The vehicle length effect on the traffic flow fundamental diagram. (English) Zbl 07458596
Summary: Recent applications of a new methodology to measure fundamental traffic relations on freeways shows that many critical parameters of the flow-density and speed-spacing diagrams depend on vehicle length. In response to this fact, this work presents a generalization of the Prigogine-Herman traffic equation for aggressive drivers which takes into account the fact that vehicles are not point-like objects but have an effective length. Our approach is similar to that introduced by Enskog for dense gases and provides the construction of fundamental diagrams which are in excellent agreement with empirical traffic data.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
References:
| [1] | B.D. Greenshields, A study of highway capacity, in: Proceedings of the Highway Rersearch Board, vol. 14, Washington 1935, pp. 448-477. |
| [2] | Kerner, B. S., Introduction to Modern Traffic Flow Theory and Control (2009), Springer-Verlag: Springer-Verlag Berlin Heidelberg · Zbl 1189.90034 |
| [3] | Helbing, D., Traffic and related self-driven many-particle systems, Rev. Modern Phys., 73, 1067-1141 (2001) |
| [4] | Treiber, M.; Kesting, A., Traffic Flow Dynamics (2013), Springer-Verlag |
| [5] | van Wageningen-Kessels, F.; van Lint, H.; Vuik, K.; Hoogendoorn, S., Genealogy of traffic flow models, EURO J. Transp. Logist., 4, 445-473 (2015) |
| [6] | Helbing, D., Improved fluid-dynamic model for vehicular traffic, Phys. Rev. E, 51, 3164-3169 (1995) |
| [7] | Helbing, D.; Treiber, M., Enskog equations for traffic flow evaluated up to Navier-Stokes order, Granul. Matter, 1, 21-31 (1998) · Zbl 1163.76434 |
| [8] | del Castillo, J. M., Three new models for the flow-density relationship, Transportmetrica, 8, 443-465 (2012) |
| [9] | Méndez, A. R.; Marques, W.; Velasco, R. M., Multi-class fundamental diagram from the Prigogine-Herman-Boltzmann equation, Phys. Scr., 94, 1-6 (2019) |
| [10] | Coifman, B., Revisiting the empirical fundamental relationship, Transp. Res. B, 68, 173-184 (2014) |
| [11] | Coifman, B., Empirical flow-density and speed-spacing relationships: Evidence of vehicle length dependency, Transp. Res. B, 78, 54-65 (2015) |
| [12] | Prigogine, I.; Herman, R., Kinetic Theory of Vehicular Traffic (1971), Elsevier: Elsevier New York London Amsterdam · Zbl 0226.90011 |
| [13] | Iannini, M. L.L.; Dickman, R., Kinetic theory of vehicular traffic, Amer. J. Phys., 84, 135-145 (2016) |
| [14] | Klar, A., Enskog-like kinetic models for vehicular traffic, J. Stat. Phys., 87, 91-114 (1997) · Zbl 0917.90124 |
| [15] | Anderson, R. L.; Herman, R.; Prigogine, I., On the statistical distribution function theory of traffic flow, Oper. Res., 10, 180-196 (1962) · Zbl 0114.09403 |
| [16] | Velasco, R. M.; Marques, W., Navier-Stokes-like equations for traffic flow, Phys. Rev. E, 72, Article 046102 pp. (2005) |
| [17] | Shvetsov, V.; Helbing, D., Macroscopic dynamics of multilane traffic, Phys. Rev. E, 59, 6328-6339 (1999) |
| [18] | Méndez, A. R.; Velasco, R. M., An alternative model in traffic flow equations, Transp. Res. B, 42, 782-797 (2008) |
| [19] | Marques, W.; Méndez, A. R., On the kinetic theory of vehicular traffic flow: Chapman-Enskog expansion versus Grad’s moment method, Physica A, 392, 3430-3440 (2013) · Zbl 1395.90087 |
| [20] | Hoogendoorn, S. P., Multiclass Continuum Modeling of Multilane Traffic Flow (1999), Delft University of Technology: Delft University of Technology Delft, (Ph.D. thesis) |
| [21] | van Wageningen-Kessels, F., Multi-Class Continuum Traffic Flow Models: Analysis and Simulation Methods (2013), Delft University of Technology: Delft University of Technology Delft, (Ph.D. thesis) |
| [22] | Zhang, H. M., New perspectives on continuum traffic flow models, Netw. Spat. Econ., 1, 9-33 (2001) |
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