«Automation and Informatization of the fuel and energy complex»

Numerical method for solving the stability problem of income at a finite time interval for homogeneous Markov chain

UDC: 004.052
DOI: -

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: homogeneous Markov chain with rewards, ergodic class of states, matrix of limiting probabilities, stationary characteristics of the chain, average income vector at a finite discrete time interval, stability problem of the average income vector, controlled homogeneous Markov chain

Annotation:

A numerical method ε is presented for solving the problem of the average income vector stability for a homogeneous Markov chain over a finite time interval, where ε is a small parameter tending to zero as the time interval increases. The set of states of the above-mentioned Markov chain is a single ergodic class. Such Markov chains are widely used when modeling various processes in complex energy systems, for example, processes related to determining certain reliability indicators and risk values in main oil and gas pipelines. The main focus is on 1) deriving an analytical expression for the average income vector at a finite time interval and 2) formulating the stability problem of this vector with respect to possible changes of the transition probabilities of the mentioned Markov chain. These transition probabilities changes lie within known bounds, i. e., they have interval estimates. These interval estimates generate a set of average income vectors, on which a partial order is introduced, allowing the formulation of two optimization problems. The solution to these optimization problems is ε-solution to the set stability problem of the income vector at a finite time interval with respect to the considered interval estimates. A numerical method for solving these optimization problems is proposed. An example illustrating the application of this numerical method is provided.

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