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Continuous-Time Markov-Modulated Chains in Operations Research
by 作者: Alexander Andronov (Author), Kristina Mahareva (Author)
Publisher Finelybook 出版社: World Scientific Publishing Company
Publication Date 出版日期: 2024-04-22
Language 语言: English
pages 页数: : 228 pages
ISBN-10 书号: 9811286159
ISBN-13 书号: 9789811286155
Book Description
Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
