×

Balanced vehicular traffic at a bottleneck. (English) Zbl 1165.90378

Summary: The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or off-ramps. The coupling conditions for the Riemann problem of the system are applied in order to treat the interface between different road sections consistently. Our numerical simulations show the appearance of synchronized flow at highway bottlenecks.

MSC:

90B20 Traffic problems in operations research
35L70 Second-order nonlinear hyperbolic equations
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Siebel, F.; Mauser, W., On the fundamental diagram of traffic flow, SIAM Journal on Applied Mathematics, 66, 4, 1150-1162 (2006) · Zbl 1102.35068
[2] Aw, A.; Rascle, M., Resurrection of “second order” models of traffic flow, SIAM Journal on Applied Mathematics, 60, 3, 916-938 (2000) · Zbl 0957.35086
[3] Zhang, H. M., A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research B, 36, 275-290 (2002)
[4] Greenberg, J. M., Extensions and amplifications of a traffic model of Aw and Rascle, SIAM Journal on Applied Mathematics, 62, 3, 729-745 (2001) · Zbl 1006.35064
[5] Greenberg, J. M.; Klar, A.; Rascle, M., Congestion on multilane highways, SIAM Journal on Applied Mathematics, 63, 3, 818-833 (2002) · Zbl 1024.35064
[6] Greenberg, J. M., Congestion redux, SIAM Journal on Applied Mathematics, 64, 4, 1175-1185 (2004) · Zbl 1053.35087
[7] Siebel, F.; Mauser, W., Synchronized flow and wide moving jams from balanced vehicular traffic, Physical Review E, 73, 6, 066108 (2006) · Zbl 1244.90060
[8] Kerner, B., The Physics of Traffic (2004), Springer: Springer Berlin
[9] Helbing, D.; Treiber, M., Critical discussion of synchronized flow, Cooperative Transportation Dynamics, 1, 2.1-2.24 (2002)
[10] Treiber, M.; Kesting, A.; Helbing, D., Delays, inaccuracies, and anticipation in microscopic traffic models, Physica A, 360, 1, 71-88 (2006)
[11] Garavello, M.; Piccoli, B., Traffic flow on a road network using the Aw-Rascle model, Communications in Partial Differential Equations, 31, 2, 243-275 (2006) · Zbl 1090.90032
[12] Herty, M.; Rascle, M., Coupling conditions for a class of “second-order” models for traffic flow, SIAM Journal on Mathematical Analysis, 38, 2, 595-616 (2006) · Zbl 1296.35094
[13] Herty, M.; Moutari, S.; Rascle, M., Optimization criteria for modelling intersections of vehicular traffic flow, Networks and Heterogeneous Media, 1, 2, 275-294 (2006) · Zbl 1131.90016
[14] B. Haut, G. Bastin, A second order model for road traffic networks, in: Proceedings of the 8th International IEEE Conference on Intelligent Transportation Systems, 2005, pp. 178-184; B. Haut, G. Bastin, A second order model for road traffic networks, in: Proceedings of the 8th International IEEE Conference on Intelligent Transportation Systems, 2005, pp. 178-184
[15] Haut, B.; Bastin, G., A second order model of road junctions in fluid models of traffic networks, Networks and Heterogeneous Media, 2, 2, 227-253 (2007) · Zbl 1161.35443
[16] Siebel, F.; Mauser, W., Simulating vehicular traffic in a network using dynamic routing, Mathematical and Computer Modelling of Dynamical Systems, 13, 1, 83-97 (2007) · Zbl 1141.90352
[17] Zhang, P.; Wong, S. C., Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models, Physical Review E, 74, 2, 026109 (2006)
[18] Zhang, P.; Wong, S. C.; Dai, S.-Q., Characteristic parameters of a wide cluster in a higher-order traffic flow model, Chinese Physics Letter, 23, 2, 516-519 (2006)
[19] Bertini, R.; Leal, M., Empirical study of traffic features at a freeway lane drop, Journal of Transportation Engineering, 131, 12, 397-407 (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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.