Study on the continuous delayed optimal flow on traffic stability in a new macro traffic model. (English) Zbl 07570640
Summary: The influence of the continuous delayed optimal flow on traffic stability is studied based on a new traffic lattice hydrodynamic model in this paper. Linear analysis derives the model’s linear stable condition and it shows that the stability of traffic flow is enhanced by considering the continuous delayed optimal flow. Also the feature of the unstable traffic flow is uncovered by the solution of the mKdV equation with nonlinear analysis. Finally, numerical simulation is carried out to intuitively show the stabilization effect of the continuous delayed optimal flow on traffic flow and the continuous delayed optimal flow should be considered in traffic theory.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
References:
| [1] | Bando, M.; Hasebe, K.; Nakayama, A.; Shibata, A.; Sugiyama, Y., Phys. Rev. E, 51, 1035 (1995) |
| [2] | Yu, S. W.; Shi, Z. K., Nonlinear Dynam., 82, 731 (2015) |
| [3] | Yu, S. W.; Shi, Z. K., Commun. Nonlinear Sci. Numer. Simul., 36, 319 (2016) · Zbl 1470.90021 |
| [4] | Xin, Q.; Yang, N.; Fu, R.; Yu, S. W.; Shi, Z. K., Physica A, 501, 338 (2018) |
| [5] | Li, Y. F.; Tang, C. C.; Li, K. Z.; He, X. Z.; Peeta, S.; Wang, Y. B., IEEE Trans. Intell. Transp. Syst., 99, 1 (2018) |
| [6] | Li, Y. F.; Tang, C. C.; Peeta, S.; Wang, Y. B., IEEE Trans. Ind. Electron., 66, 4618 (2019) |
| [7] | Li, Y. F.; Tang, C. C.; Li, K. Z.; Peeta, S.; He, X. Z.; Wang, Y. B., Transp. Res. C, 93, 525 (2018) |
| [8] | Treiber, M.; Kesting, A., Transp. Res. B, 117, 613 (2018) |
| [9] | Xin, Q.; Fu, R.; Yuan, W.; Liu, Q. L.; Yu, S. W., Physica A, 508, 806 (2018) |
| [10] | Davis, L. C., Physica A, 503, 818 (2018) · Zbl 1514.93045 |
| [11] | Yu, S. W.; Shi, Z. K., Measurement, 64, 34 (2015) |
| [12] | Wu, X.; Zhao, X. M.; Song, H. S.; Xin, Q.; Yu, S. W., Physica A, 515, 192 (2019) · Zbl 1514.90108 |
| [13] | Spiliopoulou, A.; Kontorinaki, M.; Papageorgiou, M.; Kopelias, P., Transp. Res. C, 41, 18 (2014) |
| [14] | Mohan, R.; Ramadurai, G., Phys. Lett. A, 381, 115 (2017) · Zbl 1377.90017 |
| [15] | Nagatani, T., Physica A, 261, 599 (1998) |
| [16] | Ge, H. X.; Cheng, R. J., Physica A, 387, 6952 (2008) |
| [17] | Kang, Y. R.; Sun, D. H., Nonlinear Dynam., 71, 531 (2013) |
| [18] | Gupta, A. K.; Redhu, P., Physica A, 392, 5622 (2013) |
| [19] | Gupta, A. K.; Redhu, P., Nonlinear Dynam., 76, 1001 (2014) · Zbl 1306.90033 |
| [20] | Kaur, R.; Sharma, S., Physica A, 471, 59 (2017) |
| [21] | Gupta, A. K.; Redhu, P., Commun. Nonlinear Sci. Numer. Simul., 19, 1600 (2014) · Zbl 1457.90052 |
| [22] | Zhang, Y. C.; Xue, Y.; Shi, Y.; Guo, Y.; Wei, F. P., Physica A, 502, 135 (2018) · Zbl 1514.90117 |
| [23] | Zhang, G., Nonlinear Dynam., 91, 809 (2018) |
| [24] | Gupta, A. K.; Sharma, S.; Redhu, P., Commun. Theor. Phys., 62, 393 (2014) · Zbl 1298.90021 |
| [25] | Redhu, P.; Siwach, V., Physica A, 492, 1473 (2018) · Zbl 1514.90088 |
| [26] | Zhang, G.; Sun, D. H.; Zhao, M., Commun. Nonlinear Sci. Numer. Simul., 54, 347 (2018) · Zbl 1510.82029 |
| [27] | Cao, B. G., Physica A, 427, 218 (2015) |
| [28] | Yang, L. Y.; Sun, D. H.; Zhao, M.; Cheng, S. L.; Zhang, G.; Liu, H., Physica A, 494, 294 (2018) · Zbl 1514.90110 |
| [29] | Zhao, H. Z.; Zhang, G.; Li, W. Y.; Gu, T. L.; Zhou, D., Physica A, 503, 1204 (2018) · Zbl 1514.90119 |
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