Analysis and Optimizations of Stochastic Networks

The behavior of a distributed system or a network is subject to many irregularities and stochastic fluctuations. Our success in solving a variety of inference and optimization tasks defined over such systems depends heavily on our ability to adequately model, reason about and learn such a behavior.

Many existing stochastic models for complex systems and algorithms for their probabilistic analysis build upon the assumption of full independence; the condition that permits efficient probabilistic analysis but that is, at the same time, frequently violated in realistic world settings with intricate stochastic dependencies and interactions among components of the system. A simple analysis of real-world network systems (such as power grids, communication or transportation networks) reveals that situations with more failures occurring at the same time are more likely than in the model with failure independence in which an occurrence of a larger number of failures tends to be a very unlikely event. An example is August 2003 power blackout that affected large areas of Eastern USA and involved a cascade of interacting failures. Under the condition of failure independence the probability of such an event would be extremely small. The aim of our work is to develop probabilistic models of stochastic behaviors of complex distributed systems that overcome this difficulty, offer good approximations of true behavior of the system, and at the same time support efficient inferences and learning.

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