Use of Discrete and Continuous Markov Chains for System Absorbing States

Abstract

The development of mathematical support and the creation on its basis of models that reflect the characteristics of the studied systems of project management is an important task of project management. The paper shows the use of Markov chains and oriented graphs in models of gradation of state of correspondence as the degree of project perfection. In the description of these models, the decomposition of the systems under investigation into certain discrete states is performed and a scheme of transitions between these states is created. The specificity of displaying different objects in homogeneous discrete-state Markov chains with discrete time is determined by the ways of calculating the transition probabilities. The model of success criteria for system absorbing states, whose presence radically changes the nature of the process, is investigated. A breakdown of the matrix to submatrices is carried out. A fundamental matrix was built, which made it possible to calculate different characteristics of the system. A fundamental matrix for a hypothetically simulated Markov absorption chain is considered, which gives the same prediction for the future regardless of the absolute value of the elapsed time. This property of the fundamental matrix illustrates the Markov property of a process, characterizing it as a process without aftereffect.