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Modeling and analysis of pooled stepped chutes
Shock formation in a traffic flow model with Arrhenius look-ahead dynamics
1. | Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States |
2. | Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419 |
References:
[1] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation, Phys. Rev. E, 51 (1995), 1035-1042.
doi: 10.1103/PhysRevE.51.1035. |
[2] |
D. Helbing, Traffic and related self-driven many-particle systems, Rev. Modern Phy., 73 (2001), 1067-1141.
doi: 10.1103/RevModPhys.73.1067. |
[3] |
W. L. Jin and H. M. Zhang, The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model, Transportation Research, B., 37 (2003), 207-223.
doi: 10.1016/S0191-2615(02)00008-5. |
[4] |
B. S. Kerner and P. Konhäuser, Structure and parameters of clusters in traffic flow, Physical Review E, 50 (1994), 54-83.
doi: 10.1103/PhysRevE.50.54. |
[5] |
A. Klar and R. Wegener, Kinetic derivation of macroscopic anticipation models for vehicular traffic, SIAM J. Appl. Math., 60 (2000), 1749-1766.
doi: 10.1137/S0036139999356181. |
[6] |
A. Kurganov and A. Polizzi, Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics, Netw. Heterog. Media, 4 (2009), 431-451.
doi: 10.3934/nhm.2009.4.431. |
[7] |
H. Y. Lee, H.-W. Lee and D. Kim, Steady-state solutions of hydrodynamic traffic models, Phys. Rev. E, 69 (2004), 016118-1-016118-7. |
[8] |
T. Li, Nonlinear dynamics of traffic jams, Physica D, 207 (2005), 41-51.
doi: 10.1016/j.physd.2005.05.011. |
[9] |
T. Li, Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion, SIAM J. Math. Anal., 40 (2008), 1058-1075.
doi: 10.1137/070690638. |
[10] |
A. J. Majda and A. L. Bertozzi, "Vorticity and Incompressible Flow," Cambridge Univ. Press, 2002. |
[11] |
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. |
[12] |
T. Nagatani, The physics of traffic jams, Rep. Prog. Phys., 65 (2002), 1331-1386.
doi: 10.1088/0034-4885/65/9/203. |
[13] |
K. Nagel, Particle hopping models and traffic flow theory, Phys. Rev. E, 53 (1996), 4655-4672.
doi: 10.1103/PhysRevE.53.4655. |
[14] |
I. Prigogine and R. Herman, "Kinetic Theory of Vehicular Traffic," American Elsevier Publishing Company Inc., New York, 1971. |
[15] |
P. I. Richards, Shock waves on highway, Operations Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[16] |
A. Sopasakis and M. Katsoulakis, Stochastic modeling and simulation of traffic flow: Asymmetric single exclusion process with Arrhenius look-ahead dynamics, SIAM J. Appl. Math., 6 (2006), 921-944.
doi: 10.1137/040617790. |
[17] |
G. B. Whitham, "Linear and Nonlinear Waves," Wiley, New York, 1974. |
show all references
References:
[1] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation, Phys. Rev. E, 51 (1995), 1035-1042.
doi: 10.1103/PhysRevE.51.1035. |
[2] |
D. Helbing, Traffic and related self-driven many-particle systems, Rev. Modern Phy., 73 (2001), 1067-1141.
doi: 10.1103/RevModPhys.73.1067. |
[3] |
W. L. Jin and H. M. Zhang, The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model, Transportation Research, B., 37 (2003), 207-223.
doi: 10.1016/S0191-2615(02)00008-5. |
[4] |
B. S. Kerner and P. Konhäuser, Structure and parameters of clusters in traffic flow, Physical Review E, 50 (1994), 54-83.
doi: 10.1103/PhysRevE.50.54. |
[5] |
A. Klar and R. Wegener, Kinetic derivation of macroscopic anticipation models for vehicular traffic, SIAM J. Appl. Math., 60 (2000), 1749-1766.
doi: 10.1137/S0036139999356181. |
[6] |
A. Kurganov and A. Polizzi, Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics, Netw. Heterog. Media, 4 (2009), 431-451.
doi: 10.3934/nhm.2009.4.431. |
[7] |
H. Y. Lee, H.-W. Lee and D. Kim, Steady-state solutions of hydrodynamic traffic models, Phys. Rev. E, 69 (2004), 016118-1-016118-7. |
[8] |
T. Li, Nonlinear dynamics of traffic jams, Physica D, 207 (2005), 41-51.
doi: 10.1016/j.physd.2005.05.011. |
[9] |
T. Li, Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion, SIAM J. Math. Anal., 40 (2008), 1058-1075.
doi: 10.1137/070690638. |
[10] |
A. J. Majda and A. L. Bertozzi, "Vorticity and Incompressible Flow," Cambridge Univ. Press, 2002. |
[11] |
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. |
[12] |
T. Nagatani, The physics of traffic jams, Rep. Prog. Phys., 65 (2002), 1331-1386.
doi: 10.1088/0034-4885/65/9/203. |
[13] |
K. Nagel, Particle hopping models and traffic flow theory, Phys. Rev. E, 53 (1996), 4655-4672.
doi: 10.1103/PhysRevE.53.4655. |
[14] |
I. Prigogine and R. Herman, "Kinetic Theory of Vehicular Traffic," American Elsevier Publishing Company Inc., New York, 1971. |
[15] |
P. I. Richards, Shock waves on highway, Operations Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[16] |
A. Sopasakis and M. Katsoulakis, Stochastic modeling and simulation of traffic flow: Asymmetric single exclusion process with Arrhenius look-ahead dynamics, SIAM J. Appl. Math., 6 (2006), 921-944.
doi: 10.1137/040617790. |
[17] |
G. B. Whitham, "Linear and Nonlinear Waves," Wiley, New York, 1974. |
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