Development of a Systematic Approach and Mathematical Support for the Evacuation Process

In modern conditions, due to the vastness of the territory of Kazakhstan, with a certain probability, natural disasters such as earthquakes, floods, avalanches, as well as accidents, destruction of buildings, epidemics, release of chemical toxic substances at industrial enterprises, fires in educational and medical institutions are possible, which justifies the relevance of modern methods and technologies for solving the problem of evacuation. The peculiarity of this work lies in the formation of an integrated approach for organizing the evacuation process both in peacetime as training for the event of an emergency situation (emergency), and in the event of the emergency itself. A conceptual diagram of an evacuation system is proposed that uses heterogeneous sources for receiving and transmitting information about the onset of an emergency. The input and output sources for receiving and transmitting information about the number of people in the building are determined. The main purpose of the system is to form an operational real-time evacuation plan. This work is the result of a phased implementation of an integrated evacuation system, which consists in building a mathematical model and a method for solving the problem of maximum flow in the network. A mathematical model has been developed for the optimal flow distribution along the Grindshiels network with the analysis of the flow formation and the characteristics of people’s motion in enclosed spaces. A game-theoretic approach and mathematical methods of the theory of hydraulic networks for finding an equilibrium state in flow-distribution networks have been developed. An algorithm for solving the evacuation problem using the graph approach is proposed. The results of this paper make it possible to systematically organize training evacuations, prepare resources, train the personnel responsible for evacuation in order to quickly respond in an emergency and carry out the evacuation process in order to avoid major consequences.