Congested traffic states in empirical observations and microscopic simulations
Open accessAbstract
We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous or oscillating. Combined states are observed as well, like the coexistence of moving localized clusters and clusters pinned at road inhomogeneities, or regions of oscillating congested traffic upstream of nearly homogeneous congested traffic. The experimental findings are consistent with a recently proposed theoretical phase diagram for traffic near on-ramps [D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. 82, 4360 (1999)]. We simulate these situations with a continuous microscopic single-lane model, the "intelligent driver model," using empirical boundary conditions. All observations, including the coexistence of states, are qualitatively reproduced by describing inhomogeneities with local variations of one model parameter. We show that the results of the microscopic model can be understood by formulating the theoretical phase diagram for bottlenecks in a more general way. In particular, a local drop of the road capacity induced by parameter variations has essentially the same effect as an on-ramp.
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- F. L. Hall and K. Agyemang-Duah, Transp. Res. Rec. 1320, 91 (1991).
- C. F. Daganzo, in Proceedings of the 13rd International Symbosium on Transportation and Traffic theory, edited by J. B. Lesort (Pergamon, Tarrytown, 1996), p. 629.
- B. S. Kerner and H. Rehborn, Phys. Rev. E 53, R4275 (1996).
- B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997).
- T. Nagatani, J. Phys. Soc. Japan 66, L1928 (1997).
- B. Persaud, S. Yagar, and R. Brownlee, Transportation Research Record 1634, 64 (1998).
- B. S. Kerner, Phys. Rev. Lett. 81, 3797 (1998).
- D. Helbing and M. Treiber, Phys. Rev. Lett. 81, 3042 (1998).
- D. Helbing and M. Treiber, Science 282, 2001 (1998).
- H. Y. Lee, H. W. Lee, and D. Kim, Phys. Rev. Lett. 81, 1130 (1998).
- H. Y. Lee, H. W. Lee, and D. Kim, Phys. Rev. E 59, 5101 (1999).
- H. Y. Lee and H. W. Lee and D. Kim, Empirical Phase Diagram of Congested Traffic Flow, Preprint cond-mat/9905292. · arXiv
- C. F. Daganzo, M. J. Cassidy, and R. L. Bertini, Transportation Research B 33, 25 (1999).
- D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. 82, 4360 (1999).
- B. S. Kerner and H. Rehborn, Internationales Verkehrswesen 5, 196 (1998).
- D. Helbing and M. Treiber, Computing in Science and Engineering (CiSE) 5, 89 (1999).
- D. Helbing, Verkehrsdynamik (Springer, Berlin, 1997).
- D. Helbing, Phys. Rev. E 55, R25 (1997).
- M. Treiber and D. Helbing, J. Phys. A 32, L17 (1999).
- S. Smulders, 7th International Conference on Road Traffic Monitoring and Control (IEE, London, 1994), pp. 145-149.
- V. Shvetsov and D. Helbing, Phys. Rev. E 59, 6328 (1999).
- B. S. Kerner and H. Rehborn, Phys. Rev. E 53, R1297 (1996).
- M. J. Lighthill and G. B. Whitham, Proc. Roy. Soc. of London A 229, 317 (1955).
- M. Cremer and F. Meißner, Traffic Prediction and Optimization Using an Efficient Macroscopic Simulation Tool. In: A. Pave, ed. Modelling and Simulation 1993, pp. 513-519. Society for Computer Simulation International, Ghent, Belgium.
- B. S. Kerner and P. Konhäuser, Phys. Rev. E 50, 54 (1994).
- M. Treiber, A. Hennecke, and D. Helbing, Phys. Rev. E 59, 239 (1999).
- G. F. Newell, Operations Research 9, 209 (1961).
- P. G. Gipps, Transportation Research B 15, 105 (1981).
- R. Wiedemann, Simulation des Straßenverkehrsflusses. Schriftenreihe des IfV, Vol. 8 (Institut für Verkehrswesen, University of Karlsruhe, Germany, 1974).
- M. Bando et al., Phys. Rev. E 51, 1035 (1995).
- S. Krauß, in Traffic and Granular Flow '97, edited by M. Schreckenberg and D. E. Wolf (Springer, Singapore, 1998), pp. 269-283.
- B. Tilch and D. Helbing, Phys. Rev. E 58, 133 (1998).
- L. D. Howe, Physica A 246, 157 (1997).
- M. Treiber and D. Helbing, "Explanation of observed features of self-organization in traffic flow". Preprint cond-mat/9901239. · arXiv
- M. Treiber, A. Hennecke, and D. Helbing, in Traffic and Granular Flow '99, edited by D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf (Springer, Berlin, 2000), in print.
- O. Biham, A. A. Middleton, and D. Levine, Phys. Rev. A 46, R6124 (1992).
- M. Cremer and J. Ludwig, Math. Comput. Simulation 28, 297 (1986).
- K. Nagel and M. Schreckenberg, J. Phys. I France 2, 2221 (1992).
- R. Barlovic, L. Santen, A. Schadschneider, and M. Schreckenberg, Traffic and Granular Flow '97 (Springer, Singapore, 1998), p. 335.
- D. Helbing and B. A. Huberman, Nature 396, 738 (1998).
- D. E. Wolf, Physica A 263, 438 (1999).
- R. D. Kühne, in Proceedings of the 9th International Symposium on Transportation and Traffic Theory, edited by I. Volmuller and R. Hamerslag (VNU Science Press, Utrecht, 1984), p. 21
- J. Treiterer and J. A. Myers, in Proc. 6th Int. Symp. on Transportation and Traffic Theory, edited by D. J. Buckley (Elsevier, New York, 1974), p. 13, empirical observation of trajectories.
- A. Hennecke, M. Treiber, and D. Helbing, in Traffic and Granular Flow '99, edited by D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf (Springer, Berlin, 2000), p. to be published.
- A. Reuschel, Österreichisches Ingenieur-Archiv 4, 193 (1950).
- R. E. Chandler, R. Herman, and E. W. Montroll, Operations Research 6, 165 (1958).
- R. Herman, E. W. Montroll, R. B. Potts, and R. W. Rothery, Operations Research 7, 86 (1959).
- D. C. Gazis, R. Herman, and R. W. Rothery, Operations Research 9, 545 (1961).
- L. C. Edie, Transp. Res. B 28, 66 (1961).
- T. Bleile, Modellierung des Fahrzeugfolgeverhaltens im innerstädtischen PKW-Verkehr, (Phd thesis, University of Stuttgart, Germany, 1999).
- M. Muramatsu and T. Nagatani, Phys. Rev. E 60, 180 (1999).
- B. S. Kerner, P. Konhäuser, and M. Schilke, Phys. Rev. E 51, 6243 (1995).
- D. C. Gazis and R. Herman, Transportation Science 26(3),223-229 (1992).
- E. Ben-Naim and P. L. Krapivsky, Phys. Rev. E 56, 6680 (1997).
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- Authors
- Treiber, M., Hennecke, A., & Helbing, D.
- Affiliations
- University of Stuttgart (DE)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2000-08-01
- Volume
- 62
- Issue
- 2
- Pages
- 1805-1824
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W1965455100
- Cited by
- 4,762
- References
- 0
- Citations by year
- 2026: 447 · 2025: 519 · 2024: 517 · 2023: 459 · 2022: 396 · 2021: 343 · 2020: 291 · 2019: 262 · 2018: 207 · 2017: 155 · 2016: 123 · 2015: 140 · 2014: 136 · 2013: 113 · 2012: 112
- FWCI
- 58.76
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft
- Bundesministerium für Bildung und Forschung
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Traffic control and management
- Physical Sciences › Engineering › Ocean Engineering › Evacuation and Crowd Dynamics
- Physical Sciences › Engineering › Building and Construction › Traffic Prediction and Management Techniques
- Keywords
- traffic congestion, intersections, phase diagram, Intelligent Driver Model, microscopic traffic simulation, on-ramps, road capacity, motorways
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