimization problems are considered in this paper: convex and linear programs, where the constraint set is defined by a finite number of moment constraints.