MANAGEMENT IN HIGH-DIMENSIONAL MARKOV SYSTEMS
DOI:
https://doi.org/10.26906/SUNZ.2022.2.027Keywords:
Markov system, calculation of distribution of states, decomposition computational pattern, states probabilities managementAbstract
A problem of analyzing Markov systems along with a large number of states has been considered. The conventional computational procedure for obtaining analytical ratios for calculating the distribution of system states is based on the use of a system of Kolmogorov differential equations. The system of linear algebraic equations being formed later can be easily solved numerically. However, the complexity of obtaining an analytical solution increases rapidly with the increase in the problem dimension. In this regard, the purpose is to develop an effective method for studying Markov systems, the computational procedure of which ensures the possibility of obtaining solutions for high-dimensional models. The method is based on the decomposition of states graph and system transitions. The obtained analytical expressions allow to set and solve the problem of rational resource distribution for changing the values of the system parameters to increase its efficiency. The method ensures the possibility of solving management problems in Markov systems along with a large number of possible states. An example of method application has been considered.Downloads
References
Dynkin E.B. Markov procedures. - M.: Fizmatlit, 1963. – 860 p.
Barucha J., Snell J. Markov procedures theory elements. - M.: Nauka, 1969. – 384 p.
Raskin L.G. Analyzing complex systems and optimal management theory elements. - M.: Sov. Radio, 1976. – 344 p.
Ditkin V.A., Prudkov A.P. Integral transformations and operational calculus. - M.: Nauka, 1974. – 544 p.
Gelfand I.M. Lectures on linear algebra. – M.: Dobrosvet, 1998. – 320 p.
Ivanov V.V. Computing techniques using ECM. - Kiev: Naukova dumka, 1986. – 584 p.
Raskin L.G. Mathematical programming. – Kh.: NTU "KhPI", 2002. – 125 p.
Raskin L.G. Analysis of Markov chains using phase aggregation of states. // Science, equipment, technology, education, health.-Kh.- NTU, 1997.
Raskin L.G., Seraya O.V. Creation of a scalar preference criterion based on the results of pairwise comparisons // Bulletin of NTU of KhPI.-Kh.: NTU of KhPI, 2003, No. 6, pp. 63-68.
