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Volumn 49, Issue , 2013, Pages 75-93

A partial differential equation formulation of Vickrey's bottleneck model, part II: Numerical analysis and computation

Author keywords

Convergence; Discrete time solution; Mixed integer linear program; System optimal dynamic traffic assignment; The Vickrey model

Indexed keywords

ALUMINUM; CONTINUOUS TIME SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; TRAFFIC CONTROL;

EID: 84875212005     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2012.10.004     Document Type: Article
Times cited : (55)

References (35)
  • 1
    • 55549134666 scopus 로고    scopus 로고
    • Dirichlet problems for some Hamilton-Jacobi equations with inequality constraints
    • Aubin J.P., Bayen A.M., Saint-Pierre P. Dirichlet problems for some Hamilton-Jacobi equations with inequality constraints. SIAM Journal on Control and Optimization 2008, 47(5):2348-2380.
    • (2008) SIAM Journal on Control and Optimization , vol.47 , Issue.5 , pp. 2348-2380
    • Aubin, J.P.1    Bayen, A.M.2    Saint-Pierre, P.3
  • 2
    • 84862819240 scopus 로고    scopus 로고
    • Continuous-time point-queue models in dynamic network loading
    • Ban X., Pang J.S., Liu H.X., Ma R. Continuous-time point-queue models in dynamic network loading. Transportation Research Part B 2011, 46(3):360-380.
    • (2011) Transportation Research Part B , vol.46 , Issue.3 , pp. 360-380
    • Ban, X.1    Pang, J.S.2    Liu, H.X.3    Ma, R.4
  • 3
    • 0003809134 scopus 로고    scopus 로고
    • Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
    • Birkhäuser.
    • Bardi, M., Capuzzo Dolcetta, I., 1997. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser.
    • (1997)
    • Bardi, M.1    Capuzzo Dolcetta, I.2
  • 4
    • 0041697501 scopus 로고    scopus 로고
    • Hyperbolic Systems of Conservation Laws
    • Oxford University Press
    • Bressan A. Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem 2000, Oxford University Press.
    • (2000) The One Dimensional Cauchy Problem
    • Bressan, A.1
  • 5
    • 81255169947 scopus 로고    scopus 로고
    • Optima and equilibria for a model of traffic flow
    • Bressan A., Han K. Optima and equilibria for a model of traffic flow. SIAM Journal on Mathematical Analysis 2011, 43(5):2384-2417.
    • (2011) SIAM Journal on Mathematical Analysis , vol.43 , Issue.5 , pp. 2384-2417
    • Bressan, A.1    Han, K.2
  • 6
    • 84872298329 scopus 로고    scopus 로고
    • Nash equilibria for a model of traffic flow with several groups of drivers
    • Bressan A., Han K. Nash equilibria for a model of traffic flow with several groups of drivers. ESAIM: Control, Optimization and Calculus of Variations 2012, 18(4):969-986.
    • (2012) ESAIM: Control, Optimization and Calculus of Variations , vol.18 , Issue.4 , pp. 969-986
    • Bressan, A.1    Han, K.2
  • 7
    • 0023207979 scopus 로고
    • Optimal time varying flows on congested networks
    • Carey M. Optimal time varying flows on congested networks. Operations Research 1987, 35(1):58-69.
    • (1987) Operations Research , vol.35 , Issue.1 , pp. 58-69
    • Carey, M.1
  • 8
    • 77952196906 scopus 로고    scopus 로고
    • Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part I: Theory
    • Claudel C.G., Bayen A.M. Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part I: Theory. IEEE Transactions on Automatic Control 2010, 55(5):1142-1157.
    • (2010) IEEE Transactions on Automatic Control , vol.55 , Issue.5 , pp. 1142-1157
    • Claudel, C.G.1    Bayen, A.M.2
  • 9
    • 0028481056 scopus 로고
    • The cell transmission model. Part I: A simple dynamic representation of highway traffic
    • Daganzo C.F. The cell transmission model. Part I: A simple dynamic representation of highway traffic. Transportation Research Part B 1994, 28(4):269-287.
    • (1994) Transportation Research Part B , vol.28 , Issue.4 , pp. 269-287
    • Daganzo, C.F.1
  • 10
    • 11144330902 scopus 로고    scopus 로고
    • A variational formulation of kinematic waves: basic theory and complex boundary conditions
    • Daganzo C.F. A variational formulation of kinematic waves: basic theory and complex boundary conditions. Transportation Research Part B 2005, 39(2):187-196.
    • (2005) Transportation Research Part B , vol.39 , Issue.2 , pp. 187-196
    • Daganzo, C.F.1
  • 11
  • 12
    • 0003448545 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • Evans L.C. Partial Differential Equations 2010, American Mathematical Society, Providence, RI. second ed.
    • (2010) Partial Differential Equations
    • Evans, L.C.1
  • 14
    • 84988147318 scopus 로고
    • Explicit formula for scalar non-linear conservation laws with boundary condition
    • Le Floch P. Explicit formula for scalar non-linear conservation laws with boundary condition. Mathematical Models and Methods in Applied Sciences 1988, 10(3):265-287.
    • (1988) Mathematical Models and Methods in Applied Sciences , vol.10 , Issue.3 , pp. 265-287
    • Le Floch, P.1
  • 15
    • 0027149988 scopus 로고
    • A variational inequality formulation of the dynamic network user equilibrium problem
    • Friesz T.L., Bernstein D., Smith T., Tobin R., Wie B. A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 1993, 41(1):80-91.
    • (1993) Operations Research , vol.41 , Issue.1 , pp. 80-91
    • Friesz, T.L.1    Bernstein, D.2    Smith, T.3    Tobin, R.4    Wie, B.5
  • 17
    • 0024772092 scopus 로고
    • Dynamic network traffic assignment considered as a continuous time optimal control problem
    • Friesz T.L., Luque J., Tobin R.L., Wie B.W. Dynamic network traffic assignment considered as a continuous time optimal control problem. Operations Research 1989, 37(6):893-901.
    • (1989) Operations Research , vol.37 , Issue.6 , pp. 893-901
    • Friesz, T.L.1    Luque, J.2    Tobin, R.L.3    Wie, B.W.4
  • 18
    • 84875232350 scopus 로고    scopus 로고
    • A partial differential equation formulation of Vickrey's bottleneck model
    • part I: Methodology and theoretical analysis. Transportation Research Part B.
    • Han, K., Friesz, T.L., Yao, T., 2013. A partial differential equation formulation of Vickrey's bottleneck model, part I: Methodology and theoretical analysis. Transportation Research Part B. doi:10.1016/j.trb.2012.10.003.
    • (2013)
    • Han, K.1    Friesz, T.L.2    Yao, T.3
  • 19
    • 84875232179 scopus 로고    scopus 로고
    • Existence of simultaneous route and departure choice dynamic user equilibrium
    • in press. Transportation Research Part B, forthcoming.
    • Han, K., Friesz, T.L., Yao, T., in press. Existence of simultaneous route and departure choice dynamic user equilibrium. Transportation Research Part B, forthcoming.
    • Han, K.1    Friesz, T.L.2    Yao, T.3
  • 20
    • 0002131828 scopus 로고    scopus 로고
    • An exact expression of dynamic traffic equilibrium
    • Pergamon Press, Oxford UK, J.B. Lesort (Ed.)
    • Heydecker B.G., Addison J.D. An exact expression of dynamic traffic equilibrium. Transportation and Traffic Theory 1996, 359-383. Pergamon Press, Oxford UK. J.B. Lesort (Ed.).
    • (1996) Transportation and Traffic Theory , pp. 359-383
    • Heydecker, B.G.1    Addison, J.D.2
  • 21
    • 0041760963 scopus 로고    scopus 로고
    • Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern
    • Kuwahara M., Akamatsu T. Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern. Transportation Research Part B 1997, 31(1):1-10.
    • (1997) Transportation Research Part B , vol.31 , Issue.1 , pp. 1-10
    • Kuwahara, M.1    Akamatsu, T.2
  • 24
    • 0034333578 scopus 로고    scopus 로고
    • A reactive dynamic user equilibrium model in network with queues
    • Li J., Fujiwara O., Kawakami S. A reactive dynamic user equilibrium model in network with queues. Transportation Research Part B 2000, 34(8):605-624.
    • (2000) Transportation Research Part B , vol.34 , Issue.8 , pp. 605-624
    • Li, J.1    Fujiwara, O.2    Kawakami, S.3
  • 25
    • 0000090588 scopus 로고
    • On kinematic waves II: a theory of traffic flow in long crowded roads
    • Lighthill M.J., Whitham J.B. On kinematic waves II: a theory of traffic flow in long crowded roads. Proceedings of the Royal Society 1955, A229:317-345.
    • (1955) Proceedings of the Royal Society , vol.A229 , pp. 317-345
    • Lighthill, M.J.1    Whitham, J.B.2
  • 26
    • 0018002683 scopus 로고
    • A model and an algorithm for the dynamic traffic assignment problem
    • Merchant D.K., Nemhauser G.L. A model and an algorithm for the dynamic traffic assignment problem. Transportation Science 1978, 12(3):183-199.
    • (1978) Transportation Science , vol.12 , Issue.3 , pp. 183-199
    • Merchant, D.K.1    Nemhauser, G.L.2
  • 27
    • 0018002555 scopus 로고
    • Optimality conditions for a dynamic traffic assignment model
    • Merchant D.K., Nemhauser G.L. Optimality conditions for a dynamic traffic assignment model. Transportation Science 1978, 12(3):200-207.
    • (1978) Transportation Science , vol.12 , Issue.3 , pp. 200-207
    • Merchant, D.K.1    Nemhauser, G.L.2
  • 28
    • 17244370185 scopus 로고    scopus 로고
    • A comparative study of some macroscopic link models used in dynamic traffic assignment
    • Nie X., Zhang H.M. A comparative study of some macroscopic link models used in dynamic traffic assignment. Networks and Spatial Economics 2005, 5(1):89-115.
    • (2005) Networks and Spatial Economics , vol.5 , Issue.1 , pp. 89-115
    • Nie, X.1    Zhang, H.M.2
  • 29
    • 0000230403 scopus 로고    scopus 로고
    • Foundations of dynamic traffic assignment: the past, the present and the future
    • Peeta S., Ziliaskopoulos A. Foundations of dynamic traffic assignment: the past, the present and the future. Networks and Spatial Economics 2001, 1(3):233-265.
    • (2001) Networks and Spatial Economics , vol.1 , Issue.3 , pp. 233-265
    • Peeta, S.1    Ziliaskopoulos, A.2
  • 30
    • 84856347013 scopus 로고
    • A general model and algorithm for the dynamic traffic assignment problems
    • Proceedings of the Fifth World Conference on Transport Research, Yokohoma, Japan.
    • Ran, B., Shimazaki, T., 1989. A general model and algorithm for the dynamic traffic assignment problems. In: Proceedings of the Fifth World Conference on Transport Research, Yokohoma, Japan.
    • (1989)
    • Ran, B.1    Shimazaki, T.2
  • 31
    • 0002842180 scopus 로고
    • Shockwaves on the highway
    • Richards P.I. Shockwaves on the highway. Operations Research 1956, 4(1):42-51.
    • (1956) Operations Research , vol.4 , Issue.1 , pp. 42-51
    • Richards, P.I.1
  • 32
    • 0005282194 scopus 로고
    • A high accuracy method for solving ODEs with discontinuous right-hand side
    • Stewart D.E. A high accuracy method for solving ODEs with discontinuous right-hand side. Numerische Mathematik 1990, 58:299-328.
    • (1990) Numerische Mathematik , vol.58 , pp. 299-328
    • Stewart, D.E.1
  • 33
    • 0000768007 scopus 로고
    • Congestion theory and transport investment
    • Vickrey W.S. Congestion theory and transport investment. The American Economic Review 1969, 59(2):251-261.
    • (1969) The American Economic Review , vol.59 , Issue.2 , pp. 251-261
    • Vickrey, W.S.1
  • 34
    • 0347108912 scopus 로고
    • Dynamic user optimal traffic assignment on congested multidestination networks
    • Wie B.W., Friesz T.L., Tobin R.L. Dynamic user optimal traffic assignment on congested multidestination networks. Transportation Research Part B 1990, 24(6):431-442.
    • (1990) Transportation Research Part B , vol.24 , Issue.6 , pp. 431-442
    • Wie, B.W.1    Friesz, T.L.2    Tobin, R.L.3
  • 35
    • 0033904403 scopus 로고    scopus 로고
    • A linear programming model for the single destination system optimal dynamic traffic assignment problem
    • Ziliaskopoulos A.K. A linear programming model for the single destination system optimal dynamic traffic assignment problem. Transportation Science 2000, 34(1):37-49.
    • (2000) Transportation Science , vol.34 , Issue.1 , pp. 37-49
    • Ziliaskopoulos, A.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.