×

zbMATH — the first resource for mathematics

A new lattice model of traffic flow with the consideration of the driver’s forecast effects. (English) Zbl 1242.90059
Summary: In this Letter, a new lattice model is presented with the consideration of the driver’s forecast effects (DFE). The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the new model can improve the stability of traffic flow by considering DFE. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis. Numerical simulation also shows that the new model can improve the stability of traffic flow by adjusting the driver’s forecast intensity parameter, which is consistent with the theoretical analysis.

MSC:
90B20 Traffic problems in operations research
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Tang, T.Q.; Huang, H.J.; Shang, H.Y., Phys. lett. A, 374, 1668, (2010) · Zbl 1236.90029
[2] Tang, T.Q.; Li, C.Y.; Huang, H.J., Phys. lett. A, 374, 3951, (2010) · Zbl 1238.90036
[3] Nagatani, T., Physica A, 261, 599, (1998)
[4] Nagatani, T., Physica A, 264, 581, (1999)
[5] Xue, Y., Acta phys. sin., 53, 25, (2004)
[6] Ge, H.X.; Dai, S.Q.; Xue, Y.; Dong, L.Y., Phys. rev. E, 71, 066119, (2005)
[7] Ge, H.X.; Cheng, R.J., Physica A, 387, 6952, (2008)
[8] Zhu, H.B., Chin. phys. B, 18, 1322, (2009)
[9] Li, X.L.; Li, Z.P.; Han, X.L.; Dai, S.Q., Commun. nonlinear sci. numer. simul., 14, 2171, (2009)
[10] Ge, H.X., Physica A, 388, 1682, (2009)
[11] Ge, H.X.; Cheng, R.J.; Lei, L., Physica A, 389, 2825, (2010)
[12] Nagatani, T., Physica A, 271, 200, (1999)
[13] Nagatani, T., Phys. rev. E, 59, 4857, (1999)
[14] Nagatani, T., Physica A, 272, 592, (1999)
[15] Nagatani, T., Physica A, 265, 297, (1999)
[16] Tang, T.Q.; Huang, H.J.; Xue, Y., Acta phys. sin., 55, 4026, (2006)
[17] Peng, G.H., Acta phys. sin., 59, 108, (2010)
[18] Li, Z.P.; Li, X.L.; Liu, F.Q., Int. J. mod. phys. C, 19, 1163, (2008)
[19] Tian, H.H.; He, H.D.; F Wei, Y.; Xue, Y.; Lu, W.Z., Physica A, 388, 2895, (2009)
[20] Tian, J.F.; Jia, B.; Li, X.G.; Gao, Z.Y., Chin. phys. B, 19, 040303, (2010)
[21] Sun, D.H.; Tian, C.; Liu, W.N., Chin. phys. B, 19, 080514, (2010)
[22] Ge, H.X.; Cheng, R.J.; Lei, L., Physica A, 389, 2825, (2010)
[23] Ge, H.X.; Cheng, R.J.; Dai, S.Q., Physica A, 357, 466, (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.