Abstract
A review of dynamic nonlinear features of spatiotemporal congested patterns in freeway traffic is presented. The basis of the review is a comparison of theoretical features of the congested patterns that are shown by a microscopic traffic flow model in the context of the Kerner's three-phase traffic theory and empirical microscopic and macroscopic pattern characteristics measured on different freeways over various days and years. In this test of the microscopic three-phase traffic flow theory, a model of an "open" road is applied: Empirical time-dependence of traffic demand and drivers' destinations are used at the upstream model boundaries. At downstream model boundary conditions for vehicle freely leaving a modeling freeway section(s) are given. Spatiotemporal congested patterns emerge, develop, and dissolve in this open freeway model with the same types of bottlenecks as those in empirical observations. It is found that microscopic three-phase traffic models can explain all known macroscopic and microscopic empirical congested pattern features (e.g., probabilistic breakdown phenomenon as a first-order phase transition from free flow to synchronized flow, moving jam emergence in synchronized flow rather than in free flow, spatiotemporal features of synchronized flow and general congested patterns at freeway bottlenecks, intensification of downstream congestion due to upstream congestion at adjacent bottlenecks). It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic behavior is qualitatively different. Model performance with respect to spatiotemporal pattern emergence and evolution cannot be tested using these traffic characteristics. The reason for this is that important spatiotemporal features of congested traffic patterns are lost in these and many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models.
Similar content being viewed by others
References
Kerner, B.S.: The Physics of Traffic. Springer, Berlin, New York (2004)
Gartner, N.H., Messer, C.J., Rathi, A. (eds.): Special Report 165: Revised Monograph on Traffic Flow Theory. Transportation Research Board, Washington, DC (1997)
Wolf, D.E.: Phys. A 263, 438 (1999)
Chowdhury, D., Santen, L., Schadschneider, A.: Phys. Rep. 329, 199 (2000)
Helbing, D.: Rev. Mod. Phys. 73, 1067–1141 (2001)
Nagatani, T.: Rep. Prog. Phys. 65, 1331–1386 (2002)
Nagel, K., Wagner, P., Woesler, R.: Operat. Res. 51, 681–716 (2003)
Mahnke, R., Kaupužs, J., Lubashevsky, I.: Phys. Rep. 408, 1–130 (2005)
Lesort, J.-B. (ed.): Transportation and traffic theory. In: Proceedings of the 13th International Symposium on Transportation and Traffic Theory. Elsevier Science Ltd., Oxford (1996)
Ceder, A. (ed.): Transportation and traffic theory. In: Proceedings of the 14th International Symposium on Transportation and Traffic Theory. Elsevier Science Ltd., Oxford (1999)
Taylor, M.A.P. (ed.): Transportation and traffic theory in the 21st century. In: Proceedings of the 15th International Symposium on Transportation and Traffic Theory. Elsevier Science Ltd., Amsterdam (2002)
Mahmassani, H.S. (ed.): Transportation and traffic theory. In: Proceedings of the 16th International Symposium on Transportation and Traffic Theory. Elsevier, Amsterdam (2005)
Wolf, D.E., Schreckenberg, M., Bachem, A. (eds.): Traffic and granular flow. In: Proceedings of the International Workshop on Traffic and Granular Flow, October 1995. World Scientific, Singapore (1995)
Schreckenberg, M., Wolf, D.E. (eds.): Traffic and granular flow '97. In: Proceedings of the International Workshop on Traffic and Granular Flow, October 1997. Springer, Singapore (1998)
Helbing, D., Herrmann, H.J., Schreckenberg, M., Wolf, D.E. (eds.): Traffic and granular flow '99. In: Proceedings of the International Workshop on Traffic and Granular Flow, October 1999. Springer, Heidelberg (2000)
Fukui, M., Sugiyama, Y., Schreckenberg, M., Wolf, D.E. (eds.): Traffic and granular flow '01. In: Proceedings of the International Workshop on Traffic and Granular Flow, October 2001. Springer, Heidelberg (2003)
Hoogendoorn, S.P., Bovy, P.H.L., Schreckenberg, M., Wolf, D.E. (eds.): Traffic and granular flow '03. In: Proceedings of the International Workshop on Traffic and Granular Flow, October 2003. Springer, Heidelberg (2005)
Leutzbach, W.: Introduction to the Theory of Traffic Flow. Springer, Berlin (1988)
Edie, L.C., Foote, R.S.: Highway Res. Board, Proc. Ann. Meet. 37, 334 (1958)
Edie, L.C., Foote. R.S.: Effect of shock waves on tunnel traffic flow. In: Highway Research Board Proceedings, vol. 39, pp. 492–505. HRB, National Research Council, Washington, DC (1960)
Edie, L.C.: Operat. Res. 9, 66–77 (1961)
Treiterer, J., Myers, J.A.: The hysteresis phenomenon in traffic flow. In: Buckley, D.J. (ed.) Proceedings of the Sixth International Symposium on Transportation and Traffic Theory, pp. 13–38. A.H. & A.W. Reed, London (1974)
Treiterer, J.: Investigation of traffic dynamics by aerial photogrammetry techniques. Ohio State University Technical Report PB 246 094, Columbus, Ohio (1975)
Koshi, M., Iwasaki, M., Ohkura, I.: Some findings and an overview on vehicular flow characteristics. In: Hurdle, V.F. et al. (eds.) Proceedings of the Eighth International Symposium on Transportation and Traffic Theory, p. 403. University of Toronto Press, Toronto, Ontario (1983)
Kerner, B.S., Konhäuser, P.: Phys. Rev. E 50, 54–83 (1994)
Kerner, B.S., Konhäuser, P., Schilke, M.: Phys. Rev. E 51, 6243–6246 (1995)
Helbing, D., Hennecke, A., Treiber, M.: Phys. Rev. Lett. 82, 4360 (1999)
Lee, H.Y., Lee, H.-W., Kim, D.: Phys. Rev. E 59, 5101 (1999)
Treiber, M., Hennecke, A., Helbing, D.: Phys. Rev. E 62, 1805–1824 (2000)
Kerner, B.S.: Phys. Rev. Lett. 81, 3797 (1998)
Kerner, B.S.: Phys. Rev. E 65, 046138 (2002)
Kerner, B.S., Klenov, S.L.: J. Phys. A: Math. Gen. 35, L31 (2002)
Kerner, B.S., Klenov, S.L., Wolf, D.E.: J. Phys. A: Math. Gen. 35, 9971–10013 (2002)
Kerner, B.S., Klenov, S.L.: e-print: physics/0507120 (2005). E-print in http://arxiv.org/abs/physics/0507120
Kerner, B.S., Klenov, S.L.: J. Phys. A: Math. Gen. 39, 1775–1809 (2006)
Kerner, B.S., Klenov, S.L.: Phys. Rev. 68, 036130 (2003)
Kerner, B.S., Klenov, S.L.: J. Phys. A: Math. Gen. 37, 8753–8788 (2004)
Neubert, L., Santen, L., Schadschneider, A., Schreckenberg, M.: Phys. Rev. E 60, 6480 (1999)
Knospe, W., Santen, L., Schadschneider, A., Schreckenberg, M.: Phys. Rev. E 65, 056133 (2002)
Knospe, W., Santen, L., Schadschneider, A., Schreckenberg, M.: Phys. Rev. E 70, 016115 (2004)
Cremer, M.: Der Verkehrsfluss auf Schnellstrassen. Springer, Berlin (1979)
Brockfeld, E., Kühne, R.D., Skabardonis, A., Wagner, P.: Trans. Res. Rec. 1852, 124–129 (2003)
Wang, Y., Papageorgiou, M., Messmer, A.: Predictive feedback routing control strategy for freeway network traffic. Proceedings of the 83rd Annual Transportation Research Board Meeting, TRB Paper No. 04-3429. TRB,Washington, DC (2004)
Brockfeld, E., Kühne, R. D.,Wagner, P.: Calibration and validation of simulation models 2004. Proceeding of the Transportation Research Board 84th Annual Meeting, TRB Paper No. 05-2152. TRB, Washington, DC (2005)
Davis, L.C.: Phys. Rev. E 69, 016108 (2004)
Lee, H.K., Barlović, R., Schreckenberg, M., Kim, D.: Phys. Rev. Lett. 92, 238702 (2004)
Jiang, R., Wu, Q.S.: J. Phys. A: Math. Gen. 37, 8197–8213 (2004)
Gipps, P.G.: Trans. Res. B. 15, 105–111 (1981); Trans. Res. B. 20, 403–414 (1986)
Krauß, S., Wagner, P., Gawron, C.: Phys. Rev. E 55, 5597 (1997)
Cowan, R.J.: Trans. Rec. 9, 371–375 (1976)
Luttinen, T.: Transport. Res. Rec. 1365 92–98 (1992)
Bovy, P.H.L. (ed.): Motorway Analysis: New Methodologies and Recent Empirical Findings. Delft University Press, Delft (1998)
Tilch, B., Helbing, D.: In: SW3, p. 333
Banks, J.: Trans. Rec. B 37, 539–554 (2004)
Gurusinghe, G.S., Nakatsuji, T., Azuta, Y., Ranjitkar, P., Tanaboriboon, Y.: Multiple car-following data using real-time kinematic global positioning system. In: Preprints of the 82nd TRB Annual Meeting, TRB Paper No. 03-4137. TRB, Washington, DC (2003)
Bendat, J.S., Piersol, A.G.: Random Data. Analysis and Measurement Procedures. Wiley, New York (1986)
Wagner, P., Lubashevsky, I.: cond-mat/0311192 (2003)
Wagner, P.: In SW5, pp. 15–27
Nagel, K., Schreckenberg, M.: J. Phys. (France) I 2, 2221 (1992)
Nagel, K., Paczuski, M.: Phys. Rev. E 51, 2909 (1995)
Schreckenberg, M., Schadschneider, A., Nagel, K., Ito, N.: Phys. Rev. E 51, 2939 (1995)
Barlović, R., Santen, L., Schadschneider, A., Schreckenberg, M.: Eur. Phys. J. B. 5, 793 (1998)
Knospe, W., Santen, L., Schadschneider, A., Schreckenberg, M.: J. Phys. A 33, L477 (2000)
Kerner, B.S., Klenov, S.L., Hiller, A.: e-print: physics/ 0507094 (2005). E-print in http://arxiv.org/abs/physics/ 0507094
Kerner, B.S., Klenov, S.L., Hiller, A.: J. Phys. A: Math. Gen. 39, 2001–2020 (2006)
Kerner, B.S., Klenov, S.L., Hiller, A., Rehborn, H.: e-print: physics/0510167 (2005). E-print in http://arxiv.org/abs/ hysics/0510167
Kerner, B.S., Klenov, S.L., Hiller, A., Rehborn, H.: Phys. Rev. E 73, 046107 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS: 89.40. + k, 47.54. + r, 64.60.Cn, 64.60.Lx
Rights and permissions
About this article
Cite this article
Kerner, B.S., Klenov, S.L. & Hiller, A. Empirical test of a microscopic three-phase traffic theory. Nonlinear Dyn 49, 525–553 (2007). https://doi.org/10.1007/s11071-006-9113-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-006-9113-1