QUALITATIVE BEHAVIOUR AND NUMERICAL APPROXIMATION OF SOLUTIONS TO CONSERVATION LAWS WITH NON-LOCAL POINT CONSTRAINTS ON THE FLUX AND MODELING OF CROWD DYNAMICS AT THE BOTTLENECKS
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | QUALITATIVE BEHAVIOUR AND NUMERICAL APPROXIMATION OF SOLUTIONS TO CONSERVATION LAWS WITH NON-LOCAL POINT CONSTRAINTS ON THE FLUX AND MODELING OF CROWD DYNAMICS AT THE BOTTLENECKS |
| Type de publication | Journal Article |
| Year of Publication | 2016 |
| Auteurs | Andreianov B, Donadello C, Razafison U, Rosini MD |
| Journal | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE |
| Volume | 50 |
| Pagination | 1269-1287 |
| Date Published | SEP-OCT |
| Type of Article | Article |
| ISSN | 0764-583X |
| Mots-clés | Braess' paradox, capacity drop, Crowd dynamics, Faster Is Slower, Finite volume scheme, non-local point constraint, Scalar conservation law |
| Résumé | In this paper we investigate numerically the model for pedestrian traffic proposed in [B. Andreianov, C. Donadello, M. D. Rosini, Math. Models Methods Appl. Sci. 24 (2014) 2685-2722]. We prove the convergence of a scheme based on a constraint finite volume method and validate it with an explicit solution obtained in the above reference. We then perform ad hoc simulations to qualitatively validate the model under consideration by proving its ability to reproduce typical phenomena at the bottlenecks, such as Faster Is Slower effect and the Braess' paradox. |
| DOI | 10.1051/m2an/2015078 |