[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | All | Home ]

Preprint 2015-006

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

Boris Andreianov, Carlotta Donadello, Ulrich Razafison and Massimiliano D. Rosini

Abstract: In this paper we investigate numerically the model for pedestrian traffic proposed in [1]. 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.

References
[1] B. Andreianov, C. Donadello, M.D. Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods in Applied Sciences 24 (13) (2014) 2685–2722; MR3260283
Paper:
Available as PDF (503 Kbytes).
Author(s):
Boris Andreianov,
Carlotta Donadello,
Ulrich Razafison,
Massimiliano D. Rosini,
Submitted by:
; 2015-03-04.