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Stochastic control of traffic patterns
1. | Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14 B, 01413, Kiev |
2. | Department of Applied Mathematics and Statistics, University of the Basque Country, E-48080 Bilbao |
3. | AKAD University of Applied Sciences, D-70469 Stuttgart, Germany |
4. | Department of Mathematics and Computer Science & Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark |
5. | Toyota Central R&D Labs, Nagakute, Aichi, Japan |
6. | Department of Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark, Denmark |
References:
[1] |
M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions,", Dover Publications, (1972).
doi: 10.1119/1.1972842. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation,, Phys. Rev. E, 51 (1995). Google Scholar |
[3] |
A. Bose and P. Ioannou, Mixed manual/semi-automated traffic: A macroscopic analysis,, Trasp. Res., 11 (2003).
doi: 10.1016/j.trc.2002.04.001. |
[4] |
A. H. Cohen, P. J. Holmes and R. H. Rand, The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model,, J. Math. Biol., 13 (1982), 345.
doi: 10.1007/BF00276069. |
[5] |
L. C. Davis, Effect of adaptive cruise control systems on traffic flow,, Phys. Rev. E, 69 (2004).
doi: 10.1103/PhysRevE.69.066110. |
[6] |
Y. Gaididei, C. Gorria, R. Berkemer, A. Kawamoto, A. Kawamoto, T. Shiga, P. L. Christiansen, M. P. Sørensen and J. Starke, Traffic jam control by time-modulating the safety distance,, Submitted., (). Google Scholar |
[7] |
Yu. B. Gaididei, R. Berkemer, J. G. Caputo, P. L. Christiansen, A. Kawamoto, T. Shiga, M. P. Sørensen and J. Starke, Analytical solutions of jam pattern formation on a ring for a class of optimal velocity traffic models,, New Journal of Phys., 11 (2009), 1.
doi: 10.1088/1367-2630/11/7/073012. |
[8] |
Yu. B. Gaididei, R. Berkemer, C. Gorria, P. L. Christiansen, A. Kawamoto, T. Shiga, M. P. Sørensen and J. Starke, Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements,, Discrete and Continuous Dynamical Systems. Series S., 4 (2011), 1167.
doi: 10.3934/dcdss.2011.4.1167. |
[9] |
C. W. Gardiner, "Handbook of Stochastic Method,'', 2nd ed. (Springer, (1989).
doi: 10.1007/978-3-662-02377-8. |
[10] |
D. Helbing, Traffic and related self-driven many-particle systems,, Rev. Modern Phys., 73 (2001), 1067.
doi: 10.1103/RevModPhys.73.1067. |
[11] |
V. In, A. Kho, J. D. Neff, A. Palacios, P. Longhini and B. K. Meadows, Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators,, Phys. Rev. Lett., 91 (2003), 244101.
doi: 10.1103/PhysRevLett.91.244101. |
[12] |
B. S. Kerner, "The physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory,", Heidelberg: Springer, (2004). Google Scholar |
[13] |
B. S. Kerner, "Introduction to Modern Traffic Flow Theory and Control. The Long Road to Three-Phase Traffic Theory,", Berlin: Springer, (2009). Google Scholar |
[14] |
S. Kikuchi, N. Uno and M. Tanaka, Impacts of shorter perception-reaction time of adapted cruise controlled vehicles on traffic flow and safety,, J. Trans. Eng., 129 (2003). Google Scholar |
[15] |
P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations,", 3rd ed., (2004).
|
[16] |
K. Konishi, H. Kokame and K. Hirata, Coupled map car-following model and its delayed-feedback control,, Phys. Rev. E 60 4000;, 60 (4000). Google Scholar |
[17] |
H. K. Lee, H.-W. Lee and D. Kim, Macroscopic traffic models from microscopic car-following models,, Phys. Rev. E, 64 (2001).
doi: 10.1103/PhysRevA.70.059902. |
[18] |
ChiYing Liang and Huei Peng, String stability analysis of adaptive cruise controlled vehicles,, JSME Int. J., 43 (2000). Google Scholar |
[19] |
P. Y. Li and A. Shrivastava, Traffic flow stability induced by constant time headway policy for adaptive cruise control vehicles,, Transp. Res., 10 (2002). Google Scholar |
[20] |
S. Maerivoet and B. De Moor, Cellular automata models of road traffic,, Phys. Reps., 419 (2005). Google Scholar |
[21] |
T. Nagatani, The physics of traffic jams,, Rep. Prog. Phys., 65 (2002), 1331. Google Scholar |
[22] |
K. Nagel and M. Schreckenberg, A cellular automaton model for freeway traffic,, J. Phys. I France, 2 (1992). Google Scholar |
[23] |
K. Nishinari, K. Sugawara, T. Kazama, A. Schadschneider and D. Chowdhury, Modelling of self-driven particles: Foraging ants and pedestrians,, Physica A, 372 (2006). Google Scholar |
[24] |
C. M. A. Pinto and M. Golubitsky, Central pattern generators for bipedal locomotion,, J. Math. Biol., 53 (2006), 474.
doi: 10.1007/s00285-006-0021-2. |
[25] |
A. Schadschneider, D. Chowdhury and K. Nishinari, "Stochastic Transport in Complex Systems,", Elsevier, (2011). Google Scholar |
[26] |
N. J. Suematsu, S. Nakata, A. Awazu and H. Nishimori, Collective behavior of inanimate boats,, Phys. Rev. E, 81 (2010). Google Scholar |
[27] |
Yu. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, Sh. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam,, New Journal of Phys., 10 (2008), 1. Google Scholar |
[28] |
A. Takamatsu, R. Tanaka and T. Fujii, Hidden symmetry in chains of biological coupled oscillators,, Phys. Rev. Lett., 92 (2004), 228102. Google Scholar |
[29] |
A. Takamatsu, R. Tanaka, T. Nakagaki, T. Fujii and I. Endo, Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum Plasmodial slime mold,, Phys. Rev. Lett., 87 (2001), 078102. Google Scholar |
[30] |
D. Tanaka, General chemotactic model of oscillators,, Phys. Rev. Lett., 99 (2007). Google Scholar |
[31] |
D. E. Wolf, M. Schreckenberg and A. Bachem, "Traffic and Granular Flow,", Word Scientific, (1996). Google Scholar |
show all references
References:
[1] |
M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions,", Dover Publications, (1972).
doi: 10.1119/1.1972842. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation,, Phys. Rev. E, 51 (1995). Google Scholar |
[3] |
A. Bose and P. Ioannou, Mixed manual/semi-automated traffic: A macroscopic analysis,, Trasp. Res., 11 (2003).
doi: 10.1016/j.trc.2002.04.001. |
[4] |
A. H. Cohen, P. J. Holmes and R. H. Rand, The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model,, J. Math. Biol., 13 (1982), 345.
doi: 10.1007/BF00276069. |
[5] |
L. C. Davis, Effect of adaptive cruise control systems on traffic flow,, Phys. Rev. E, 69 (2004).
doi: 10.1103/PhysRevE.69.066110. |
[6] |
Y. Gaididei, C. Gorria, R. Berkemer, A. Kawamoto, A. Kawamoto, T. Shiga, P. L. Christiansen, M. P. Sørensen and J. Starke, Traffic jam control by time-modulating the safety distance,, Submitted., (). Google Scholar |
[7] |
Yu. B. Gaididei, R. Berkemer, J. G. Caputo, P. L. Christiansen, A. Kawamoto, T. Shiga, M. P. Sørensen and J. Starke, Analytical solutions of jam pattern formation on a ring for a class of optimal velocity traffic models,, New Journal of Phys., 11 (2009), 1.
doi: 10.1088/1367-2630/11/7/073012. |
[8] |
Yu. B. Gaididei, R. Berkemer, C. Gorria, P. L. Christiansen, A. Kawamoto, T. Shiga, M. P. Sørensen and J. Starke, Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements,, Discrete and Continuous Dynamical Systems. Series S., 4 (2011), 1167.
doi: 10.3934/dcdss.2011.4.1167. |
[9] |
C. W. Gardiner, "Handbook of Stochastic Method,'', 2nd ed. (Springer, (1989).
doi: 10.1007/978-3-662-02377-8. |
[10] |
D. Helbing, Traffic and related self-driven many-particle systems,, Rev. Modern Phys., 73 (2001), 1067.
doi: 10.1103/RevModPhys.73.1067. |
[11] |
V. In, A. Kho, J. D. Neff, A. Palacios, P. Longhini and B. K. Meadows, Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators,, Phys. Rev. Lett., 91 (2003), 244101.
doi: 10.1103/PhysRevLett.91.244101. |
[12] |
B. S. Kerner, "The physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory,", Heidelberg: Springer, (2004). Google Scholar |
[13] |
B. S. Kerner, "Introduction to Modern Traffic Flow Theory and Control. The Long Road to Three-Phase Traffic Theory,", Berlin: Springer, (2009). Google Scholar |
[14] |
S. Kikuchi, N. Uno and M. Tanaka, Impacts of shorter perception-reaction time of adapted cruise controlled vehicles on traffic flow and safety,, J. Trans. Eng., 129 (2003). Google Scholar |
[15] |
P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations,", 3rd ed., (2004).
|
[16] |
K. Konishi, H. Kokame and K. Hirata, Coupled map car-following model and its delayed-feedback control,, Phys. Rev. E 60 4000;, 60 (4000). Google Scholar |
[17] |
H. K. Lee, H.-W. Lee and D. Kim, Macroscopic traffic models from microscopic car-following models,, Phys. Rev. E, 64 (2001).
doi: 10.1103/PhysRevA.70.059902. |
[18] |
ChiYing Liang and Huei Peng, String stability analysis of adaptive cruise controlled vehicles,, JSME Int. J., 43 (2000). Google Scholar |
[19] |
P. Y. Li and A. Shrivastava, Traffic flow stability induced by constant time headway policy for adaptive cruise control vehicles,, Transp. Res., 10 (2002). Google Scholar |
[20] |
S. Maerivoet and B. De Moor, Cellular automata models of road traffic,, Phys. Reps., 419 (2005). Google Scholar |
[21] |
T. Nagatani, The physics of traffic jams,, Rep. Prog. Phys., 65 (2002), 1331. Google Scholar |
[22] |
K. Nagel and M. Schreckenberg, A cellular automaton model for freeway traffic,, J. Phys. I France, 2 (1992). Google Scholar |
[23] |
K. Nishinari, K. Sugawara, T. Kazama, A. Schadschneider and D. Chowdhury, Modelling of self-driven particles: Foraging ants and pedestrians,, Physica A, 372 (2006). Google Scholar |
[24] |
C. M. A. Pinto and M. Golubitsky, Central pattern generators for bipedal locomotion,, J. Math. Biol., 53 (2006), 474.
doi: 10.1007/s00285-006-0021-2. |
[25] |
A. Schadschneider, D. Chowdhury and K. Nishinari, "Stochastic Transport in Complex Systems,", Elsevier, (2011). Google Scholar |
[26] |
N. J. Suematsu, S. Nakata, A. Awazu and H. Nishimori, Collective behavior of inanimate boats,, Phys. Rev. E, 81 (2010). Google Scholar |
[27] |
Yu. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, Sh. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam,, New Journal of Phys., 10 (2008), 1. Google Scholar |
[28] |
A. Takamatsu, R. Tanaka and T. Fujii, Hidden symmetry in chains of biological coupled oscillators,, Phys. Rev. Lett., 92 (2004), 228102. Google Scholar |
[29] |
A. Takamatsu, R. Tanaka, T. Nakagaki, T. Fujii and I. Endo, Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum Plasmodial slime mold,, Phys. Rev. Lett., 87 (2001), 078102. Google Scholar |
[30] |
D. Tanaka, General chemotactic model of oscillators,, Phys. Rev. Lett., 99 (2007). Google Scholar |
[31] |
D. E. Wolf, M. Schreckenberg and A. Bachem, "Traffic and Granular Flow,", Word Scientific, (1996). Google Scholar |
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