Abstract
Mathematical modeling of crowd flows in a building is studied. The study is based on a modification of the discrete CTM macromodel built on guaranteed estimates. Two methods for an approximate calculation of the reachability set—the number of people in each room at the next point in time—are proposed. Interval estimates and estimates in the form of sets of two-dimensional projections are constructed. The proposed algorithms are illustrated by numerical examples.
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Notes
In all formulas, we for brevity omit the dependence of the functions \({{f}_{{ij}}}\), \({{f}_{{ji}}}\), and \(\alpha _{j}^{{(i)}}\) on \(t\).
The support function of a compact set \(X\) in the direction \(l\) is defined by \(\rho (l\,|\,X) = \mathop {\sup }\limits_{x \in X} {\kern 1pt} \langle l,x\rangle \).
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Funding
The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2022-284.
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Translated by A. Klimontovich
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Zaitseva, M.V., Tochilin, P.A. Constructing Estimates of Reachability Sets in Crowd Flows Modeling. Comput. Math. and Math. Phys. 63, 1527–1539 (2023). https://doi.org/10.1134/S0965542523070163
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DOI: https://doi.org/10.1134/S0965542523070163