A hybrid model for traffic flow and crowd dynamics with random individual properties
Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistica...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.393 |
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| _version_ | 1832590109470359552 |
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| author | Veronika Schleper |
| author_facet | Veronika Schleper |
| author_sort | Veronika Schleper |
| collection | DOAJ |
| description | Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models. |
| format | Article |
| id | doaj-art-3c50af04b5ff4660996c157137072f2b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-3c50af04b5ff4660996c157137072f2b2025-01-24T02:31:45ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112239341310.3934/mbe.2015.12.393A hybrid model for traffic flow and crowd dynamics with random individual propertiesVeronika Schleper0Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, D-70569 StuttgartBased on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.393random initial data.traffic flownon-local conservation lawscrowd dynamics |
| spellingShingle | Veronika Schleper A hybrid model for traffic flow and crowd dynamics with random individual properties Mathematical Biosciences and Engineering random initial data. traffic flow non-local conservation laws crowd dynamics |
| title | A hybrid model for traffic flow and crowd dynamics with random individual properties |
| title_full | A hybrid model for traffic flow and crowd dynamics with random individual properties |
| title_fullStr | A hybrid model for traffic flow and crowd dynamics with random individual properties |
| title_full_unstemmed | A hybrid model for traffic flow and crowd dynamics with random individual properties |
| title_short | A hybrid model for traffic flow and crowd dynamics with random individual properties |
| title_sort | hybrid model for traffic flow and crowd dynamics with random individual properties |
| topic | random initial data. traffic flow non-local conservation laws crowd dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.393 |
| work_keys_str_mv | AT veronikaschleper ahybridmodelfortrafficflowandcrowddynamicswithrandomindividualproperties AT veronikaschleper hybridmodelfortrafficflowandcrowddynamicswithrandomindividualproperties |