Analytical computation of Markov chain using Padé approximations

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Abstract

The transient analysis of finite-state, continuous-time Markov chains is determined using Padé approximations in the complex plane. Many applications are required to provide interruption-free service for long missions. For these systems, the probability that a system operates without failure during some interval is of interest. We will consider the general problem of finding the state probability vector of a discrete-state, continuous-time Markov chain. We employ Padé approximation as our analytical tool to determine the state probabilities.

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    †

    Hamidreza Amindavar received the B.S.E.E. degree, the M.S.E.E. degree, the M.S. in applied mathematics and the Ph.D. in electrical engineering from The University of Washington, Seattle. Currently, he serves as a teaching consultant for the professional engineering review company in Seattle. His research interests include operations research, fault tolerant computing, radar signal processing and numerical analysis.

    §

    Arun K. Somani received the B.E. degree from the B.I.T.S., Pilanj, Raj., India, the MTech degree from the I.I.T., New Delhi, India, and the M.S.E.E. and the Ph.D. degrees in electrical engineering from McGill University, Montreal. He is currently an Associate Professor in the Department of Electrical Engineering and the Department of Computer Science and Engineering at the University of Washington, Seattle. Professor Somani's research interests are in the areas of theory and practice of fault tolerant computing, parallel computer system, interconnection networks, computer architecture, and VLSI systems.

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