Mathematical models and methods for solving the problem of evacuation

Kozbakova A. Kalizhanova A. Malikova F. Amirgaliyev Z. Kartbayev T. Sharipova B. Aitkulov Z. Astanayeva A.
31 July 2021 Little Lion Scientific

Journal of Theoretical and Applied Information Technology
2021 #99 Issue 14 3529 - 3541 pp.

The problem of evacuation of people from closed premises such as universities, colleges and schools is considered. The peculiarity of this work lies in the formation of an integrated approach for organizing the evacuation process in peacetime as a training for an emergency. 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 evacuation plan in real time. The optimal solution to the problem of maximum network flow is implemented using a game-theoretic approach. A mathematical model has been developed for the optimal distribution of the flow along the grindshill network with the analysis of the flow formation and the characteristics of the ways of people moving in closed 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.

Algorithm , Evacuation , Graph , Mathematical modeling , Maximum flow , Method

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Almaty Technological University, Kazakhstan
Institute of Information and Computing Technologies CS MES RK, Almaty, Kazakhstan
Almaty University of Energy and Communications, Almaty, Kazakhstan

Almaty Technological University
Institute of Information and Computing Technologies CS MES RK
Almaty University of Energy and Communications

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