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Volumn 4, Issue 3, 2009, Pages 605-623

Numerical approximation of continous traffic congestion equilibria

Author keywords

Eikonal equation; Fast marching method; Subgradient descent; Trafic congestion; Wardrop equilibria

Indexed keywords

EIKONAL EQUATION; FAST MARCHING METHODS; SUBGRADIENT DESCENT; TRAFIC CONGESTION; WARDROP EQUILIBRIUM;

EID: 70249111146     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2009.4.605     Document Type: Article
Times cited : (15)

References (20)
  • 1
    • 34347221602 scopus 로고    scopus 로고
    • Markovian traffic equilibrium
    • J.-B. Baillon and R. Cominetti, Markovian traffic equilibrium, Math. Prog., 111 (2008), 33-56.
    • (2008) Math. Prog , vol.111 , pp. 33-56
    • Baillon, J.-B.1    Cominetti, R.2
  • 2
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, Asymptotic Anal., 4 (1991), 271-283.
    • (1991) Asymptotic Anal , vol.4 , pp. 271-283
    • Barles, G.1    Souganidis, P.E.2
  • 6
    • 0040059911 scopus 로고    scopus 로고
    • On viscosity solutions of fully nonlinear equations with measurable ingredient
    • L. Caffarelli, M. G. Crandall, M. Kocan and A. Swiech, On viscosity solutions of fully nonlinear equations with measurable ingredient, Comm. on Pure and Appl. Math., 49 (1999), 365-398.
    • (1999) Comm. on Pure and Appl. Math , vol.49 , pp. 365-398
    • Caffarelli, L.1    Crandall, M.G.2    Kocan, M.3    Swiech, A.4
  • 7
    • 33745641319 scopus 로고    scopus 로고
    • Shape-from-Shading with discontinuous image brightness
    • F. Camilli and E. Prados, Shape-from-Shading with discontinuous image brightness, Appl. Num. Math., 56 (2006), 1225-1237.
    • (2006) Appl. Num. Math , vol.56 , pp. 1225-1237
    • Camilli, F.1    Prados, E.2
  • 8
    • 55549113567 scopus 로고    scopus 로고
    • Optimal transportation with traffic congestion and Wardrop equilibria
    • G. Carlier, C. Jimenez and F. Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria, SIAM Journal on Control and Opt., 47 (2008), 1330-1350.
    • (2008) SIAM Journal on Control and Opt , vol.47 , pp. 1330-1350
    • Carlier, G.1    Jimenez, C.2    Santambrogio, F.3
  • 9
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • M. G. Crandall and P.-L. Lions, Two approximations of solutions of Hamilton-Jacobi equations, Math. Comp., 43 (1984), 1-19.
    • (1984) Math. Comp , vol.43 , pp. 1-19
    • Crandall, M.G.1    Lions, P.-L.2
  • 10
    • 37049000150 scopus 로고    scopus 로고
    • Fast Semi-Lagrangian schemes for the Eikonal equation and applications
    • E. Cristiani and M. Falcone, Fast Semi-Lagrangian schemes for the Eikonal equation and applications, SIAM J. Numer. Anal., 45 (2007), 1979-2011.
    • (2007) SIAM J. Numer. Anal , vol.45 , pp. 1979-2011
    • Cristiani, E.1    Falcone, M.2
  • 12
    • 34147120474 scopus 로고
    • A note on two problems in connection with graphs
    • E. W. Dijkstra, A note on two problems in connection with graphs, Numerische Mathematic, 1 (1959), 269-271.
    • (1959) Numerische Mathematic , vol.1 , pp. 269-271
    • Dijkstra, E.W.1
  • 13
    • 0026880997 scopus 로고
    • A viscosity solution approach to shape from shading
    • E. Rouy and A. Tourin, A viscosity solution approach to shape from shading, SIAM Journal on Numerical Analysis, 29 (1992), 867-884.
    • (1992) SIAM Journal on Numerical Analysis , vol.29 , pp. 867-884
    • Rouy, E.1    Tourin, A.2
  • 14
    • 0029966538 scopus 로고    scopus 로고
    • A fast marching level set method for monotonically advancing fronts
    • J. A. Sethian, A fast marching level set method for monotonically advancing fronts, Proc. Natl. Acad. Sci. USA, 93 (1996), 1591-1595.
    • (1996) Proc. Natl. Acad. Sci. USA , vol.93 , pp. 1591-1595
    • Sethian, J.A.1
  • 16
    • 1842511489 scopus 로고    scopus 로고
    • Ordered upwind methods for static hamilton-jacobi equations: Theory and algorithms
    • J. A. Sethian and A. Vladimirsky, Ordered upwind methods for static hamilton-jacobi equations: Theory and algorithms, SIAM J. Numer. Anal., 41 (2003), 325-363.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 325-363
    • Sethian, J.A.1    Vladimirsky, A.2
  • 17
    • 46549091075 scopus 로고
    • Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
    • P. E. Souganidis, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Differential Equations, 59 (1985), 1-43.
    • (1985) J. Differential Equations , vol.59 , pp. 1-43
    • Souganidis, P.E.1
  • 18
    • 0029373106 scopus 로고
    • Efficient algorithms for globally optimal trajectories
    • J. N. Tsitsiklis, Efficient algorithms for globally optimal trajectories, IEEE Tran. Automatic. Control, 40 (1995), 1528-1538.
    • (1995) IEEE Tran. Automatic. Control , vol.40 , pp. 1528-1538
    • Tsitsiklis, J.N.1
  • 19
    • 1542342359 scopus 로고    scopus 로고
    • Topics in Optimal Transportation
    • American Mathematical Society, Providence, RI
    • C. Villani, "Topics in Optimal Transportation," Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003.
    • (2003) Graduate Studies in Mathematics , vol.58
    • Villani, C.1
  • 20
    • 0003310913 scopus 로고
    • Some theoretical aspects of road traffic research
    • J. G. Wardrop, Some theoretical aspects of road traffic research, Proc. Inst. Civ. Eng., 2 (1952), 325-378.
    • (1952) Proc. Inst. Civ. Eng , vol.2 , pp. 325-378
    • Wardrop, J.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.