Continuos-time Markov-modulated Chains In Operations Research

Released on by Alexander M Andronov
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  • Continuos-time Markov-modulated Chains In Operations Research Book Detail

  • Author : Alexander M Andronov
  • Release Date : 2024-04-22
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 227
  • ISBN 13 : 9811286175
  • File Size : 21,21 MB
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Continuos-time Markov-modulated Chains In Operations Research by Alexander M Andronov PDF Summary

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.

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Discrete-Time Markov Chains

Discrete-Time Markov Chains

File Size : 13,13 MB
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Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from exi