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Coupling of microscopic and phase transition models at boundary

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  • This paper deals with coupling conditions between the classical microscopic Follow The Leader model and a phase transition (PT) model. We propose a solution at the interface between the two models. We describe the solution to the Riemann problem.
    Mathematics Subject Classification: Primary: 90B20; Secondary: 35L65.

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  • [1]

    D. Amadori, Initial-boundary value problems for nonlinear systems of conservation laws, NoDEA Nonlinear Differential Equations Appl., 4 (1997), 1-42.doi: 10.1007/PL00001406.

    [2]

    A. Aw, A. Klar, T. Materne and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63 (2002), 259-278.doi: 10.1137/S0036139900380955.

    [3]

    A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow, SIAM J. Appl. Math., 60 (2000), 916-938.doi: 10.1137/S0036139997332099.

    [4]

    S. Blandin, J. Argote, A. M. Bayen and D. B. Work, Phase transition model of non-stationary traffic flow: Definition, properties and solution method, Transportation Research Part B: Methodological, 52 (2013), 31-55.

    [5]

    S. Blandin, D. Work, P. Goatin, B. Piccoli and A. Bayen, A general phase transition model for vehicular traffic, SIAM J. Appl. Math., 71 (2011), 107-127.doi: 10.1137/090754467.

    [6]

    R. M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), 708-721.doi: 10.1137/S0036139901393184.

    [7]

    R. M. Colombo, F. Marcellini and M. Rascle, A 2-phase traffic model based on a speed bound, SIAM J. Appl. Math., 70 (2010), 2652-2666.doi: 10.1137/090752468.

    [8]

    C. F. Daganzo, Requiem for second-order fluid approximations of traffic flow, Transportation Research Part B, 29 (1995), 277-286.doi: 10.1016/0191-2615(95)00007-Z.

    [9]

    F. Dubois and P. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations, 71 (1988), 93-122.doi: 10.1016/0022-0396(88)90040-X.

    [10]

    M. Garavello and B. Piccoli, Coupling of lwr and phase transition models at boundary, Journal of Hyperbolic Differential Equations, 10 (2013), 577-636.

    [11]

    D. C. Gazis, R. Herman and R. W. Rothery, Nonlinear follow-the-leader models of traffic flow, Operations Res., 9 (1961), 545-567.doi: 10.1287/opre.9.4.545.

    [12]

    P. Goatin, The Aw-Rascle vehicular traffic flow model with phase transitions, Math. Comput. Modelling, 44 (2006), 287-303.doi: 10.1016/j.mcm.2006.01.016.

    [13]

    D. Helbing, From microscopic to macroscopic traffic models, in "A perspective look at nonlinear media,'' Lecture Notes in Phys., Springer, (1998), 122-139.doi: 10.1007/BFb0104959.

    [14]

    D. Helbing, A. Hennecke, V. Shvetsov and M. Treiber, Micro- and macro-simulation of freeway traffic, Traffic flow-modelling and simulation, Math. Comput. Modelling, 35 (2002), 517-547.doi: 10.1016/S0895-7177(02)80019-X.

    [15]

    C. Lattanzio and B. Piccoli, Coupling of microscopic and macroscopic traffic models at boundaries, Math. Models Methods Appl. Sci., 20 (2010), 2349-2370.doi: 10.1142/S0218202510004945.

    [16]

    M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317-345.doi: 10.1098/rspa.1955.0089.

    [17]

    S. Moutari and M. Rascle, A hybrid Lagrangian model based on the Aw-Rascle traffic flow model, SIAM J. Appl. Math., 68 (2007), 413-436.doi: 10.1137/060678415.

    [18]

    H. J. Payne, Models of freeway traffic and control, in mathematical models of public systems, Simul. Counc. Proc., 1 (1971).

    [19]

    I. Prigogine and R. Herman, Kinetic theory of vehicular traffic, American Elsevier Pub. Co., 1971.

    [20]

    P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.doi: 10.1287/opre.4.1.42.

    [21]

    G. B. Whitham, "Linear and Nonlinear Waves,'' Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974.

    [22]

    D. B. Work, S. Blandin, O.-P. Tossavainen, B. Piccoli and A. M. Bayen, A traffic model for velocity data assimilation, Appl. Math. Res. Express. AMRX, 1 (2010), 1-35.

    [23]

    H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B: Methodological, 36 (2002), 275-290.doi: 10.1016/S0191-2615(00)00050-3.

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