Geodesic
Optimizing fire-fighting water supply systems using spatial metrics
Journal of computational and engineering mathematics, Tome 7 (2020) no. 4, pp. 3-16.

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The current trend in the construction of new urban areas involves the coordination of a comprehensive preliminary planning of all systems and networks of power supply, water supply, drainage complexes, laying of communication networks and other communication networks of construction objects with the layout of residential buildings. In the paper there is an optimization of the number and type of distribution of hydrants of external fire-fighting water supply and pumping stations using various metrics that measure distance. The optimization of the dependence of the type of hydrant water supply networks on pumping stations is considered, considering the real practical tasks of providing fire-fighting water supply, taking into account the size, location and shape of modern buildings. The analysis of maps and standards revealed that the concept of distance implies only distance in a straight line that does not correspond to the modern layout of the development of subdistricts and significantly complicates the ability of firefighters to work. In the first part of the work, we present a mathematical model that optimizes both the number and the location of the set of hydrants that fully serve a given development area. The optimization algorithm uses a metric different from Euclidean distance. At the same time, it is assumed that the developed models are applicable for various types of development of subdistricts (line building, regular building, cluster housing, sporadic building, etc.). In the second part of the paper, we optimize the number of placement of pumping stations and the type of pipeline network connecting the fire-fighting water supply and pumping stations. To this end, we use the computer determination of the coordinates of the Torricelli – Steiner point implemented for an arbitrary set of consumer points and various spatial metrics.
Keywords: location algorithm, fire hydrant, fire-fighting water supply, modelling, spatial metrics, Torricelli – Steiner points. 
@article{JCEM_2020_7_4_a0,
     author = {A. V. Kalach and V. A. Rodin and S. V. Sinegubov},
     title = {Optimizing fire-fighting water supply systems using spatial metrics},
     journal = {Journal of computational and engineering mathematics},
     pages = {3--16},
     publisher = {mathdoc},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2020_7_4_a0/}
}
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A. V. Kalach; V. A. Rodin; S. V. Sinegubov. Optimizing fire-fighting water supply systems using spatial metrics. Journal of computational and engineering mathematics, Tome 7 (2020) no. 4, pp. 3-16. http://geodesic.mathdoc.fr/item/JCEM_2020_7_4_a0/