From discrete to continuous Wardrop equilibria

Networks and Heterogeneous Media

Volumn 7, Issue 2, 2012, Pages 219-241

  Baillon, Jean Bernard ^a   Carlier, Guillaume ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Eikonal equation; Trffic congestion; Wardrop equilibria; convergence

Indexed keywords

GEOMETRICAL OPTICS;

CONGESTED NETWORKS; CONTINUOUS MODELS; CONVERGENCE THEORY; CONVEX MINIMIZATION; EIKONAL EQUATION; OPTIMAL TRANSPORT; TRFFIC CONGESTION; WARDROP EQUILIBRIUM;

WEBSITES;

EID: 84865554218     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2012.7.219     Document Type: Article

References (9)

1. J.-B. Baillon and R. Cominetti, Markovian traffic equilibrium, Math. Prog., 111 (2008), 33-56.
2. M. Beckmann, C. McGuire and C. Winsten, "Studies in Economics of Transportation," Yale University Press, New Haven, 1956.
3. F. Benmansour, G. Carlier, G. Peyre and F. Santambrogio, Numerical approximation of continuous traffic congestion eq ilibria, Netw. Heterog. Media, 4 (2009), 605-623.
4. A. Braides, "Γ-Convergence for Beginners," Oxford Lecture Series in Mathematics and its Applications, 22, Oxford University Press, Oxford, 2002.
5. L. Brasco, G. Carlier and F. Santambrogio, Congested traffic dynamics, weak flows and very degenerate elliptic equations, Journal de Mathematiques Pures et Appliquees (9), 93 (2010),
6. G. Carlier, C. Jimenez and F. Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria, SIA J. Control Optim., 47 (2008), 1330-1350.
7. G. Dal Maso, "An Introduction to Γ-Convergence," Progress in Nonlinear Differential Equations and their Applications, 8, Birkhãuser Boston, Inc., Boston, MA, 1993.
8. C. Villani, "Topics in Optimal Transportation," Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003.
9. J. G. Wardrop, Some theoretical aspects of road traffic research, Proc. Inst. Civ. Eng., 2 (1952), 325-378.