## Computations with Markov Chains: Proceedings of the 2nd International Workshop on the Numerical Solution of Markov ChainsComputations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers. |

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### Contents

Transient Colutions of Markov Processes by Krylov | 7 |

On Cyclic Reduction Applied to a Class | 21 |

A Markov Modulated Nearly Completely | 39 |

Copyright | |

26 other sections not shown

### Other editions - View all

Computations with Markov Chains: Proceedings of the 2nd International ... William J. Stewart No preview available - 2012 |

### Common terms and phrases

aggregation algebra applied approach approximation arrival process assume automata batch block GI/M/1 block M/G/l form block Toeplitz bound buffer calculated coefficients complexity components computation consider convergence corresponding CRAY T3D CTMC cyclic reduction defined denote derived diagonal digraph dimension DSPN DTMC eigenvalues eigenvector elements enabled entries equations equivalent error example exponential exponentially distributed factorization finite firing function Gaussian elimination GI/M/1 or block given graph Hence implementation initial input isomorphism iterative methods Krylov subspace linear systems lumpability M-matrix Markov chain Markov process Markovian matrix exponential MRSPN multiple obtained operations parameters partition performance Petri Nets Poisson polynomial preconditioned preconditioner probability vector problem queue reachable recursive requires server SIAM SMCs solving sources space steady-state distribution step stochastic matrix stochastic Petri nets stochastic process structure techniques Theorem Toeplitz matrix transient analysis transition matrix transition rate triangular values zero