RESEARCH ABSORBING STATES OF THE SYSTEM USING MARKOV CHAINS AND FUNDAMENTAL MATRIX

Abstract

The article discusses the use Markov chains to research models that reflect the essential properties of systems, including methods of measuring the parameters of projects and assess their effectiveness. In the study carried out by its decomposition system for certain discrete state and create a diagram of transitions between these states. Specificity displays various objects Markov homogeneous chains with discrete states and discrete time determined by the method of calculation of transition probabilities. A model of success criteria for absorbing state system that is universal for all projects. A breakdown of passages to the matrix submatrices. The variation elements under matrix Q n with growth linked to the definition of important quantitative characteristics of absorbing circuits: 1) the probability of achieving the status of absorbing any given; 2) the mean number of steps needed to achieve the absorbing state; 3) the mean time that the system spends in each state to hit irreversible system in absorbing state. Built fundamental matrix that allowed calculating the different characteristics of the system. Considered fundamental matrix for supposedly modeled absorbing Markov chain, which gives the forecast for the behavior of the system in the future regardless of the absolute value of the time elapsed from the starting point. This property illustrates the fundamental matrix Markov process that characterizes it as a process without aftereffect.