A hybrid model for traffic flow and crowd dynamics with random individual properties

Veronika Schleper

doi:10.3934/mbe.2015.12.393

Article Contents

2015, Volume 12, Issue 2: 393-413. Doi: 10.3934/mbe.2015.12.393 open access

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A hybrid model for traffic flow and crowd dynamics with random individual properties

Veronika Schleper^1,

1.
Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, D-70569 Stuttgart

Received: March 31, 2014

Revised: May 31, 2014

Published: November 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L40, 35L65, 90B20, 35R60.

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