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A continuum traffic flow model with the consideration of coupling effect for two-lane freeways. (English) Zbl 1270.90017

Summary: A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.

MSC:

90B20 Traffic problems in operations research
Full Text: DOI

References:

[1] Lighthill, M.J., Whitham, G.B.: On kinematic waves: A theory of traffic flow on long crowded roads. Proc. R. Soc. London-Ser. A. 229, 317–345 (1955) · Zbl 0064.20906 · doi:10.1098/rspa.1955.0089
[2] Richards, P.I.: Shock waves on the highway. Operations Research. 4, 42–51 (1956) · doi:10.1287/opre.4.1.42
[3] Payne, H.J.: Models of Freeway Traffic and Control. Mathematical Methods of Public Systems. 1, 51–60 (1971)
[4] Newell, G.: Nonlinear effects in the dynamics of car following. Operations Research. 9, 209–229 (1961) · Zbl 0211.52301 · doi:10.1287/opre.9.2.209
[5] Daganzo, C.F.: Requiem for second-order fluid approximation of traffic flow. Transportation Rcsearch-B. 29, 277–286 (1995) · doi:10.1016/0191-2615(95)00007-Z
[6] Del Castillo, J.M., Pintado, P., Benitez, F.G.: A formulation of reaction time of traffic flow models. In: Daganzo, C.F. ed. Transportation and Traffic Theory. Elsevier, Amsterdam. 387–405 (1993)
[7] Kihne, R.D.: Macroscopic freeway model for dense trafficstopstart waves and incident detection. In: Volmuller J., Hamerslag R., eds. Proceedings of 9th International Symposium on Transportation and Traffic Theory. VNU Science Press, Netherland, 21–42 (1984)
[8] Ross, P.: Traffic dynamics. Transportation Rcsearch-B. 22, 421–435 1988 · doi:10.1016/0191-2615(88)90023-9
[9] Papageorgiou, M., Blosseville, J.M., Hadj-Salem H.: Macroscopic modeling of traffic flow on the Boulevard Peripherique in Paris. Transportation Rcsearch-B. 23, 29–47 (1989) · doi:10.1016/0191-2615(89)90021-0
[10] Michaloupolos, R., Yi, P., Lyrintzis, A.S.: Continuum modeling of traffic dynamics for congested freeways. Transportation Rcsearch-B. 27, 315–332 (1993) · doi:10.1016/0191-2615(93)90041-8
[11] Zhang, H.M.: A theory of nonequilibrium traffic flow. Transportation Rcsearch-B. 32, 485–498 (1998) · doi:10.1016/S0191-2615(98)00014-9
[12] Jiang, R., Wu, Q.S., Zhu, Z.J.: A new continuum model for traffic flow and numerical tests. Transportation Rcsearch-B. 36, 405–419 (2002) · doi:10.1016/S0191-2615(01)00010-8
[13] Jiang, R., Wu, Q.S., Zhu Z.J.: Full velocity difference model for a car-following theory. Phys. Rev. E. 64, 017101 (2001) · doi:10.1103/PhysRevE.64.017101
[14] Jiang, R., Wu, Q.S.: Analysis of the structural properties of the solutions to speed gradient traffic flow model. Acta Mechanica Sinica. 20, 106–112 (2004)
[15] Jiang, R., Wu, Q.S.: Study on propagation speed of small disturbance from a car-following approach. Transportation Rcsearch-B. 37, 85–99 (2003) · doi:10.1016/S0191-2615(02)00004-8
[16] Zhang, H.M.: On the consistency of a class of traffic flow models. Transportation Rcsearch-B. 37, 101–105 (2003) · doi:10.1016/S0191-2615(01)00040-6
[17] Xue, Y., Dai, S.Q.: Continuum traffic model with the consideration of two delay time scales. Phys. Rev. E. 68, 066123 (2003) · doi:10.1103/PhysRevE.68.066123
[18] Daganzo, C.F.: A continuum theory of traffic dynamics for freeways with special lanes. Transportation Rcsearch-B. 31, 83–102 (1997) · doi:10.1016/S0191-2615(96)00017-3
[19] Wu, Z.: A fluid dynamics model for low speed traffic system. Acta Mechanica Sinica. 26, 149–157 (1994) (in Chinese)
[20] Tang, T.Q., Huang, H.J.: Traffic flow model of two lanes and numerical calculation. Chinese Science Bulletin. 49, 1937–1943 (2004)
[21] Tang, T.Q., Huang, H.J.: Wave propertie s of a traffic flow model for freeways with two lanes. Journal of Beijing University of Aeronautics and Astronautics. 31, 1121–1124 (2005)
[22] Huang, H.J., Tang, T.Q., Gao, Z.Y.: Continuum modeling for two-lane traffic flow. Acta Mechanica Sinica. 22, 131–137 (2006) · Zbl 1200.90046 · doi:10.1007/s10409-006-0101-y
[23] Tang, C.F., Jiang, R., Wu, Q.S.: Extended speed gradientmodel for traffic flow on two-lane freeways. Chinese Physics. 16, 1570–1576 (2007) · doi:10.1088/1009-1963/16/6/013
[24] Liu, G.Q.: Modelling of freeway merging and diverging flow dynamics. Appl. Math. Model. 20, 459–469 (1996) · Zbl 0869.90024 · doi:10.1016/0307-904X(95)00165-G
[25] Whitham, G.B.: Linear and nonlinear moves. John Wiley and Sons, Inc, New York (1974) · Zbl 0373.76001
[26] Zhang, H.M.: Analyses of the stability and wave properties of a new continuum traffic theory. Transportation Rcsearch-B. 33, 399–415 (1999) · doi:10.1016/S0191-2615(98)00044-7
[27] Del Castillo, J.M., Benitez, F.G.: On functional form of the speed-density relationship-I: general theory. Transportation Rcsearch-B. 29, 373–406 (1995) · doi:10.1016/0191-2615(95)00008-2
[28] Wager, P., Nagel, K., Wolf, D.E.: Realistic mufti-lane traffic rules for cellular automata. Physica A. 234, 687–698 (1997) · doi:10.1016/S0378-4371(96)00308-1
[29] Knospe, W., Santen, L., Schadschneider, A., et al.: A realistic two-lane traffic model for highway traffic. J. Phys. A. 35, 3369–3388 (2002) · Zbl 0996.90028 · doi:10.1088/0305-4470/35/15/302
[30] Herrmann, M., Kerner, B.S.: Local cluster effect in different traffic flow models. Physica A. 255: 163–188 (1998) · doi:10.1016/S0378-4371(98)00102-2
[31] Kerner, B.S., Konhäuser, P.: Cluster efect in initially homogeneous traffic flow. Phys. Rev. E. 48, R2335–2338 (1993) · doi:10.1103/PhysRevE.48.R2335
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