Algorithms for forming the coefficient matrix of a system of differential equations Chapman-Kolmogorov models of non-stationary service systems

Abstract The paper considers a new approach to building models of nonstationary service systems based on: the formation of all possible states of a nonstationary service system with a finite number of applications and rules of transition between them; the formation of the coefficient matrix of Chapman-Kolmogorov differential equation system; the numbering procedure for all states. A critical analysis is made of the algorithms for the formation of the coefficient matrix and the numbering procedure for all states: sequential, recursive and recursive with grouping. Its comparison with the recursive algorithm is given, as well as the optimal structure for storing the list of states for the sequential algorithm. Recommendations for the practical application of software implementations of the considered algorithms are discussed. Theoretical foundations for building and calculating models of nonstationary service systems have been developed. It is compared to the recursive algorithm. The optimal structure for storing the list of states for a sequential algorithm is given.

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