The principal investigator studies theoretical and computational problems involving Markov chains, stochastic matrices, and their applications. He examines the sensitivity of the Perron eigenvector of a stochastic matrix, develops efficient methods to compute that eigenvector, and studies the structure of stochastic matrices and their related Markov chains. Computational methods include algorithms suitable for parallel processors. Stochastic matrices and Markov chains arise naturally in the formulation of problems in a broad variety of areas in engineering, economics, operations research, and the physical and social sciences -- for example, in econometric models and in scheduling problems where the clients to be served arrive in random fashion. When cast in the form of a system of equations, many such problems have features that correspond to the eigenvectors of the system.
