Titlebook: Kronecker Modeling and Analysis of Multidimensional Markovian Systems; Tuğrul Dayar Book 2018 Springer Nature Switzerland AG 2018 Multi-di

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ethereal

,Vector–Kronecker Product Multiplication,The basic operation underlying iterative analysis of multidimensionalCTMCs withgenerator matrices represented using sums ofKronecker products isvector–Kronecker product multiplication. Therein, the challenge is to perform this operation in as little of memory and as fast as possible.

虚假

Steady-State Analysis,Classical. for the solution of a linear system of equations as in (.) start with aninitial approximation. At each iteration, they modify the entries of the current approximation in a particular way to obtain a new approximation with the objective that the approximations eventuallyconverge to the true solution [., .].

表示问

Transient Analysis,Transient analysis fors MCs refers to computing the probability distribution at a particular time instant starting from an initial probability distribution. As such, steady state need not exist to carry out transient analysis, and the more interesting problem formulation turns out to be related to CTMCs.

起来了

1431-8598 -follow manner the Kronecker structure associated with the t.This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product st

热心

Book 2018usly published book .Analyzing Markov Chains using Kronecker Products .(Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics..

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漂泊

Book 2018rticular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided

Fillet,Filet

Introduction,ones, satisfying Markovian assumptions. Such systems are often composed of multiple subsystems that interact through various transitions in a well-defined manner. In this setting, the modeling of the system at hand is typically based on representing the . of each subsystem with what is called a . an

煞费苦心

Avoiding Unreachable States,ubmodels. Assuming that there are . such interacting submodels, the state space of submodel . was denoted by . with . for . = 1, ., ., and . represented the Cartesian product of the submodel state spaces. Because the Cartesian product of multiple submodel state spaces is used in its definition witho