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Fundamental diagrams for kinetic equations of traffic flow
1. | Department of Mathematics and Computer Science, University of Cagliari, Viale Merello 92, 09123 Cagliari, Italy |
2. | Istituto per le Applicazioni del Calcolo "M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma |
References:
[1] |
A. Bellouquid, E. De Angelis and L. Fermo, Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach, Math. Models Methods Appl. Sci., 22 (2012), 1140003, 35 pp.
doi: 10.1142/S0218202511400033. |
[2] |
S. Blandin, G. Bretti, C. Cutolo and B. Piccoli, Numerical simulations of traffic data via fluid dynamic approach, Appl. Math. Comput., 210 (2009), 441-454.
doi: 10.1016/j.amc.2009.01.057. |
[3] |
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. |
[4] |
I. Bonzani and L. Mussone, From experiments to hydrodynamic traffic flow models. I. Modelling and parameter identification, Math. Comput. Modelling, 37 (2003), 1435-1442.
doi: 10.1016/S0895-7177(03)90051-3. |
[5] |
R. M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), 708-721.
doi: 10.1137/S0036139901393184. |
[6] |
V. Coscia, M. Delitala and P. Frasca, On the mathematical theory of vehicular traffic flow. II. Discrete velocity kinetic models, Internat. J. Non-Linear Mech., 42 (2007), 411-421.
doi: 10.1016/j.ijnonlinmec.2006.02.008. |
[7] |
C. F. Daganzo, A variational formulation of kinematic waves: Solution methods, Transport. Res. B-Meth., 39 (2005), 934-950.
doi: 10.1016/j.trb.2004.05.003. |
[8] |
P. Degond and M. Delitala, Modelling and simulation of vehicular traffic jam formation, Kinet. Relat. Models, 1 (2008), 279-293.
doi: 10.3934/krm.2008.1.279. |
[9] |
M. Delitala and A. Tosin, Mathematical modeling of vehicular traffic: A discrete kinetic theory approach, Math. Models Methods Appl. Sci., 17 (2007), 901-932.
doi: 10.1142/S0218202507002157. |
[10] |
L. Fermo and A. Tosin, A fully-discrete-state kinetic theory approach to modeling vehicular traffic, SIAM J. Appl. Math., 73 (2013), 1533-1556.
doi: 10.1137/120897110. |
[11] |
M. Garavello and B. Piccoli, Traffic Flow on Networks - Conservation Laws Models, AIMS Series on Applied Mathematics, 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006. |
[12] |
M. Günther, A. Klar, T. Materne and R. Wegener, Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations, SIAM J. Appl. Math., 64 (2003), 468-483.
doi: 10.1137/S0036139902404700. |
[13] |
B. S. Kerner, The Physics of Traffic, Springer, Berlin, 2004.
doi: 10.1007/978-3-540-40986-1. |
[14] |
J. Li and M. Zhang, Fundamental diagram of traffic flow, Transp. Res. Record, 2260 (2011), 50-59.
doi: 10.3141/2260-06. |
[15] |
G. F. Newell, A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks, Transport. Res. B-Meth., 27 (1993), 289-303.
doi: 10.1016/0191-2615(93)90039-D. |
[16] |
B. Piccoli and A. Tosin, Vehicular traffic: A review of continuum mathematical models, in Encyclopedia of Complexity and Systems Science, (ed., R. A. Meyers), 22, Springer, New York, 2009, 9727-9749.
doi: 10.1007/978-0-387-30440-3_576. |
show all references
References:
[1] |
A. Bellouquid, E. De Angelis and L. Fermo, Towards the modeling of vehicular traffic as a complex system: A kinetic theory approach, Math. Models Methods Appl. Sci., 22 (2012), 1140003, 35 pp.
doi: 10.1142/S0218202511400033. |
[2] |
S. Blandin, G. Bretti, C. Cutolo and B. Piccoli, Numerical simulations of traffic data via fluid dynamic approach, Appl. Math. Comput., 210 (2009), 441-454.
doi: 10.1016/j.amc.2009.01.057. |
[3] |
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. |
[4] |
I. Bonzani and L. Mussone, From experiments to hydrodynamic traffic flow models. I. Modelling and parameter identification, Math. Comput. Modelling, 37 (2003), 1435-1442.
doi: 10.1016/S0895-7177(03)90051-3. |
[5] |
R. M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), 708-721.
doi: 10.1137/S0036139901393184. |
[6] |
V. Coscia, M. Delitala and P. Frasca, On the mathematical theory of vehicular traffic flow. II. Discrete velocity kinetic models, Internat. J. Non-Linear Mech., 42 (2007), 411-421.
doi: 10.1016/j.ijnonlinmec.2006.02.008. |
[7] |
C. F. Daganzo, A variational formulation of kinematic waves: Solution methods, Transport. Res. B-Meth., 39 (2005), 934-950.
doi: 10.1016/j.trb.2004.05.003. |
[8] |
P. Degond and M. Delitala, Modelling and simulation of vehicular traffic jam formation, Kinet. Relat. Models, 1 (2008), 279-293.
doi: 10.3934/krm.2008.1.279. |
[9] |
M. Delitala and A. Tosin, Mathematical modeling of vehicular traffic: A discrete kinetic theory approach, Math. Models Methods Appl. Sci., 17 (2007), 901-932.
doi: 10.1142/S0218202507002157. |
[10] |
L. Fermo and A. Tosin, A fully-discrete-state kinetic theory approach to modeling vehicular traffic, SIAM J. Appl. Math., 73 (2013), 1533-1556.
doi: 10.1137/120897110. |
[11] |
M. Garavello and B. Piccoli, Traffic Flow on Networks - Conservation Laws Models, AIMS Series on Applied Mathematics, 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006. |
[12] |
M. Günther, A. Klar, T. Materne and R. Wegener, Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations, SIAM J. Appl. Math., 64 (2003), 468-483.
doi: 10.1137/S0036139902404700. |
[13] |
B. S. Kerner, The Physics of Traffic, Springer, Berlin, 2004.
doi: 10.1007/978-3-540-40986-1. |
[14] |
J. Li and M. Zhang, Fundamental diagram of traffic flow, Transp. Res. Record, 2260 (2011), 50-59.
doi: 10.3141/2260-06. |
[15] |
G. F. Newell, A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks, Transport. Res. B-Meth., 27 (1993), 289-303.
doi: 10.1016/0191-2615(93)90039-D. |
[16] |
B. Piccoli and A. Tosin, Vehicular traffic: A review of continuum mathematical models, in Encyclopedia of Complexity and Systems Science, (ed., R. A. Meyers), 22, Springer, New York, 2009, 9727-9749.
doi: 10.1007/978-0-387-30440-3_576. |
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