Abstract
A review of an experimental study of traffic phases and phase transitions in traffic flow is presented. A critical comparison of model results with real features of traffic phases is given. A qualitative theory of congested traffic which has recently been developed is discussed.
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M.J. Lighthill, and G.B. Whitham., “ On Kinematic Waves: A Theory of Traffic on Long Crowed Roads, ” Proc. Royal Society A, 229, 1995, pp. 317-345.
R. Herman, E.W. Montroll, R.B. Potts, and R.W. Rothery, “ Traffic Dynamics: Analysis of stability in car following, ” Operations Res., 7, 1959, pp. 86-106.
D.C. Gazis, R. Herman, and R.W. Rothery, “ Nonlinear Follow-the-Leader Models of Traffic Flow, ” Operations Res., 9, 1961, pp. 545-567.
G.F. Newell, “ Nonlinear Effects in the Dynamic of Car Following, ” Operations Res., 9, 1961, pp. 209-229.
I. Prigogine, and R. Herman, Kinetic Theory of Vehicular Traffic American, New York: Elsevier, 1971.
H.J. Payne, “ Models of Freeway Traffic and Control, ” In G.A. Beke (ed.), Mathematical Models of Public Systems, Vol. 1. La Jolla, CA: Simulation Council, 1971, pp. 51-61.
R. Wiedemann, Simulation des Verkehrsflusses, Karlsruhe: University of Karlsruhe, 1974.
P.G. Gipps, “ A Behavioral Car-Following Model for Computer Simulation, ” Trans. Res. B, 15, 1981, pp. 105-111.
G.F. Newell, Applications of Queuing Theory, London: Chapman Hall, 1982.
C.F. Daganzo, Fundamentals of Transportation and Traffic Operations, New York: Elsevier Science Inc., 1997.
J.-B. Lesort, (ed.), “ Transportation and Traffic Theory, ” Proceedings of the 13th International Symposium on Transportation and Traffic Theory, Oxford: Elsevier Science Ltd., 1996.
A. Ceder, (ed.), “ Transportation and Traffic Theory, ” Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Oxford: Elsevier Science Ltd., 1999.
D.E. Wolf, M. Schreckenberg, and A. Bachem (eds.), “ Traffic and Granular Flow, ” Proceedings of the International Workshop on Traffic and Granular Flow, Singapore: World Scientific, October 1995, 1996.
M. Schreckenberg, and D.E. Wolf (eds.), “ Traffic and Granular Flow '97, ” Proceedings of the International Workshop on Traffic and Granular Flow, Singapore: Springer, October 1997, 1998.
D. Helbing, H.J. Herrmann, M. Schreckenberg, and D.E. Wolf (eds.), “ Traffic and Granular Flow '99, ” Proceedings of the International Workshop on Traffic and Granular Flow, Heidelberg: Springer, October 1999, 2000.
K. Nagel, and M. Schreckenberg, “ A Cellular Automaton Model for Freeway Traffic, ” J Phys. (France) I, 2, 1992, pp. 2221-2229.
G.B. Whitham, “ Exact Solutions for a Discrete System Arising in the Traffic Flow, ” Proc. R. Soc. London A, 428, 1990, pp. 49-69.
M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, “ Dynamical Model of Traffic Congestion and Numerical Simulation, ” Phys. Rev. E, 51, 1995, pp. 1035-1042.
B.S. Kerner, and P. KonhaÈuser, “ Cluster Effect in Initially Homogeneous Traffic Flow, ” Phys. Rev. E, 48, 1993, R2335-R2338.
B.S. Kerner, and P. KonhaÈuser, “ Structure and Parameters of Clusters in Traffic Flow, ” Phys. Rev. E, 50, 1994, pp. 54-83.
M. Herrmann, and B.S. Kerner, “ Local Cluster Effect in Different Traffic Flow Models, ” Physica A, 255, 1998, 163-188.
M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, “ Phenomenological Study of Dynamical Model of Traffic Flow, ” J. Phys. I France, 5, 1995, pp. 1389-1399.
S. Krauû, P. Wagner, and C. Gawron, “ Metastable States in a Microscopic Model of Traffic, ” Phys. Rev. E, 53, 1997, pp. 5597-5607.
R. Barlovic, L. Santen, A. Schadschneider, and M. Schreckenberg, “ Metastable States in Cellular Automata for Traffic Flow, ” Eur. Phys. J. B, 5, 1998, pp. 793-800.
D. Helbing, and M. Schreckenberg, “ Cellular Automata Simulating Experimental Properties of Traffic Flow, ” Phys. Rev. E, 59, 1999, pp. R2505-R2509.
M. Treiber, A. Hennecke, and D. Helbing, “ Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model, ” Phys. Rev. E, 59, 1999, pp. 239-252.
R. Mahnke, and J. KaupuzÏs, “ Stochastic Theory of Freeway Traffic, ” Phys. Rev. E, 59, 1999, 117-125.
G.B. Whitham, Linear and Nonlinear Waves, New York: Wiley, 1974.
A.D. May, Traffic Flow Fundamental, New Jersey: Prentice Hall Inc., 1990.
M. Cremer, Der Verkehrsfluss auf Schnellstrassen, Berlin: Springer, 1974.
W. Leutzbach, Introduction to the Theory of Traffic Flow, Berlin: Springer, 1988.
D. Helbing, Verkehrsdynamik, Berlin Heidelberg: Springer; Rev. Mod. Phys., (2001) (to appear).
R. Kuèhne, “ Macroscopic Freeway Model for Dense Traffic, ” In U. Brannolte (ed.), Highway Capacity and Level of Service, A. A. Balkema: Rotterdam, pp. 211-233, 1991.
M. Rickert, K. Nagel, M. Schreckenberg, and Latour, “ Two-Lane Traffic Simulation for Cellular Automata, ” Physica A, 231, 1996, pp. 534-550.
K. Angel, D.E. Wolf, P. Wagner, and P. Simon, “ Two-Lane Traffic rules for Cellular Automata: A Systematic Approach, ” Phys. Rev. E, 58, 1998, pp. 1425-1437.
B.S. Kerner, S.L. Klenov, and P. KonhaÈuser, “ Asymptotic Theory of Traffic Jams, ” Phys. Rev. E, 56, 1997, pp. 4200-4216.
B.S. Kerner, P. KonhaÈuser, and M. Schilke, “ Deterministic Spontaneous Appearance of Traffic Jams in Slightly Inhomogeneous Traffic Jams, ” Phys. Rev. E, 51, 1995, pp. 6243-6246.
H.Y. Lee, H.-W. Lee, and D. Kim, “ Orig in of Synchronized Traffic Flow on Highways and its Dynamic Phase Transitions, ” Phys. Rev. Lett., 81, 1998, pp. 1130-1133.
D.M. Helbing, and M. Treiber, “ Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition, ” Phys. Rev. Lett., 81, 1998, pp. 3042-3045.
D. Helbing, A. Hennecke, and M. Treiber, “ Phase Diagram of Traffic States in the Presence of Inhomogeneities, ” Phys. Rev. Lett., 82, 1999, pp. 4360-4363.
H.Y. Lee, H.-W. Lee, and D. Kim, “ Dynamic states of a continuum traffic equation with on-ramp, ” Phys. Rev. E, 59, 1999, pp. 5101-5111.
M. Treiber, A. Hennecke, and D. Helbing, “Congested Traffic States in Empirical Observations and Microscopic Simulations,” Cond-mat=0002177.
D. Chowdhury, L. Santen, and A. Schadschneider, “ Statistical Physics of Vehicular TrafFIc and Some Related Systems, ” Physics Reports, 329, 2000, pp. 199-268.
T. Nagatani, “ Bunching of Cars in Asymmetric Exclusion Models for Freeway Traffic, ” Phys. Rev. E, 51, 1995, pp. 922-928.
B.S. Kerner, P. KonhaÈuser, and M. Schilke, “ Dipole-layer' Effect in Dene Traffic Flow, ” Phys. Lett. A, 215, 1996, pp. 45-56.
B.S. Kerner, P. KonhaÈuser, and M. Roèdiger, “ Appearance of Moving Local Clusters of Vehicles on Highway with Bottlenecks, ” In Proceedings of the Second World Congress on the Intelligent Transport Systems. Vol. IV, Tokyo: VERTIS, pp. 1911-1914, 1995.
D. Helbing, “ Improved Fluid-dynamic Model for Vehicular Traffic, ” Phys. Rev. E, 51, 1995, pp. 3164-3169.
P. Nelson, “ A Kinetic Model of Vehicular Traffic and is Associated Bimodal Equilibrium Solutions, ” Transp. Theory Stat. Phys. 24, 1995, pp. 383-409. “On Deterministic Developments of Traffic Stream Models,” Transp. Res. B, 29, 1995, pp. 297-302.
R. Wegener, and A. Klar, “ A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model, ” Transp. Theory Stat. Phys., 25, 1996, pp. 785-794.
D. Helbing, “ Gas-Kinetic Derivation of Navier-Stokes-Like Traffic Equations, ” Phys. Rev. E, 53, 1996, pp. 2366-2381.
R. Mahnke, and N. Pieret, “ Stochastic Master-Equation Approach to Aggregation in Freeway Traffic, ” Phys. Rev. E, 56, 1997, pp. 2666-2671.
P. Wagner, K. Nagel, and D.E. Wolf, “ Second Order Continuum Traffic Flow Model, ” Physica A, 234, 1996, pp. 687-695.
E. Tomer, L. Safonov, and S. Havlin, “ Presence of Many Stable Nonhomogeneous States in an Inertial Car Following Model, ” Phys. Rev. Lett., 84, 2000, pp. 382-385.
D. Helbing, and A. Griener, “ Modeling and Simulation of Multilane Traffic Flow, ” Phys. Rev. E, 1997, pp. 55, 5498-5508.
H.M. Zhang, “ An Analysis of the Stability and Waves Properties of a New Continuum Theory, ” Trans. Rec. B, 33, 1999, pp. 387-398.
M. Koshi, M. Iwasaki, and I. Ohkura, “ Some Findings and an Overview on Vehicular Flow Characteristics, ” In V.F. Hurdle, E. Hauer, and G.N. Stewart (eds.), Proceedings of 8th International Symposium on Transportation and Traffic Theory, Toronto, Ontario: University of Toronto Press, pp. 403-425, 1983.
F.L. Hall, B.L. Allen, and M.A. Gunter, “ Empirical Analysis of Freeway Flow-Density Relationships, ” Trans. Res. A, 20, 1986, pp. 197-210.
J.H. Banks, “ Freeway Speed-Flow-Concentration Relationships: More Evidence and Interpretations, ” Transportation Research Record, 1225, 1989, pp. 53-60.
F.L. Hall, V.F. Hurdle, and J.H. Banks, “ Synthesis of Recent Works on the Nature of Speed-Flow and Flow-Occupancy (or Density) Relationships on Freeways, ” Transportation Research Record, 1365, 1992, pp. 12-18.
F.L. Hall, and F.O. Montgomery, “ Investigation of an Alternative Interpretation of the Speed-Flow Relationship for UK Motor Ways, ” Traffic Engineering and Control, 34, 1993, pp. 420-425.
L.C. Edie, and R.S. Foote, “ Experiments on Single-Lane Flow in Tunnels, ” In R. Herman (ed.), Proceedings of Symposium on the Theory of Traffic Flow, New York: Elsevier, pp. 175-192, 1959.
J. Treiterer, “ Investigation of Traffic Dynamics by Aerial Photogrammetric Techniques, ” Ohio State University Technical Report PB 246 094. Columbus, Ohio: Ohio State University, 1975.
P.H.L. Bovy, (ed.), Motorway Analysis: New Methodologies and Recent Empirical Findings, Delf: Delft University, Press Delft, 1998.
W. Brilon, and M. Ponzlet, “ Application of Traffic Flow Models, ” In D.E. Wolf, M. Schreckenberg, and A. Bachem (eds.), Traffic and Granular Flow. Proceedings of the International Workshop on Traffic and Granular Flow, Singapore: World Scientific, October 1995, pp. 23-40, 1996.
B.S. Kerner, and H. Rehborn, “ Experimental Properties of Complexity in Traffic Flow, ” Phys. Rev. E, 53, 1996, pp. R4275-R4278.
B.S. Kerner, “ A Theory of Congested Traffic Flow, ” In R. Rysgaard (ed.), Proceedings of the 3rd Symposium on Highway Capacity and Level of Service, Vol. 2, Denmark: Road Directorate Denmark, pp. 621-642, 1998.
B.S. Kerner, and H. Rehborn, “ Experimental Properties of Phase Transitions in Traffic Flow, ” Phys. Rev. Lett., 79, 1997, pp. 4030-4033.
B.S. Kerner, “ Experimental Features of Self-Organization in Traffic Flow, ” Phys. Rev. Lett., 81, 1998, pp. 3797-3800.
B.S. Kerner, “ Traffic Flow: Experiment and Theory, ” In M. Schreckenberg, and D.E. Wolf (eds.), Proceedings of the International Workshop on Traffic and Granular Flow. Traffic and Granular Flow'97, Singapore: Springer, October 1997, pp. 239-267, 1998.
B.S. Kerner, “ Theory of Congested Traffic Flow: Self Organization without Bottlenecks. Transportation and Traffic Theory, ” In A. Ceder (ed.), Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Oxford: Elsevier Science Ltd, pp. 147-171, 1999.
B.S. Kerner, “ Congested Traffic Flow: Observations and Theory, ” Transportation Research Record, 1678, 1999, pp. 160-167.
B.S. Kerner, “ The Physics of Traffic, ” Physic World, 12, 1999, pp. 25-30.
B.S. Kerner, and V.V. Osipov, Autosolitons: A New Approach to Problems of Self-Organization and Turbulence, Dordrecht, Boston, London: Kluwer, 1994.
B.S. Kerner, and H. Rehborn, “ Experimental Features and Characteristics of Traffic Jams, ” Phys. Rev. E, 53, 1996, pp. R1297-R1300.
B.S. Kerner, and H. Rehborn, “ Messungen des Verkehrsflusses: Charakteristische Eigenschafften von Staus auf Autobahnen, ” Internationales Verkehrswesen, 50, 1998, pp. 196-203.
B.S. Kerner, H. Rehborn, and H. Kirschfink, “ Method for the Automatic Monitoring of Traffic Including the Analysis of Back-up Dynamics, ” German patent DE 196 47 127 (www.depanet.de) (US-patent US 586 1820 (dips-2.dips.org)), 1998.
B.S. Kerner, H. Rehborn, and H. Kirschfink, “ Automatische Stauverfolgung auf Autobahnen Strassenver-kehrstechnik, ” No. 9, 1997, pp. 430-438.
B.S. Kerner, H. Rehborn, and M. Aleksic, “ Forecasting of Traffic Congestion. Traffic and Granular Flow' 99, ” In D. Helbing, H.J. Herrmann, M. Schreckenberg, and D.E. Wolf (eds.), Proceedings of the International Workshop on Traffic and Granular Flow, Heidelberg: Springer, October 1999, 2000.
B.S. Kerner, “ Synchronized Flow as a New Traffic Phase and Related Problems for Traffic Flow Modelling, ” Mathematical and Computer Modelling, (to appear), 2001.
W. Brilon, and N. Wu, “ Evaluation of Cellular Automata for Traffic Flow Simulation on Freeway and Urban Streets, ” In W. Brilon, F. Huber, M. Schreckenberg, and H. Wallentowitz (eds.), Traffic and Mobility, Berlin: Springer, 1999.
P. Wagner, “ Traffic Simulations using Cellular Automata: Comparison with Reality. Traffic and Granular Flow, ” In D.E. Wolf, M. Schreckenberg, and A. Bachem, (eds.), Proceedings of the International Workshop on Traffic and Granular Flow, Singapore: World Scientific, October 1995, 1996.
B.S. Kerner, “ Phase Transitions in Traffic Flow. Traffic and Granular Flow' 99, ” In D. Helbing, H.J. Herrmann, M. Schreckenberg, and D.E. Wolf (eds.), Proceedings of the International Workshop on Traffic and Granular Flow, Heidelberg: Springer, October 1999, 2000.
L. Neubert, L. Santen, A. Schadschneider, and M. Schreckenberg, “ Single-Vehicle Data of Highway Traffic: A Statistical Analysis, ” Phys. Rev. E, 60, 1999, pp. 6480-6490.
B.S. Kerner, “ Theory of Breakdown Phenomenon at Highway Bottlenecks, ” In Preprints of the 79th TRB Annual Meeting, Washington D.C., January 9-13, 2000, Paper No. 00-1573, Washington, DC: 2000; Transportation Research Record, 1710, 2000, pp. 136-144.
I.A. Lubashevsky, and R. Mahnke, “ Order Parameter as an Additional State Variable of Unstable Traffic Flow, ” In D. Helbing, H.J. Herrmann, M. Schreckenberg, and D.E. Wolf (eds.), Traffic and Granular Flow' 99. Proceedings of the International Workshop on Traffic and Granular Flow, Heidelberg: Springer, October 1999, 2000.
B.S. Kerner, “ Experimental Features of the Emergence of moving Jams in Free Traffic Flow, ” J. Phys. A: Math. and General, 33, 2000, pp. L221-L228.
B. Persaud, S. Yagar, and R. Brownlee, “ Exploration of the Breakdown Phenomenon in Freeway Traffic, ” Transportation Research Record, 1634, 1998, pp. 64-72.
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Kerner, B.S. Complexity of Synchronized Flow and Related Problems for Basic Assumptions of Traffic Flow Theories. Networks and Spatial Economics 1, 35–76 (2001). https://doi.org/10.1023/A:1011577010852
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DOI: https://doi.org/10.1023/A:1011577010852