Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Traffic Breakdown, Modeling Approaches to

  • Boris S. Kerner
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_559-2

Glossary

Bottleneck

Traffic breakdown occurs mostly at road bottlenecks. Just as defects and impurities are important for phase transitions in complex spatially distributed systems of various nature, so are bottlenecks in vehicular traffic. A road bottleneck can be a result of roadworks, on- and off-ramps, a decrease in the number of freeway lanes, road curves and road gradients, traffic signal, etc.

Congested Traffic

Congested traffic is defined as a state of traffic in which the average speed is lower than the minimum average speed that is possible in free flow.

F → S transition

In all known observations, traffic breakdown at a highway bottleneck is a phase transition from the free flow phase to synchronized flow phase (F → S transition). The empirical traffic breakdown (F → S transition) exhibits the nucleation nature. The empirical nucleation nature of traffic breakdown is explained by the metastability of free flow with respect to the F → S transition at the bottleneck. The terms t...

This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

I would like to thank Sergey Klenov for help and useful suggestions. We thank our partners for their support in the project “MEC-View – Object detection for automated driving based on Mobile Edge Computing,” funded by the German Federal Ministry of Economic Affairs and Energy.

Bibliography

  1. Ahn S, Cassidy MJ (2007) Freeway traffic oscillations and vehicle lane-change maneuvers. In: Allsop RE, Bell MGH, Hydecker BG (eds) Transportation and traffic theory 2007. Elsevier, Amsterdam, pp 691–710Google Scholar
  2. Aw A, Rascle M (2000) Resurrection of “second order” models of traffic flow. SIAM J Appl Math 60:916–938MathSciNetzbMATHCrossRefGoogle Scholar
  3. Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1994) Structure stability of congestion in traffic dynamics. Jpn J Appl Math 11:203–223MathSciNetzbMATHCrossRefGoogle Scholar
  4. Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995a) Dynamical model of traffic congestion and numerical simulation. Phys Rev E 51:1035–1042ADSCrossRefGoogle Scholar
  5. Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995b) Phenomenological study of dynamical model of traffic flow. J Phys I France 5:1389–1399CrossRefGoogle Scholar
  6. Banks JH (1989) Freeway speed-flow-concentration relationships: more evidence and interpretations (with discussion and closure). Transp Res Rec 1225:53–60Google Scholar
  7. Banks JH (1990) Two-capacity phenomenon at freeway bottlenecks: a basis for ramp metering? Transp Res Rec 1287:20–28Google Scholar
  8. Barlović R, Santen L, Schadschneider A, Schreckenberg M (1998) Metastable states in cellular automata for traffic flow. Eur Phys J B 5:793–800ADSCrossRefGoogle Scholar
  9. Bellomo N, Coscia V, Delitala M (2002) On the mathematical theory of vehicular traffic flow I. Fluid dynamic and kinetic modelling. Math Models Methods Appl Sci 12:1801–1843MathSciNetzbMATHCrossRefGoogle Scholar
  10. Berg P, Woods A (2001) On-ramp simulations and solitary waves of a car-following model. Phys Rev E 64:035602(R)ADSCrossRefGoogle Scholar
  11. Bovy PHL (ed) (1998) Motorway analysis: new methodologies and recent empirical findings. Delft University Press, DelftGoogle Scholar
  12. Brilon W, Zurlinden H (2004) Kapazität von Straßen als Zufallsgröße. Straßenverkehrstechnik 4:164Google Scholar
  13. Brilon W, Geistefeld J, Regler M (2005a) Reliability of freeway traffic flow: a stochastic concept of capacity. In: Mahmassani HS (ed) Transportation and traffic theory. Proceedings of the 16th international symposium on transportation and traffic theory. Elsevier, Amsterdam, pp 125–144Google Scholar
  14. Brilon W, Regler M, Geistefeld J (2005b) Zufallscharakter der Kapazität von Autobahnen und praktische Konsequenzen – Teil 1. Straßenverkehrstechnik 3:136Google Scholar
  15. Brockfeld E, Kühne RD, Skabardonis A, Wagner P (2003) Toward benchmarking of microscopic traffic flow models. Trans Res Rec 1852:124–129CrossRefGoogle Scholar
  16. Brockfeld E, Kühne RD, Wagner P (2005) Calibration and validation of simulation models. In: Proceeding of the transportation research board 84th annual meeting, TRB paper no. 05-2152. TRB, Washington, DCGoogle Scholar
  17. Ceder A (ed) (1999) Transportation and traffic theory. In: Proceedings of the 14th international symposium on transportation and traffic theory. Elsevier Science Ltd, OxfordGoogle Scholar
  18. Chandler RE, Herman R, Montroll EW (1958) Traffic dynamics: studies in car following. Oper Res 6:165–184MathSciNetCrossRefGoogle Scholar
  19. Chowdhury D, Santen L, Schadschneider A (2000) Statistical physics of vehicular traffic and some related systems. Phys Rep 329:199ADSMathSciNetCrossRefGoogle Scholar
  20. Cowan RJ (1976) Useful headway models. Trans Rec 9:371–375CrossRefGoogle Scholar
  21. Cremer M (1979) Der Verkehrsfluss auf Schnellstrassen. Springer, BerlinCrossRefGoogle Scholar
  22. Daganzo CF (1994) The cell-transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transp Res B 28:269–287CrossRefGoogle Scholar
  23. Daganzo CF (1995) The cell transmission model, part II: network traffic. Transp Res B 29:79–93CrossRefGoogle Scholar
  24. Daganzo CF (1997) Fundamentals of transportation and traffic operations. Elsevier Science, New YorkCrossRefGoogle Scholar
  25. Daganzo CF, Cassidy MJ, Bertini RL (1999) Possible explanations of phase transitions in highway traffic. Transp Res A 33:365–379Google Scholar
  26. Davis LC (2004a) Multilane simulations of traffic phases. Phys Rev E 69:016108ADSCrossRefGoogle Scholar
  27. Davis LC (2004b) Effect of adaptive cruise control systems on traffic flow. Phys Rev E 69:066110ADSCrossRefGoogle Scholar
  28. Davis LC (2006a) Controlling traffic flow near the transition to the synchronous flow phase. Physica A 368:541–550ADSCrossRefGoogle Scholar
  29. Davis LC (2006b) Effect of cooperative merging on the synchronous flow phase of traffic. Physica A 361:606–618ADSCrossRefGoogle Scholar
  30. Davis LC (2007) Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp. Physica A 379:274–290ADSCrossRefGoogle Scholar
  31. Davis LC (2008) Driver choice compared to controlled diversion for a freeway double on-ramp in the framework of three-phase traffic theory. Physica A 387:6395–6410ADSCrossRefGoogle Scholar
  32. Davis LC (2014) Nonlinear dynamics of autonomous vehicles with limits on acceleration. Physica A 405:128–139ADSMathSciNetCrossRefGoogle Scholar
  33. Davis LC (2016) Improving traffic flow at a 2-to-1 lane reduction with wirelessly connected, adaptive cruise control vehicles. Physica A 451:320–332ADSCrossRefGoogle Scholar
  34. Edie LC (1961) Car-following and steady state theory for non-congested traffic. Oper Res 9:66–77MathSciNetzbMATHCrossRefGoogle Scholar
  35. Edie LC, Foote RS (1958) Traffic flow in tunnels. Highway Res Board Proc Ann Meet 37:334–344Google Scholar
  36. Edie LC, Foote RS (1960) Effect of shock waves on tunnel traffic flow. In: Highway research board proceedings, vol 39. HRB, National Research Council, Washington, DC, pp 492–505Google Scholar
  37. Edie LC, Herman R, Lam TN (1980) Observed multilane speed distribution and the kinetic theory of vehicular traffic. Transp Sci 14:55–76CrossRefGoogle Scholar
  38. Elefteriadou L (2014) An introduction to traffic flow theory. Springer optimization and its applications, vol 84. Springer, BerlinzbMATHCrossRefGoogle Scholar
  39. Elefteriadou L, Roess RP, McShane WR (1995) Probabilistic nature of breakdown at freeway merge junctions. Transp Res Rec 1484:80–89Google Scholar
  40. Elefteriadou L, Kondyli A, Brilon W, Hall FL, Persaud B, Washburn S (2014) Enhancing ramp metering algorithms with the use of probability of breakdown models. J Transp Eng 140:04014003CrossRefGoogle Scholar
  41. Fukui M, Sugiyama Y, Schreckenberg M, Wolf DE (eds) (2003) Traffic and granular flow’ 01. Springer, HeidelbergzbMATHGoogle Scholar
  42. Gao K, Jiang R, Hu S-X, Wang B-H, Wu Q-S (2007) Cellular-automaton model with velocity adaptation in the framework of Kerner’s three-phase traffic theory. Phys Rev E 76:026105ADSCrossRefGoogle Scholar
  43. Gartner NH, Messer CJ, Rathi A (eds) (1997) Special report 165: revised monograph on traffic flow theory. Transportation Research Board, Washington, DCGoogle Scholar
  44. Gazis DC (2002) Traffic theory. Springer, BerlinzbMATHGoogle Scholar
  45. Gazis DC, Herman R, Potts RB (1959) Car-following theory of steady-state traffic flow. Oper Res 7:499–505MathSciNetCrossRefGoogle Scholar
  46. Gazis DC, Herman R, Rothery RW (1961) Nonlinear follow-the-leader models of traffic flow. Oper Res 9:545–567MathSciNetzbMATHCrossRefGoogle Scholar
  47. Gipps PG (1981) Behavioral car-following model for computer simulation. Trans Res B 15:105–111CrossRefGoogle Scholar
  48. Greenshields BD (1935) A study of traffic capacity. In: Highway research board proceedings, (Highway Research Board, Washington, DC), vol 14, pp 448–477Google Scholar
  49. Haight FA (1963) Mathematical theories of traffic flow. Academic, New YorkzbMATHGoogle Scholar
  50. Hall FL, Agyemang-Duah K (1991) Freeway capacity drop and the definition of capacity. Trans Res Rec 1320:91–98Google Scholar
  51. Hall FL, Hurdle VF, Banks JH (1992) Synthesis of recent work on the nature of speed-flow and flow-occupancy (or density) relationships on freeways. Transp Res Rec 1365:12–18Google Scholar
  52. Hausken K, Rehborn H (2015) Game-theoretic context and interpretation of Kerners three-phase traffic theory. In: Hausken K, Zhuang J (eds) Game theoretic analysis of congestion, safety and security. Springer series in reliability engineering. Springer, Berlin, pp 113–141Google Scholar
  53. He S, Guan W, Song L (2010) Explaining traffic patterns at on-ramp vicinity by a driver perception model in the framework of three-phase traffic theory. Physica A 389:825–836ADSCrossRefGoogle Scholar
  54. Hegyi A, Bellemans T, De Schutter B (2017) Freeway traffic management and control. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC. Springer, BerlinGoogle Scholar
  55. Helbing D (2001) Traffic and related self-driven many-particle systems. Rev Mod Phys 73:1067–1141ADSCrossRefGoogle Scholar
  56. Helbing D, Hennecke A, Treiber M (1999) Phase diagram of traffic states in the presence of Inhomogeneities. Phys Rev Lett 82:4360–4363ADSCrossRefGoogle Scholar
  57. Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) (2000) Traffic and granular flow’ 99. Springer, HeidelbergzbMATHGoogle Scholar
  58. Helbing D, Treiber M, Kesting A, Schönhof M (2009) Theoretical vs. empirical classification and prediction of congested traffic states. Eur Phys J B 69:583–598ADSCrossRefGoogle Scholar
  59. Herman R, Montroll EW, Potts RB, Rothery RW (1959) Traffic dynamics: analysis of stability in car following. Oper Res 7:86–106MathSciNetCrossRefGoogle Scholar
  60. Herrmann M, Kerner BS (1998) Local cluster effect in different traffic flow models. Physica A 255:163–188ADSCrossRefGoogle Scholar
  61. Highway Capacity Manual (2000) National Research Council, Transportation Research Board, Washington, DCGoogle Scholar
  62. Highway Capacity Manual (2010) National Research Council, Transportation Research Board, Washington, DCGoogle Scholar
  63. Hoogendoorn SP, Luding S, PHL B, Schreckenberg M, Wolf DE (eds) (2005) Traffic and granular flow’ 03. Springer, HeidelbergGoogle Scholar
  64. Hu X-J, Wang W, Yang H (2012) Mixed traffic flow model considering illegal lanechanging behavior: simulations in the framework of Kerners three-phase theory. Physica A 391:5102–5111ADSCrossRefGoogle Scholar
  65. Jiang R, Wu QS (2004) Spatial-temporal patterns at an isolated on-ramp in a new cellular automata model based on three-phase traffic theory. J Phys A Math Gen 37:8197–8213ADSMathSciNetzbMATHCrossRefGoogle Scholar
  66. Jiang R, Wu QS (2005) Toward an improvement over Kerner-Klenov-Wolf three-phase cellular automaton model. Phys Rev E 72:067103ADSCrossRefGoogle Scholar
  67. Jiang R, Wu QS (2007) Dangerous situations in a synchronized flow model. Physica A 377:633–640ADSCrossRefGoogle Scholar
  68. Jiang R, Hu M-B, Wang R, Wu Q-S (2007) Spatiotemporal congested traffic patterns in macroscopic version of the Kerner-Klenov speed adaptation model. Phys Lett A 365:6–9ADSCrossRefGoogle Scholar
  69. Jiang R, Hu MB, Zhang HM, Gao ZY, Jia B, Wu QS, Yang M (2014) Traffic experiment reveals the nature of car-following. PLoS One 9:e94351ADSCrossRefGoogle Scholar
  70. Jiang R, Hu M-B, Zhang HM, Gao ZY, Jia B, Wu QS (2015) On some experimental features of car-following behavior and how to model them. Transp Res B 80:338–354CrossRefGoogle Scholar
  71. Jiang R, Jin C-J, Zhang HM, Huang Y-X, Tian J-F, Wang W, Hu M-B, Wang H, Jia B (2017) Experimental and empirical investigations of traffic flow instability. Transp Res Proc 23:157–173CrossRefGoogle Scholar
  72. Kerner BS (1998a) Theory of congested traffic flow. In: Rysgaard R (ed) Proceedings of the 3rd symposium on highway capacity and level of service, vol 2, road directorate. Ministry of Transport, pp 621–642Google Scholar
  73. Kerner BS (1998b) Empirical features of self-organization in traffic flow. Phys Rev Lett 81:3797–3400ADSzbMATHCrossRefGoogle Scholar
  74. Kerner BS (1998c) Traffic flow: experiment and theory. In: Schreckenberg M, Wolf DE (eds) Traffic and granular flow’97. Springer, Singapore, pp 239–267Google Scholar
  75. Kerner BS (1999a) Congested traffic flow: observations and theory. Trans Res Rec 1678:160–167CrossRefGoogle Scholar
  76. Kerner BS (1999b) The physics of traffic. Phys World 12:25–30CrossRefGoogle Scholar
  77. Kerner BS (1999c) Theory of congested traffic flow: self-organization without bottlenecks. In: Ceder A (ed) Transportation and traffic theory. Elsevier Science, London, pp 147–171Google Scholar
  78. Kerner BS (2000) Experimental features of the emergence of moving jams in free traffic flow. J Phys A 33:L221–L228ADSzbMATHCrossRefGoogle Scholar
  79. Kerner BS (2001) Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories. Netw Spat Econ 1:35–76CrossRefGoogle Scholar
  80. Kerner BS (2002a) Synchronized flow as a new traffic phase and related problems for traffic flow modelling. Math Comput Model 35:481–508MathSciNetzbMATHCrossRefGoogle Scholar
  81. Kerner BS (2002b) Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks. Phys Rev E 65:046138ADSCrossRefGoogle Scholar
  82. Kerner BS (2004a) The physics of traffic. Springer, Berlin/New YorkCrossRefGoogle Scholar
  83. Kerner BS (2004b) Verfahren zur Ansteuerung eines in einem Fahrzeug befindlichen verkehrsadaptiven Assistenzsystems, German patent publication DE 10308256A1. https://google.com/patents/DE10308256A1; Patent WO 2004076223A1 (2004) https://google.com/patents/WO2004076223A1; EU Patent EP 1597106B1 (2006); German patent DE 502004001669D1 (2006)
  84. Kerner BS (2005) Control of spatiotemporal congested traffic patterns at highway bottlenecks. Physica A 355:565–601ADSCrossRefGoogle Scholar
  85. Kerner BS (2007a) Control of spatiotemporal congested patterns at highway bottlenecks. IEEE Trans ITS 8:308–320ADSGoogle Scholar
  86. Kerner BS (2007b) On-ramp metering based on three-phase traffic theory I. Traffic Eng Control 48:28–35Google Scholar
  87. Kerner BS (2007c) On-ramp metering based on three-phase theory – part III. Traffic Eng Control 48:68–75Google Scholar
  88. Kerner BS (2007d) Three-phase traffic theory and its applications for freeway traffic control. In: Inweldi PO (ed) Transportation research trends. Nova Science Publishers, New York, pp 1–97Google Scholar
  89. Kerner BS (2007e) Method for actuating a traffic-adaptive assistance system which is located in a vehicle, USA patent US 20070150167A1. https://google.com/patents/US20070150167A1; USA patent US 7451039B2 (2008)
  90. Kerner BS (2007f) Betriebsverfahren fr ein fahrzeug- seitiges verkehrsadaptives Assistenzsystem, German patent publication DE 102007008253A1. https://register.dpma.de/DPMAregister/pat/PatSchrifteneinsicht?docId=DE102007008253A1; German patent publication DE 102007008257A1. https://register.dpma.de/DPMAregister/pat/PatSchrifteneinsicht?docId=DE102007008257A1; German patent publication DE 102007008254A1
  91. Kerner BS (2009a) Traffic congestion, modelling approaches to. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9302–9355CrossRefGoogle Scholar
  92. Kerner BS (2009b) Traffic congestion, spatiotemporal features of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9355–9411CrossRefGoogle Scholar
  93. Kerner BS (2009c) Introduction to modern traffic flow theory and control. Springer, Berlin/New YorkzbMATHCrossRefGoogle Scholar
  94. Kerner BS (2013) Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: a brief review. Physica A 392:5261–5282ADSMathSciNetCrossRefGoogle Scholar
  95. Kerner BS (2015a) Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: growing wave of increase in speed in synchronized flow. Phys Rev E 92:062827ADSCrossRefGoogle Scholar
  96. Kerner BS (2015b) Failure of classical traffic flow theories: a critical review. Elektrotech Inf 132:417–433CrossRefGoogle Scholar
  97. Kerner BS (2016) Failure of classical traffic flow theories: stochastic highway capacity and automatic driving. Physica A 450:700–747ADSMathSciNetCrossRefGoogle Scholar
  98. Kerner BS (2017a) Breakdown in traffic networks: fundamentals of transportation science. Springer, Berlin/New YorkCrossRefGoogle Scholar
  99. Kerner BS (2017b) Traffic networks, breakdown in. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC. Springer, Berlin. https://10.1007/978.3.642.27737.5701.1
  100. Kerner BS (2017c) Physics of autonomous driving based on three-phase traffic theory. Springer, Berlin. arXiv:1710.10852v3. http://arxiv.org/abs/1710.10852
  101. Kerner BS (2018) Traffic congestion, spatiotemporal features of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC. Springer, BerlinGoogle Scholar
  102. Kerner BS, Klenov SL (2002) A microscopic model for phase transitions in traffic flow. J Phys A Math Gen 35:L31–L43ADSMathSciNetzbMATHCrossRefGoogle Scholar
  103. Kerner BS, Klenov SL (2003) Microscopic theory of spatio-temporal congested traffic patterns at highway bottlenecks. Phys Rev E 68:036130ADSCrossRefGoogle Scholar
  104. Kerner BS, Klenov SL (2005) Probabilistic breakdown phenomenon at on-ramps bottlenecks in three-phase traffic theory. Cond-mat/0502281, e-print in http://arxiv.org/abs/cond-mat/0502281
  105. Kerner BS, Klenov SL (2006a) Probabilistic breakdown phenomenon at on-ramp bottlenecks in three-phase traffic theory: congestion nucleation in spatially nonhomogeneous traffic. Physica A 364:473–492ADSCrossRefGoogle Scholar
  106. Kerner BS, Klenov SL (2006b) Probabilistic breakdown phenomenon at on-ramp bottlenecks in three-phase traffic theory. Transp Res Rec 1965:70–78CrossRefGoogle Scholar
  107. Kerner BS, Klenov SL (2006c) Deterministic microscopic three-phase traffic flow models. J Phys A Math Gen 39:1775–1809ADSMathSciNetzbMATHCrossRefGoogle Scholar
  108. Kerner BS, Klenov SL (2009a) Traffic breakdown, probabilistic theory of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9282–9302CrossRefGoogle Scholar
  109. Kerner BS, Klenov SL (2009b) Phase transitions in traffic flow on multilane roads. Phys Rev E 80:056101ADSCrossRefGoogle Scholar
  110. Kerner BS, Klenov SL (2018) Traffic breakdown, mathematical probabilistic approaches to. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLCGoogle Scholar
  111. Kerner BS, Konhäuser P (1993) Cluster effect in initially homogeneous traffic flow. Phys Rev E 48:R2335–R2338ADSCrossRefGoogle Scholar
  112. Kerner BS, Konhäuser P (1994) Structure and parameters of clusters in traffic flow. Phys Rev E 50:54–83ADSCrossRefGoogle Scholar
  113. Kerner BS, Rehborn H (1996a) Experimental features and characteristics of traffic jams. Phys Rev E 53:R1297–R1300ADSCrossRefGoogle Scholar
  114. Kerner BS, Rehborn H (1996b) Experimental properties of complexity in traffic flow. Phys Rev E 53:R4275–R4278ADSCrossRefGoogle Scholar
  115. Kerner BS, Rehborn H (1997) Experimental properties of phase transitions in traffic flow. Phys Rev Lett 79:4030–4033ADSCrossRefGoogle Scholar
  116. Kerner BS, Konhäuser P, Schilke M (1995) Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow. Phys Rev E 51:6243–6246ADSCrossRefGoogle Scholar
  117. Kerner BS, Konhäuser P, Schilke M (1996) Dipole-layer” effect in dense traffic flow. Phys Lett A 215:45–56ADSCrossRefGoogle Scholar
  118. Kerner BS, Klenov SL, Wolf DE (2002) Cellular automata approach to three-phase traffic theory. J Phys A Math Gen 35:9971–10013ADSMathSciNetzbMATHCrossRefGoogle Scholar
  119. Kerner BS, Klenov SL, Hiller A (2006a) Criterion for traffic phases in single vehicle data and empirical test of a microscopic three-phase traffic theory. J Phys A Math Gen 39:2001–2020ADSzbMATHCrossRefGoogle Scholar
  120. Kerner BS, Klenov SL, Hiller A, Rehborn H (2006b) Microscopic features of moving traffic jams. Phys Rev E 73:046107ADSCrossRefGoogle Scholar
  121. Kerner BS, Klenov SL, Hiller A (2007) Empirical test of a microscopic three-phase traffic theory. Non Dyn 49:525–553zbMATHCrossRefGoogle Scholar
  122. Kerner BS, Klenov SL, Schreckenberg M (2011) Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow. Phys Rev E 84:046110ADSCrossRefGoogle Scholar
  123. Kerner BS, Klenov SL, Hermanns G, Schreckenberg M (2013a) Effect of driver overacceleration on traffic breakdown in three-phase cellular automaton traffic flow models. Physica A 392:4083–4105ADSMathSciNetCrossRefGoogle Scholar
  124. Kerner BS, Rehborn H, Schäfer R-P, Klenov SL, Palmer J, Lorkowski S, Witte N (2013b) Traffic dynamics in empirical probe vehicle data studied with three-phase theory: spatiotemporal reconstruction of traffic phases and generation of jam warning messages. Physica A 392:221–251ADSCrossRefGoogle Scholar
  125. Kerner BS, Klenov SL, Schreckenberg M (2014) Probabilistic physical characteristics of phase transitions at highway bottlenecks: incommensurability of three-phase and two-phase traffic-flow theories. Phys Rev E 89:052807ADSCrossRefGoogle Scholar
  126. Kerner BS, Koller M, Klenov SL, Rehborn H, Leibel M (2015) The physics of empirical nuclei for spontaneous traffic breakdown in free flow at highway bottlenecks. Physica A 438:365–397ADSCrossRefGoogle Scholar
  127. Knospe W, Santen L, Schadschneider A, Schreckenberg M (2000) Towards a realistic microscopic description of highway traffic. J Phys A Math Gen 33:L477–L485ADSMathSciNetzbMATHCrossRefGoogle Scholar
  128. Knospe W, Santen L, Schadschneider A, Schreckenberg M (2002) Single-vehicle data of highway traffic: microscopic description of traffic phases. Phys Rev E 65:056133ADSzbMATHCrossRefGoogle Scholar
  129. Knospe W, Santen L, Schadschneider A, Schreckenberg M (2004) Empirical test for cellular automaton models of traffic flow. Phys Rev E 70:016115ADSCrossRefGoogle Scholar
  130. Kokubo S, Tanimoto J, Hagishima A (2011) A new cellular automata model including a decelerating damping effect to reproduce Kerners three-phase theory. Physica A 390:561–568ADSCrossRefGoogle Scholar
  131. Kometani E, Sasaki T (1958) On the stability of traffic flow. J Oper Res Soc Jpn 2:11–26MathSciNetGoogle Scholar
  132. Kometani E, Sasaki T (1959) A safety index for traffic with linear spacing. Oper Res 7:704–720CrossRefGoogle Scholar
  133. Koshi M (2003) An interpretation of a traffic engineer on vehicular traffic flow. In: Fukui M, Sugiyama Y, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’ 01. Springer, Heidelberg, pp 199–210CrossRefGoogle Scholar
  134. Koshi M, Iwasaki M, Ohkura I (1983) Some findings and an overview on vehiclular flow characteristics. In: Hurdle VF (ed) Proceedings of 8th international symposium on transportation and traffic theory. University of Toronto Press, Toronto, p 403Google Scholar
  135. Krauß S, Wagner P, Gawron C (1997) Metastable states in a microscopic model of traffic flow. Phys Rev E 55:5597–5602ADSCrossRefGoogle Scholar
  136. Kuhn TS (2012) The structure of scientific revolutions, 4th edn. The University of Chicago Press, ChicagoCrossRefGoogle Scholar
  137. Kühne R (1991) Traffic patterns in unstable traffic flow on freeway. In: Brannolte U (ed) Highway capacity and level of service. A.A. Balkema, Rotterdam, pp 211–223Google Scholar
  138. Laval JA (2007) Linking synchronized flow and kinematic waves. In: Schadschneider A, Pöschel T, Kühne R, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’05. Proceedings of the international workshop on traffic and granular flow. Springer, Berlin, pp 521–526Google Scholar
  139. Lee HY, Lee H-W, Kim D (1999) Dynamic states of a continuum traffic equation with on-ramp. Phys Rev E 59:5101–5111ADSCrossRefGoogle Scholar
  140. Lee HK, Barlović R, Schreckenberg M, Kim D (2004) Mechanical restriction versus human overreaction triggering congested traffic states. Phys Rev Lett 92:238702ADSCrossRefGoogle Scholar
  141. Lesort J-B (ed) (1996) Transportation and traffic theory. In: Proceedings of the 13th international symposium on transportation and traffic theory. Elsevier Science Ltd, OxfordGoogle Scholar
  142. Leutzbach W (1988) Introduction to the theory of traffic flow. Springer, BerlinCrossRefGoogle Scholar
  143. Li XG, Gao ZY, Li KP, Zhao XM (2007) Relationship between microscopic dynamics in traffic flow and complexity in networks. Phys Rev E 76:016110ADSCrossRefGoogle Scholar
  144. Lighthill MJ, Whitham GB (1955) On kinematic waves. I Flow movement in long rives. II A theory of traffic flow on long crowded roads. Proc Roy Soc A 229:281–345ADSzbMATHCrossRefGoogle Scholar
  145. Lorenz M, Elefteriadou L (2000) A probabilistic approach to defining freeway capacity and breakdown. Trans Res Cir E-C018, pp 84–95Google Scholar
  146. Maerivoet S, De Moor B (2005) Cellular automata models of road traffic. Phys Rep 419:1–64ADSMathSciNetCrossRefGoogle Scholar
  147. Mahmassani HS (ed) (2005) Transportation and traffic theory. In: Proceedings of the 16th international symposium on transportation and traffic theory. Elsevier, AmsterdamGoogle Scholar
  148. Mahnke R, Kaupuzˇs J, Lubashevsky I (2005) Probabilistic description of traffic flow. Phys Rep 408:1–130ADSCrossRefGoogle Scholar
  149. Mahnke R, Kaupuzˇs J, Lubashevsky I (2009) Physics of stochastic processes: how randomness acts in time. Wiley-VCH, WeinheimzbMATHGoogle Scholar
  150. May AD (1990) Traffic flow fundamentals. Prentice-Hall, Englewood CliffsGoogle Scholar
  151. Molzahn S-E, Kerner BS, Rehborn H, Klenov SL, Koller M (2017) Analysis of speed disturbances in empiricalsingle vehicle probe data before traffic breakdown. IET Intell Transp Syst 11:604–612.  https://doi.org/10.1049/iet-its.2016.0315 CrossRefGoogle Scholar
  152. Nagatani T (1998) Modified KdV equation for jamming transition in the continuum models of traffic. Physica A 261:599–607ADSMathSciNetCrossRefGoogle Scholar
  153. Nagatani T (1999) Jamming transition in a two-dimensional traffic flow model. Phys Rev E 59:4857–4864ADSCrossRefGoogle Scholar
  154. Nagatani T (2002) The physics of traffic jams. Rep Prog Phys 65:1331–1386ADSCrossRefGoogle Scholar
  155. Nagatani T, Nakanishi K (1998) Delay effect on phase transitions in traffic dynamics. Phys Rev E 57:6415–6421ADSCrossRefGoogle Scholar
  156. Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J Phys (France) I 2:2221–2229ADSCrossRefGoogle Scholar
  157. Nagel K, Wolf DE, Wagner P, Simon P (1998) Two-lane traffic rules for cellular automata: a systematic approach. Phys Rev E 58:1425–1437ADSCrossRefGoogle Scholar
  158. Nagel K, Wagner P, Woesler R (2003) Still flowing: approaches to traffic flow and traffic jam modeling. Oper Res 51:681–716MathSciNetzbMATHCrossRefGoogle Scholar
  159. Newell GF (1961) Nonlinear effects in the dynamics of car following. Oper Res 9:209–229zbMATHCrossRefGoogle Scholar
  160. Newell GF (1982) Applications of queuing theory. Chapman Hall, LondonzbMATHCrossRefGoogle Scholar
  161. Newell GF (2002) A simplified car-following theory: a lower order model. Transp Res B 36:195–205CrossRefGoogle Scholar
  162. Papageorgiou M (1983) Application of automatic control concepts in traffic flow modeling and control. Springer, Berlin/New YorkzbMATHCrossRefGoogle Scholar
  163. Papageorgiou M, Kotsialos A (2000) Freeway ramp metering: an overview. In: Proceedings of the 3rd annual IEEE conference on intelligent transportation systems (ITSC 2000), Dearborn, pp 228–239Google Scholar
  164. Papageorgiou M, Kotsialos A (2002) Freeway ramp metering: an overview. IEEE Trans Intell Transp Syst 3(4):271–280CrossRefGoogle Scholar
  165. Papageorgiou M, Papamichail I (2008) Overview of traffic signal operation policies for ramp metering. Transp Res Rec 2047:28–36CrossRefGoogle Scholar
  166. Papageorgiou M, Blosseville J-M, Hadj-Salem H (1990a) Modelling and real-time control of traffic flow on the southern part of Boulevard Priphrique in Paris: Part I: Modelling. Transp Res Part A 24A(5):345–359CrossRefGoogle Scholar
  167. Papageorgiou M, Blosseville J-M, Hadj-Salem H (1990b) Modelling and real-time control of traffic flow on the southern part of Boulevard Priphrique in Paris: Part II: Coordinated on-ramp metering. Transp Res Part A 24A(5):361–370CrossRefGoogle Scholar
  168. Papageorgiou M, Hadj-Salem H, Blosseville J-M (1991) ALINEA: a local feedback control law for on-ramp metering. Transp Res Rec 1320:58–64Google Scholar
  169. Papageorgiou M, Hadj-Salem H, Middelham F (1997) ALINEA local ramp metering summary of field results. Transp Res Rec 1603:90–98CrossRefGoogle Scholar
  170. Papageorgiou M, Diakaki C, Dinopoulou V, Kotsialos A, Wang Y (2003) Review of road traffic control strategies. In: Proceedings of the IEEE, vol 91, pp 2043–2067Google Scholar
  171. Papageorgiou M, Wang Y, Kosmatopoulos E, Papamichail I (2007) ALINEA maximizes motorway throughput – an answer to flawed criticism. Traffic Eng Control 48(6):271–276Google Scholar
  172. Payne HJ (1971) Models of freeway traffic and control. In: Bekey GA (ed) Mathematical models of public systems, vol 1. Simulation council, La JollaGoogle Scholar
  173. Payne HJ (1979) FREEFLO: a macroscopic simulation model of freeway traffic. Transp Res Rec 772:68–75Google Scholar
  174. Persaud BN, Yagar S, Brownlee R (1998) Exploration of the breakdown phenomenon in freeway traffic. Trans Res Rec 1634:64–69CrossRefGoogle Scholar
  175. Pipes LA (1953) An operational analysis of traffic dynamics. J Appl Phys 24:274–287ADSMathSciNetCrossRefGoogle Scholar
  176. Pottmeier A, Thiemann C, Schadschneider A, Schreckenberg M (2007) Mechanical restriction versus human overreaction: accident avoidance and two-lane simulations. In: Schadschneider A, Pöschel T, Kühne R, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’05. Proceedings of the international workshop on traffic and granular flow. Springer, Berlin, pp 503–508Google Scholar
  177. Prigogine I, Herman R (1971) Kinetic theory of vehicular traffic. American Elsevier, New YorkzbMATHGoogle Scholar
  178. Qian Y-S, Feng X, Jun-Wei Zeng J-W (2017) A cellular automata traffic flow model for three-phase theory. Physica A 479:509–526ADSMathSciNetCrossRefGoogle Scholar
  179. Rakha H, Tawfik A (2009) Traffic networks: dynamic traffic routing, assignment, and assessment. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9429–9470CrossRefGoogle Scholar
  180. Rehborn H, Klenov SL (2009) Traffic prediction of congested patterns. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9500–9536CrossRefGoogle Scholar
  181. Rehborn H, Koller M (2014) A study of the influence of severe environmental conditions on common traffic congestion features. J Adv Transp 48:1107–1120CrossRefGoogle Scholar
  182. Rehborn H, Palmer J (2008) ASDA/FOTO based on Kerner’s three-phase traffic theory in North Rhine-Westphalia and its integration into vehicles. In: Intelligent Vehicles Symposium, IEEE, pp 186–191Google Scholar
  183. Rehborn H, Klenov SL, Palmer J (2011a) An empirical study of common traffic congestion features based on traffic data measured in the USA, the UK, and Germany. Physica A 390:4466–4485ADSCrossRefGoogle Scholar
  184. Rehborn H, Klenov SL, Palmer J (2011b) Common traffic congestion features studied in USA, UK, and Germany based on Kerner’s three-phase traffic theory. In: Intelligent Vehicles symposium (IV), IEEE, pp 19–24Google Scholar
  185. Rehborn H, Klenov SL, Koller M (2017) Traffic prediction of congested patterns. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLCGoogle Scholar
  186. Rempe F, Franeck P, Fastenrath U, Bogenberger K (2016) Online freeway traffic estimation with real floating car data. In: Proceedings of 2016 I.E. 19th international conference on ITS, pp 1838–1843Google Scholar
  187. Rempe F, Franeck P, Fastenrath U, Bogenberger K (2017) A phase-based smoothing method for accurate traffic speed estimation with floating car data. Trans Res C 85:644–663CrossRefGoogle Scholar
  188. Richards PI (1956) Shockwaves on the highway. Oper Res 4:42–51CrossRefGoogle Scholar
  189. Saifuzzaman M, Zheng Z (2014) Incorporating human-factors in car-following models: a review of recent developments and research needs. Transp Res C 48:379–403CrossRefGoogle Scholar
  190. Schadschneider A, Pöschel T, Kühne R, Schreckenberg M, Wolf DE (eds) (2007) Traffic and granular flow’05. In: Proceedings of the international workshop on traffic and granular flow. Springer, BerlinGoogle Scholar
  191. Schadschneider A, Chowdhury D, Nishinari K (2011) Stochastic transport in complex systems. Elsevier Science, New YorkzbMATHGoogle Scholar
  192. Schönhof M, Helbing D (2007) Empirical features of congested traffic states and their implications for traffic modelling. Transp Sc 41:135–166CrossRefGoogle Scholar
  193. Schönhof M, Helbing D (2009) Transp Res B 43:784–797CrossRefGoogle Scholar
  194. Schreckenberg M, Wolf DE (eds) (1998) Traffic and granular flow’97. In: Proceedings of the international workshop on traffic and granular flow. Springer, SingaporeGoogle Scholar
  195. Siebel F, Mauser W (2006) Synchronized flow and wide moving jams from balanced vehicular traffic. Phys Rev E 73:066108ADSMathSciNetzbMATHCrossRefGoogle Scholar
  196. Smaragdis E, Papageorgiou M (2003, 1856) Series of new local ramp metering strategies. Transp Res Rec:74–86Google Scholar
  197. Takayasu M, Takayasu H (1993) Phase transition and 1/f type noise in one dimensional asymmetric particle dynamics. Fractals 1:860–866zbMATHCrossRefGoogle Scholar
  198. Tanga CF, Jiang R, Wu QS (2007) Phase diagram of speed gradient model with an on-ramp. Physica A 377:641–650ADSCrossRefGoogle Scholar
  199. Taylor MAP (ed) (2002) Transportation and traffic theory in the 21st century. In: Proceedings of the 15th international symposium on transportation and traffic theory. Elsevier Science Ltd, AmsterdamGoogle Scholar
  200. Tian J-F, Treiber M, Ma SF, Jia B, Zhang WY (2015) Microscopic driving theory with oscillatory congested states: model and empirical verification. Transp Res B 71:138–157CrossRefGoogle Scholar
  201. Tian J-F, Jiang R, Jia B, Gao Z-Y, Ma SF (2016a) Empirical analysis and simulation of the concave growth pattern of traffic oscillations. Transp Res B 93:338–354CrossRefGoogle Scholar
  202. Tian J-F, Jiang R, Li G, Treiber M, Jia B, Zhu CQ (2016b) Improved 2D intelligent driver model in the framework of three-phase traffic theory simulating synchronized flow and concave growth pattern of traffic oscillations. Transp Rec F 41:55–65CrossRefGoogle Scholar
  203. Tian J-F, Li G, Treiber M, Jiang R, Jia N, Ma SF (2016c) Cellular automaton model simulating spatiotemporal patterns, phase transitions and concave growth pattern of oscillations in traffic flow. Transp Rec B 93:560–575CrossRefGoogle Scholar
  204. Tomer E, Safonov L, Havlin S (2000) Presence of many stable nonhomogeneous states in an inertial car-following model. Phys Rev Lett 84:382–385ADSCrossRefGoogle Scholar
  205. Treiber M, Kesting A (2013) Traffic flow dynamics. Springer, BerlinzbMATHCrossRefGoogle Scholar
  206. Treiber M, Hennecke A, Helbing D (2000) Congested traffic states in empirical observations and microscopic simulations. Phys Rev E 62:1805–1824ADSzbMATHCrossRefGoogle Scholar
  207. Treiber M, Kesting A, Helbing D (2010) Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transp Res B 44:983–1000CrossRefGoogle Scholar
  208. Treiterer J (1967) Improvement of traffic flow and safety by longitudinal control. Transp Res 1:231–251CrossRefGoogle Scholar
  209. Treiterer J (1975) Investigation of traffic dynamics by aerial photogrammetry techniques. Ohio State University technical report PB 246 094, ColumbusGoogle Scholar
  210. Treiterer J, Myers JA (1974) The hysteresis phenomenon in traffic flow. In: Buckley DJ (ed) Proceedings of 6th international symposium on transportation and traffic theory. A.H. & AW Reed, London, pp 13–38Google Scholar
  211. Treiterer J, Taylor JI (1966) Traffic flow investigations by photogrammetric techniques. Highway Res Rec 142:1–12Google Scholar
  212. Wang R, Jiang R, Wu QS, Liu M (2007) Synchronized flow and phase separations in single-lane mixed traffic flow. Physica A 378:475–484ADSCrossRefGoogle Scholar
  213. Wardrop JG (1952) Some theoretical aspects of road traffic research. In: Proceedings of institute of civil engineering 1(3):325–362 PART 1.  https://doi.org/10.1680/ipeds.1952.11259
  214. Whitham GB (1974) Linear and nonlinear waves. Wiley, New YorkzbMATHGoogle Scholar
  215. Wiedemann R (1974) Simulation des Verkehrsflusses. University of Karlsruhe, KarlsruheGoogle Scholar
  216. Wolf DE (1999) Cellular automata for traffic simulations. Physica A 263:438–451ADSMathSciNetCrossRefGoogle Scholar
  217. Xiang Z-T, Li Y-J, Chen Y-F, Xiong L (2013) Simulating synchronized traffic flow and wide moving jam based on the brake light rule. Physica A 392:5399–5413ADSCrossRefGoogle Scholar
  218. Yang H, Lu J, Hu X-J, Jiang J (2013) A cellular automaton model based on empirical observations of a drivers oscillation behavior reproducing the findings from Kerners three-phase traffic theory. Physica A 392:4009–4018ADSMathSciNetCrossRefGoogle Scholar
  219. Zurlinden H (2003) Ganzjahresanalyse des Verkehrsflusses auf Straßen. Schriftenreihe des Lehrstuhls für Verkehrswesen der Ruhr-Universität Bochum, Heft 26, BochumGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2018

Authors and Affiliations

  1. 1.Physics of Transport and TrafficUniversity Duisburg-EssenDuisburgGermany