О МОДЕЛИРОВАНИИ СЛУЧАЙНЫХ ПРОЦЕССОВ В АГРОПРОМЫШЛЕННОМ КОМПЛЕКСЕ

Abstract

Research was carried out with the aim of mathematical description of random deviations of the incoming flow of raw materials, to justify the necessary rational modes of operation of continuously operating units in the agro-industrial complex. The incoming flow is given by the average value and random deviations in different directions. The intensity of the deviation from the average value up or down can be different. The numerical characteristics of the incoming stream are determined by processing statistical observations. Two tasks are considered separately. In the first, in order to determine the time or cyclicity of response to changes in the incoming flow, their total number is studied. For this, a pure reproduction model was used. On the basis of the constructed model, the numerical values of the probability that by the time t there will be n deviations are calculated. Such a function Pn(t) has its maximum for any value of n. When solving the second problem, it is assumed that deviations of the average value of the incoming flow in different directions can partially or completely compensate for one another. To take into account such features of a random flow, a model of reproduction and death was used. The calculation of the corresponding probabilities is reduced to solving a system of differential equations, taking into account the normalization condition P0+P1+P2+ … Pn=1. Calculations have shown that if the deflection intensities in different directions are equal, the probability graphs Pn(t) have a common time asymptote. Consequently, deviations with the same intensity, having different signs, compensate for one another. If the intensities are not equal, then the probabilities Pn(t) go to their individual asymptotes. This means that the input stream with random deviations takes its stationary state with some reduced rate. The considered mathematical models make it possible to calculate the probabilistic values of the incoming flow parameters and their changes over time. This makes it possible to justify the necessary rational mode of operation of continuously operating units, taking into account random deviations of the incoming flow