TY - JOUR
T1 - Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model
AU - Mazaré, Pierre Emmanuel
AU - Dehwah, Ahmad H.
AU - Claudel, Christian G.
AU - Bayen, Alexandre M.
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2011/12
Y1 - 2011/12
N2 - In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.
AB - In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.
UR - http://hdl.handle.net/10754/561940
UR - https://linkinghub.elsevier.com/retrieve/pii/S0191261511001044
UR - http://www.scopus.com/inward/record.url?scp=80455174671&partnerID=8YFLogxK
U2 - 10.1016/j.trb.2011.07.004
DO - 10.1016/j.trb.2011.07.004
M3 - Article
SN - 0191-2615
VL - 45
SP - 1727
EP - 1748
JO - Transportation Research Part B: Methodological
JF - Transportation Research Part B: Methodological
IS - 10
ER -