Titlebook: Computations with Markov Chains; Proceedings of the 2 William J. Stewart Conference proceedings 1995 Springer Science+Business Media New Yo

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On Cyclic Reduction Applied to a Class of Toeplitz-Like Matrices Arising in Queueing Problems, we devise a fast algorithm for computing the probability invariant vector of stochastic matrices of a wide class of Toeplitz-like matrices arising in queueing problems. We prove that for any block Toeplitz matrix . in block Hessenberg form it is possible to carry out the cyclic reduction algorithm

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A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue, than the service rate. The system therefore may oscillate between stable and unstable modes of behaviour. We investigate the limiting distribution as the expected sojourn times in the various environments increase to infinity. We show that the limiting behaviour of the stationary distribution is si

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Preconditioned Krylov Subspace Methods for the Numerical Solution of Markov Chains,ularly successful class of techniques based on this principle is that of Krylov subspace methods which utilise subspaces of the form span{., A.,…., A..}. This general principle can be used to solve linear systems and eigenvalue problems which arise when computing stationary probability distributions

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A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains, for solving large chains thanks to their potential for parallel computation and robustness. We show that the block Cimmino method is particularly well-suited if the chain is nearly uncoupled, a condition which is often met in the applications. This is due to the favorable spectral distribution of t

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Iterative Methods for Queueing Models with Batch Arrivals,jugate gradient (PCG) method. The preconditioners are constructed by exploiting the near-Toeplitz structure of the generator matrix of the model and are products of circulant matrices and band-Toeplitz matrices. We prove that if the number of servers . is fixed independent of the queue size n, then

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Transient Solutions of Markov Processes by Krylov Subspaces,olution of continuous time Markov processes. We consider the Krylov subspace approximation method which has been analysed by Gallopoulos and Saad for solving partial differential equations and linear ordinary differential equations [., .]. We place special emphasis on error bounds and stepsize contr

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