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Tugrul Dayar's Analyzing markov chains using kronecker products : theory PDF

By Tugrul Dayar

ISBN-10: 1461441900

ISBN-13: 9781461441908

Creation -- Preliminaries -- Iterative tools -- Decompositional equipment -- Matrix-Analytic equipment -- Conclusion.653Computer technological know-how

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Extra info for Analyzing markov chains using kronecker products : theory and applications

Example text

L/ /; ! 1 ! l/ ; D ! l/ ; ! 1 ! l/ ; D ! s; s/j; 1/ is the uniformization parameter of the power method and ! 0; 2/ is the relaxation parameter of the BJOR and BSOR methods. Here, forward iteration refers to computing unknowns ordered toward the beginning of the state space earlier than unknowns ordered later in the state space. The power method works at level l D H since it is a point method. Furthermore, BJOR and BSOR reduce to the block Jacobi (BJacobi) and block Gauss–Seidel (BGS) methods for !

1). So far, various preconditioners have been proposed for Kronecker structured representations such as those based on truncated Neumann series [139, 141], the cheap and separable preconditioner [25], circulant preconditioners for a specific class of problem [41], and the Kronecker sum preconditioner [144], which has been shown to work effectively on some small problems. The Kronecker product approximate preconditioner for MCs based on Kronecker products developed in a sequence of papers [98–100], although encouraging, is in the form of a prototype implementation.

Closedness implies that the number of customers circulating in the QN remains constant; there are no arrivals to the network from the outside, there are no departures to the outside, and the number of customers inside the network neither increases nor decreases as a result of the queueing discipline and the service process. A customer departs from a queue after getting service and joins a(nother) queue, possibly the same one it departed from. If a QN is not closed, it is said to be open. Regarding service distributions, hypoexponential, hyperexponential, Coxian, and Erlang are all PH and have rational Laplace transforms.

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Analyzing markov chains using kronecker products : theory and applications by Tugrul Dayar

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