Modeling of systems with a closed loop of material resources circulation

Abstract

The work is devoted to the problem of artificial realization of the unique property of living systems to self-recovery due to the existence in them of mechanisms of accumulation and closed circulation of material resources. The problem of developing a mathematical model that reproduces the processes of functioning of such systems is being solved. A functional diagram of these processes is built, in which the stages of active use of resources, their recovery and subsequent accumulation as a reserve are highlighted. The formal description of the system is made in the class of stochastic models with continuous time – in the form of a Markov process with a discrete set of states. Analytical expressions for the final probabilities of each of its states were found on the basis of the hypothesis of the Poisson character of event streams in the system. As an assessment of the system’s ability to self-recovery, the probability of its functioning with the maximum amount of resources capable of being processed by the system was calculated. Using a numerical example, a quantitative study of the dependence of this estimate on the main variable parameters of the closed-loop system was carried out: the number of recovery channels, the intensity of these channels, and the amount of resources accumulated in the reserve. The presence of an accumulated stock of resources in the system allows ensuring high indicators of its efficiency with a significant decrease in the requirements for the total intensity of resource recovery.