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Computing travel times from filtered traffic states
A justification of a LWR model based on a follow the leader description
1. | Department of Mathematics and Applications, University of Milano-Bicocca, Via Cozzi, 53, 20125 Milano, Italy |
References:
[1] |
B. Argall, E. Cheleshkin, J. M. Greenberg, C. Hinde and P.-J. Lin, A rigorous treatment of a follow-the-leader traffic model with traffic lights present, SIAM J. Appl. Math., 63 (2002), 149-168.
doi: 10.1137/S0036139901391215. |
[2] |
S. Benzoni-Gavage and R. M. Colombo, An $n$-populations model for traffic flow, European J. Appl. Math., 14 (2003), 587-612.
doi: 10.1017/S0956792503005266. |
[3] |
A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
[4] |
R. M. Colombo and A. Marson, A Hölder continuous ODE related to traffic flow, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), 759-772.
doi: 10.1017/S0308210500002663. |
[5] |
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. |
[6] |
R. M. Colombo and E. Rossi, On the micro-macro limit in traffic flow, to appear in Rend. Semin. Mat. Univ. Padova. |
[7] |
G. Costeseque, Analyse et Modelisation du Trafic Routier: Passage du Microscopique au Macroscopique, Master's Thesis, Ecole des Ponts ParisTech, 2011. |
[8] |
S. N. Kružkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81 (1970), 228-255. |
[9] |
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002.
doi: 10.1017/CBO9780511791253. |
[10] |
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. |
[11] |
K. Radhakrishnan and A. C. Hindmarsh, Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations, LLNL report UCRL-ID-113855, National Aeronautics and Space Administration, Lewis Research Center, 1993.
doi: 10.2172/15013302. |
[12] |
P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[13] |
E. Rossi, On the Micro-Macro Limit in Traffic Flow, Master's thesis, Università Cattolica del Sacro Cuore, Brescia, 2012. |
show all references
References:
[1] |
B. Argall, E. Cheleshkin, J. M. Greenberg, C. Hinde and P.-J. Lin, A rigorous treatment of a follow-the-leader traffic model with traffic lights present, SIAM J. Appl. Math., 63 (2002), 149-168.
doi: 10.1137/S0036139901391215. |
[2] |
S. Benzoni-Gavage and R. M. Colombo, An $n$-populations model for traffic flow, European J. Appl. Math., 14 (2003), 587-612.
doi: 10.1017/S0956792503005266. |
[3] |
A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
[4] |
R. M. Colombo and A. Marson, A Hölder continuous ODE related to traffic flow, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), 759-772.
doi: 10.1017/S0308210500002663. |
[5] |
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. |
[6] |
R. M. Colombo and E. Rossi, On the micro-macro limit in traffic flow, to appear in Rend. Semin. Mat. Univ. Padova. |
[7] |
G. Costeseque, Analyse et Modelisation du Trafic Routier: Passage du Microscopique au Macroscopique, Master's Thesis, Ecole des Ponts ParisTech, 2011. |
[8] |
S. N. Kružkov, First order quasilinear equations with several independent variables, Mat. Sb. (N.S.), 81 (1970), 228-255. |
[9] |
R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002.
doi: 10.1017/CBO9780511791253. |
[10] |
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. |
[11] |
K. Radhakrishnan and A. C. Hindmarsh, Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations, LLNL report UCRL-ID-113855, National Aeronautics and Space Administration, Lewis Research Center, 1993.
doi: 10.2172/15013302. |
[12] |
P. I. Richards, Shock waves on the highway, Operations Res., 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[13] |
E. Rossi, On the Micro-Macro Limit in Traffic Flow, Master's thesis, Università Cattolica del Sacro Cuore, Brescia, 2012. |
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