Computational Methods in Markov Chains

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This project emphasizes practical as well as theoretical aspects surrounding the application and implementation of algorithms for computing stationary probabilities of discrete Markov chains. Special attention is devoted to applications in which discrete models are used to understand and analyze the dynamics of large systems comprised of a collection of loosely coupled subsystems such as in the study of queuing models and networks, telecommunications, computer performance evaluation, stochastic automata networks, and economic modeling and forecasting. Algorithmic facets concern the development and analysis of parallel multilevel methods based on aggregation/disaggregation techniques---both direct and iterative--- and some of these techniques are applied to problems involving stochastic automata networks. An architectural aspect involves the identification of features of vector and parallel computers that are best suited for implementing Markov chain algorithms. Theoretical components involve studying properties of Markov chains. These ideas are then used to generate error analyses aimed at understanding the convergence and stability properties of multilevel aggregation/disaggregation algorithms.