Development of a systematic approach and mathematical support for the evacuation process
Keywords:maximum flow, optimal plan, Grindshiels network, Nash equilibrium, evacuation planning
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.
- Kalizhanova, A. U., Kozbakova, A. H. (2017). Matematicheskie i komp'yuternye modeli evakuatsii. Almaty, 205.
- Belyaev, S. V. (1938). Evakuatsiya zdaniy massovogo naznacheniya. Moscow: Izdatel'stvo «Vsesoyuznoy Akademii Arhitektury».
- Predtechenskiy, V. M., Milinskiy, A. I. (1979). Proektirovanie zdaniy s uchetom organizatsii dvizheniya lyudskih potokov. Moscow: Stroyizdat, 375.
- Holshchevnikov, V. V. (1983). Lyudskie potoki v zdaniyah, sooruzheniyah i na territorii ih kompleksov. Moscow: MISI.
- Holshchevnikov, V. V., Samoshin, D. A., Isaevich, I. I. (2009). Naturnye nablyudeniya lyudskih potokov. Moscow: Akademiya GPS MCHS Rossii, 191.
- Cappuccio, J. (2000). A Computer-Based Timed Egress Simulation. SFPE Journal of Fire Protection Engineering, 8, 11–12.
- Fahy, R. (1996). EXIT89: High-Rise Evacuation Model - Recent Enhancements and Example Applications. International Interflam Conference «Inter- flam '96». Cambridge, 1001–1005.
- Weinroth, J. (1989). An adaptable microcomputer model for evacuation management. Fire Technology, 25 (4), 291–307. doi: https://doi.org/10.1007/bf01040378
- Fahy, R. (1996). Enhancement of EXIT89 and Analysis of World Trade Center Data. NIST, 684, 45.
- Stepantsov, M. E. (2003). Model' napravlennogo dvizheniya tolpy s elementami analiza situatsii. Elektronniy zhurnal «Issledovano v Rossii», 89, 991–995.
- Hartama, D., Windarto, A. P., Wanto, A. (2018). Evacuation Planning for Disaster Management by Using The Relaxation Based Algorithm and Route Choice Model. IJISTECH (International Journal Of Information System & Technology), 2 (1), 7. doi: https://doi.org/10.30645/ijistech.v2i1.14
- Hamacher, H. W., Tjandra, S. A. (2001). Mathematical Modeling of Evacuation Problems: A State of The Art. Berichte des Fraunhofer ITWN, Nr. 24.
- Malodushev, S. V., Rogov, A. A., Voronov, R. V. (2019). Mathematical model for evacuation people from corridor-type buildings. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 15 (3), 375–384. doi: https://doi.org/10.21638/11702/spbu10.2019.307
- Ng, C. T., Cheng, T. C. E., Levner, E., Kriheli, B. (2020). Optimal bi-criterion planning of rescue and evacuation operations for marine accidents using an iterative scheduling algorithm. Annals of Operations Research, 296 (1-2), 407–420. doi: https://doi.org/10.1007/s10479-020-03632-6
- Schiopu, C. (2019). Maximum flows in bipartite dynamic networks. SERIES III - MATEMATICS, INFORMATICS, PHYSICS, 61 (12) (1), 177–198. doi: https://doi.org/10.31926/but.mif.2019.12.61.1.14
- Abusalama, J., Razali, S., Choo, Y.-H., Momani, L., Alkharabsheh, A. (2020). Dynamic real-time capacity constrained routing algorithm for evacuation planning problem. Indonesian Journal of Electrical Engineering and Computer Science, 20 (3), 1388. doi: https://doi.org/10.11591/ijeecs.v20.i3.pp1388-1396
- Pyakurel, U., Nath, H. N., Dempe, S., Dhamala, T. N. (2019). Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal. Mathematics, 7 (10), 993. doi: https://doi.org/10.3390/math7100993
- Feng, J., Wang, Q. (2019). Emergency safety evacuation decision based on dynamic Gaussian Bayesian network. IOP Conference Series: Materials Science and Engineering, 688, 055076. doi: https://doi.org/10.1088/1757-899x/688/5/055076
- Smirnova, A. T. (1999). Fundamentals of life safety. Moscow, 104–107.
- Amirgaliyev, Y., Kovalenko, A., Kalizhanova, A., Kozbakova, A. (2015). Modeling of Networks Flows of Grinshilds Types. Vestnik KazNU, 3 (86), 184–190.
- Kovalenko, A. G., Vlasova, I. A., Borisova, S. P. (2006). Teoriya igr i issledovanie operatsiy. Samara: Izdatel'stvo «Samarskiy universitet», 147.
- Volkov, I. K., Zagoruyko, E. A. (2000). Issledovanie operatsiy. Moscow: Izd-vo MGTU im. N.E. Baumana, 436.
- Vasin, A. A., Morozov, V. V. (2005). Teoriya igr i modeli matematicheskoy ekonomiki. Moscow: MAKS Press, 237.
- Gorlach, B. A. (2013). Issledovanie operatsiy. Sankt-Peterburg: "Lan'", 448.
- Kosorukov, O. A., Mishchenko, A. V. (2003). Issledovanie operatsiy. Moscow: Izdatel'stvo «Ekzamen», 448.
- Germeyer, Yu. B. (1971). Vvedenie v teoriyu issledovaniya operatsiy. Moscow: Nauka, 358.
- Fon Neyman, Dzh., Morgenshtern, O. (1970). Teoriya igr i ekonomicheskoe povedenie. Moscow: «Nauka», 707.
How to Cite
Copyright (c) 2021 Yedilkhan Amirgaliyev, Aliya Kalizhanova, Ainur Kozbakova, Zhalau Aitkulov, Aygerim Astanayeva
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with PC TECHNOLOGY CENTER, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher PC TECHNOLOGY CENTER does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.