Multi-class kinematic wave theory of traffic flow
The kinematic wave theory of traffic flow was independently developed by Lighthill and Whitham [Lighthill, M.J., Whitham, G.B., 1955. On kinematic waves. II. A theory of traffic flow on long crowded roads. Procedings of Royal Society A 229, 281-345] and Richards [Richards, P.I., 1956. Shockwaves on the highway. Operations Research 4, 42-51]. The original LWR model was extended in different directions to incorporate more and realistic details. The distinction of classes in traffic flow has received considerable attention recently. This paper proposes a framework for the different existing multi-class extensions of the kinematic wave theory. It turns out that the difference between all models lies in the assumption on how several classes interact. A new model is proposed where classes interact on a non-cooperative way. Slow vehicles act as moving bottlenecks for the fast vehicles, while fast vehicles maximize their speed without influencing slower vehicles. This leads to anisotropic behaviour of the traffic stream. This means that vehicles only react on stimuli in front of them. The new multi-class model is presented and illustrated in the moving bottleneck example of Newell [Newell, G.F., 1998. A moving bottleneck. Transportation Research Part B 32(8), 531-537].
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Volume (Year): 42 (2008)
Issue (Month): 6 (July)
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- Daganzo, Carlos F. & Lin, Wei-Hua & Del Castillo, Jose M., 1997. "A simple physical principle for the simulation of freeways with special lanes and priority vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 31(2), pages 103-125, April.
- Newell, G. F., 1998. "A moving bottleneck," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 531-537, November.
- Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
- Daganzo, Carlos F., 2002. "A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 131-158, February.
- Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
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- Daganzo, Carlos F., 1997. "A continuum theory of traffic dynamics for freeways with special lanes," Transportation Research Part B: Methodological, Elsevier, vol. 31(2), pages 83-102, April.
- Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
- Holland, Edward N. & Woods, Andrew W., 1997. "A continuum model for the dispersion of traffic on two-lane roads," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 473-485, November.
- Zhang, H. M., 2003. "Anisotropic property revisited--does it hold in multi-lane traffic?," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 561-577, July.
- Daganzo, Carlos F., 1995. "A finite difference approximation of the kinematic wave model of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 261-276, August.
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