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A macroscopic model to reproduce self-organization near exits

Abraham Sylla Institut Denis Poisson, Tours (France)
Abraham Sylla Institut Denis Poisson, Tours (France)
When May 03, 2019
from 04:00 PM to 05:00 PM
Where LH 006
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Abstract:  The LWR framework is the simplest one that can be used to describe macroscopically pedestrian traffic in a corridor. One of the typical features of pedestrian flows is self-organization.

Here, we focus on self-organization near exits.
Point constraints were introduced in [1] in the LWR model in order to account for localized in space phenomena that may occur at exists (such as traffic lights or toll gate in the context of road traffic) and which act as obstacles. In [2] the authors were able to reproduce the main effects linked to the “capacity drop” that are the Faster Is Slower effect and the Braess’ paradox. Moreover, in [3] the authors considered a wide family of nonlocal models with point constraint, and attempted to reproduce the self-organization feature using one of such models.
Our goal is to further in this direction.
The model we propose interpolates between two states of the traffic, the organized and the disorganized ones. It is determined by the presence of two levels of constraints and by an organization parameter which evolves through an ODE. Numerical simulations done by a finite volume scheme show that this model can indeed reproduce the self-organization in certain regimes.
After recalling some classical notions about conservation laws with flux constraint, we will present a well-posedness result for our model as well as numerical simulations.
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