Mathematical Modeling of Main Classes of Stochastic Productive Systems

Abstract

Introduction. The article deals with mathematical models of two main classes of processes in stochastic productive systems. For a multistage system, conditions of belonging to a “just-in-time” class or a class with infinite support of the time distribution function for productive operations are determined. Materials and Methods. Descriptions and investigations of models are carried out by trajectory (martingale) methods. For “just-in-time” systems and multistage stochastic productive systems, terms and methods of random walks in a random environment and birth and death processes are used. The results are formulated as descriptions of intensity characteristics of equalizers of point counting processes. Results. Two theorems are given and proved; they justify the proposed classification of the mathematical models of productive systems. The criteria of the belonging of the stochastic productive system to the class “just-in-time” are given. A theorem on the incompatibility of groups of “just-in-time” systems and systems infinite support of the time distribution for operations is proved. Discussion and Conclusion. The results show the feasibility of analyzing stochastic productive systems by martingale methods. The descriptions of terms of intensities of the equalizers time of productive processes admit generalization.