Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Complexity and Systems Science pp 1–89Cite as

Traffic Breakdown, Modeling Approaches to

  • Living reference work entry
  • First Online:

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...

This is a preview of subscription content, log in via an institution.

Bibliography

  • 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 691–710

    Google Scholar 

  • Aw A, Rascle M (2000) Resurrection of “second order” models of traffic flow. SIAM J Appl Math 60:916–938

    Article  MathSciNet  MATH  Google Scholar 

  • Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1994) Structure stability of congestion in traffic dynamics. Jpn J Appl Math 11:203–223

    Article  MathSciNet  MATH  Google Scholar 

  • Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995a) Dynamical model of traffic congestion and numerical simulation. Phys Rev E 51:1035–1042

    Article  ADS  Google Scholar 

  • Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995b) Phenomenological study of dynamical model of traffic flow. J Phys I France 5:1389–1399

    Article  Google Scholar 

  • Banks JH (1989) Freeway speed-flow-concentration relationships: more evidence and interpretations (with discussion and closure). Transp Res Rec 1225:53–60

    Google Scholar 

  • Banks JH (1990) Two-capacity phenomenon at freeway bottlenecks: a basis for ramp metering? Transp Res Rec 1287:20–28

    Google Scholar 

  • Barlović R, Santen L, Schadschneider A, Schreckenberg M (1998) Metastable states in cellular automata for traffic flow. Eur Phys J B 5:793–800

    Article  ADS  Google Scholar 

  • 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 12:1801–1843

    Article  MathSciNet  MATH  Google Scholar 

  • Berg P, Woods A (2001) On-ramp simulations and solitary waves of a car-following model. Phys Rev E 64:035602(R)

    Article  ADS  Google Scholar 

  • Bovy PHL (ed) (1998) Motorway analysis: new methodologies and recent empirical findings. Delft University Press, Delft

    Google Scholar 

  • Brilon W, Zurlinden H (2004) Kapazität von Straßen als Zufallsgröße. Straßenverkehrstechnik 4:164

    Google Scholar 

  • 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 125–144

    Google Scholar 

  • Brilon W, Regler M, Geistefeld J (2005b) Zufallscharakter der Kapazität von Autobahnen und praktische Konsequenzen – Teil 1. Straßenverkehrstechnik 3:136

    Google Scholar 

  • Brockfeld E, Kühne RD, Skabardonis A, Wagner P (2003) Toward benchmarking of microscopic traffic flow models. Trans Res Rec 1852:124–129

    Article  Google Scholar 

  • 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, DC

    Google Scholar 

  • Ceder A (ed) (1999) Transportation and traffic theory. In: Proceedings of the 14th international symposium on transportation and traffic theory. Elsevier Science Ltd, Oxford

    Google Scholar 

  • Chandler RE, Herman R, Montroll EW (1958) Traffic dynamics: studies in car following. Oper Res 6:165–184

    Article  MathSciNet  Google Scholar 

  • Chowdhury D, Santen L, Schadschneider A (2000) Statistical physics of vehicular traffic and some related systems. Phys Rep 329:199

    Article  ADS  MathSciNet  Google Scholar 

  • Cowan RJ (1976) Useful headway models. Trans Rec 9:371–375

    Article  Google Scholar 

  • Cremer M (1979) Der Verkehrsfluss auf Schnellstrassen. Springer, Berlin

    Book  Google Scholar 

  • Daganzo CF (1994) The cell-transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transp Res B 28:269–287

    Article  Google Scholar 

  • Daganzo CF (1995) The cell transmission model, part II: network traffic. Transp Res B 29:79–93

    Article  Google Scholar 

  • Daganzo CF (1997) Fundamentals of transportation and traffic operations. Elsevier Science, New York

    Book  Google Scholar 

  • Daganzo CF, Cassidy MJ, Bertini RL (1999) Possible explanations of phase transitions in highway traffic. Transp Res A 33:365–379

    Google Scholar 

  • Davis LC (2004a) Multilane simulations of traffic phases. Phys Rev E 69:016108

    Article  ADS  Google Scholar 

  • Davis LC (2004b) Effect of adaptive cruise control systems on traffic flow. Phys Rev E 69:066110

    Article  ADS  Google Scholar 

  • Davis LC (2006a) Controlling traffic flow near the transition to the synchronous flow phase. Physica A 368:541–550

    Article  ADS  Google Scholar 

  • Davis LC (2006b) Effect of cooperative merging on the synchronous flow phase of traffic. Physica A 361:606–618

    Article  ADS  Google Scholar 

  • Davis LC (2007) Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp. Physica A 379:274–290

    Article  ADS  Google Scholar 

  • 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 387:6395–6410

    Article  ADS  Google Scholar 

  • Davis LC (2014) Nonlinear dynamics of autonomous vehicles with limits on acceleration. Physica A 405:128–139

    Article  ADS  MathSciNet  Google Scholar 

  • Davis LC (2016) Improving traffic flow at a 2-to-1 lane reduction with wirelessly connected, adaptive cruise control vehicles. Physica A 451:320–332

    Article  ADS  Google Scholar 

  • Edie LC (1961) Car-following and steady state theory for non-congested traffic. Oper Res 9:66–77

    Article  MathSciNet  MATH  Google Scholar 

  • Edie LC, Foote RS (1958) Traffic flow in tunnels. Highway Res Board Proc Ann Meet 37:334–344

    Google Scholar 

  • 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 492–505

    Google Scholar 

  • Edie LC, Herman R, Lam TN (1980) Observed multilane speed distribution and the kinetic theory of vehicular traffic. Transp Sci 14:55–76

    Article  Google Scholar 

  • Elefteriadou L (2014) An introduction to traffic flow theory. Springer optimization and its applications, vol 84. Springer, Berlin

    Book  MATH  Google Scholar 

  • Elefteriadou L, Roess RP, McShane WR (1995) Probabilistic nature of breakdown at freeway merge junctions. Transp Res Rec 1484:80–89

    Google Scholar 

  • 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 140:04014003

    Article  Google Scholar 

  • Fukui M, Sugiyama Y, Schreckenberg M, Wolf DE (eds) (2003) Traffic and granular flow’ 01. Springer, Heidelberg

    MATH  Google Scholar 

  • 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 76:026105

    Article  ADS  Google Scholar 

  • Gartner NH, Messer CJ, Rathi A (eds) (1997) Special report 165: revised monograph on traffic flow theory. Transportation Research Board, Washington, DC

    Google Scholar 

  • Gazis DC (2002) Traffic theory. Springer, Berlin

    MATH  Google Scholar 

  • Gazis DC, Herman R, Potts RB (1959) Car-following theory of steady-state traffic flow. Oper Res 7:499–505

    Article  MathSciNet  Google Scholar 

  • Gazis DC, Herman R, Rothery RW (1961) Nonlinear follow-the-leader models of traffic flow. Oper Res 9:545–567

    Article  MathSciNet  MATH  Google Scholar 

  • Gipps PG (1981) Behavioral car-following model for computer simulation. Trans Res B 15:105–111

    Article  Google Scholar 

  • Greenshields BD (1935) A study of traffic capacity. In: Highway research board proceedings, (Highway Research Board, Washington, DC), vol 14, pp 448–477

    Google Scholar 

  • Haight FA (1963) Mathematical theories of traffic flow. Academic, New York

    MATH  Google Scholar 

  • Hall FL, Agyemang-Duah K (1991) Freeway capacity drop and the definition of capacity. Trans Res Rec 1320:91–98

    Google Scholar 

  • 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 1365:12–18

    Google Scholar 

  • 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 113–141

    Google Scholar 

  • 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 389:825–836

    Article  ADS  Google Scholar 

  • 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, Berlin

    Google Scholar 

  • Helbing D (2001) Traffic and related self-driven many-particle systems. Rev Mod Phys 73:1067–1141

    Article  ADS  Google Scholar 

  • Helbing D, Hennecke A, Treiber M (1999) Phase diagram of traffic states in the presence of Inhomogeneities. Phys Rev Lett 82:4360–4363

    Article  ADS  Google Scholar 

  • Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) (2000) Traffic and granular flow’ 99. Springer, Heidelberg

    MATH  Google Scholar 

  • Helbing D, Treiber M, Kesting A, Schönhof M (2009) Theoretical vs. empirical classification and prediction of congested traffic states. Eur Phys J B 69:583–598

    Article  ADS  Google Scholar 

  • Herman R, Montroll EW, Potts RB, Rothery RW (1959) Traffic dynamics: analysis of stability in car following. Oper Res 7:86–106

    Article  MathSciNet  Google Scholar 

  • Herrmann M, Kerner BS (1998) Local cluster effect in different traffic flow models. Physica A 255:163–188

    Article  ADS  Google Scholar 

  • Highway Capacity Manual (2000) National Research Council, Transportation Research Board, Washington, DC

    Google Scholar 

  • Highway Capacity Manual (2010) National Research Council, Transportation Research Board, Washington, DC

    Google Scholar 

  • Hoogendoorn SP, Luding S, PHL B, Schreckenberg M, Wolf DE (eds) (2005) Traffic and granular flow’ 03. Springer, Heidelberg

    Google Scholar 

  • 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 391:5102–5111

    Article  ADS  Google Scholar 

  • 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 37:8197–8213

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Jiang R, Wu QS (2005) Toward an improvement over Kerner-Klenov-Wolf three-phase cellular automaton model. Phys Rev E 72:067103

    Article  ADS  Google Scholar 

  • Jiang R, Wu QS (2007) Dangerous situations in a synchronized flow model. Physica A 377:633–640

    Article  ADS  Google Scholar 

  • 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 365:6–9

    Article  ADS  Google Scholar 

  • 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:e94351

    Article  ADS  Google Scholar 

  • 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 80:338–354

    Article  Google Scholar 

  • 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 23:157–173

    Article  Google Scholar 

  • 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 621–642

    Google Scholar 

  • Kerner BS (1998b) Empirical features of self-organization in traffic flow. Phys Rev Lett 81:3797–3400

    Article  ADS  MATH  Google Scholar 

  • Kerner BS (1998c) Traffic flow: experiment and theory. In: Schreckenberg M, Wolf DE (eds) Traffic and granular flow’97. Springer, Singapore, pp 239–267

    Google Scholar 

  • Kerner BS (1999a) Congested traffic flow: observations and theory. Trans Res Rec 1678:160–167

    Article  Google Scholar 

  • Kerner BS (1999b) The physics of traffic. Phys World 12:25–30

    Article  Google Scholar 

  • Kerner BS (1999c) Theory of congested traffic flow: self-organization without bottlenecks. In: Ceder A (ed) Transportation and traffic theory. Elsevier Science, London, pp 147–171

    Google Scholar 

  • Kerner BS (2000) Experimental features of the emergence of moving jams in free traffic flow. J Phys A 33:L221–L228

    Article  ADS  MATH  Google Scholar 

  • Kerner BS (2001) Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories. Netw Spat Econ 1:35–76

    Article  Google Scholar 

  • Kerner BS (2002a) Synchronized flow as a new traffic phase and related problems for traffic flow modelling. Math Comput Model 35:481–508

    Article  MathSciNet  MATH  Google Scholar 

  • Kerner BS (2002b) Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks. Phys Rev E 65:046138

    Article  ADS  Google Scholar 

  • Kerner BS (2004a) The physics of traffic. Springer, Berlin/New York

    Book  Google Scholar 

  • 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)

  • Kerner BS (2005) Control of spatiotemporal congested traffic patterns at highway bottlenecks. Physica A 355:565–601

    Article  ADS  Google Scholar 

  • Kerner BS (2007a) Control of spatiotemporal congested patterns at highway bottlenecks. IEEE Trans ITS 8:308–320

    ADS  Google Scholar 

  • Kerner BS (2007b) On-ramp metering based on three-phase traffic theory I. Traffic Eng Control 48:28–35

    Google Scholar 

  • Kerner BS (2007c) On-ramp metering based on three-phase theory – part III. Traffic Eng Control 48:68–75

    Google Scholar 

  • 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 1–97

    Google Scholar 

  • 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)

  • 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

  • Kerner BS (2009a) Traffic congestion, modelling approaches to. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9302–9355

    Chapter  Google Scholar 

  • Kerner BS (2009b) Traffic congestion, spatiotemporal features of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9355–9411

    Chapter  Google Scholar 

  • Kerner BS (2009c) Introduction to modern traffic flow theory and control. Springer, Berlin/New York

    Book  MATH  Google Scholar 

  • Kerner BS (2013) Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: a brief review. Physica A 392:5261–5282

    Article  ADS  MathSciNet  Google Scholar 

  • 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 92:062827

    Article  ADS  Google Scholar 

  • Kerner BS (2015b) Failure of classical traffic flow theories: a critical review. Elektrotech Inf 132:417–433

    Article  Google Scholar 

  • Kerner BS (2016) Failure of classical traffic flow theories: stochastic highway capacity and automatic driving. Physica A 450:700–747

    Article  ADS  MathSciNet  Google Scholar 

  • Kerner BS (2017a) Breakdown in traffic networks: fundamentals of transportation science. Springer, Berlin/New York

    Book  Google Scholar 

  • 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

  • Kerner BS (2017c) Physics of autonomous driving based on three-phase traffic theory. Springer, Berlin. arXiv:1710.10852v3. http://arxiv.org/abs/1710.10852

  • Kerner BS (2018) Traffic congestion, spatiotemporal features of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC. Springer, Berlin

    Google Scholar 

  • Kerner BS, Klenov SL (2002) A microscopic model for phase transitions in traffic flow. J Phys A Math Gen 35:L31–L43

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kerner BS, Klenov SL (2003) Microscopic theory of spatio-temporal congested traffic patterns at highway bottlenecks. Phys Rev E 68:036130

    Article  ADS  Google Scholar 

  • 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

  • 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 364:473–492

    Article  ADS  Google Scholar 

  • Kerner BS, Klenov SL (2006b) Probabilistic breakdown phenomenon at on-ramp bottlenecks in three-phase traffic theory. Transp Res Rec 1965:70–78

    Article  Google Scholar 

  • Kerner BS, Klenov SL (2006c) Deterministic microscopic three-phase traffic flow models. J Phys A Math Gen 39:1775–1809

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kerner BS, Klenov SL (2009a) Traffic breakdown, probabilistic theory of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9282–9302

    Chapter  Google Scholar 

  • Kerner BS, Klenov SL (2009b) Phase transitions in traffic flow on multilane roads. Phys Rev E 80:056101

    Article  ADS  Google Scholar 

  • 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 LLC

    Google Scholar 

  • Kerner BS, Konhäuser P (1993) Cluster effect in initially homogeneous traffic flow. Phys Rev E 48:R2335–R2338

    Article  ADS  Google Scholar 

  • Kerner BS, Konhäuser P (1994) Structure and parameters of clusters in traffic flow. Phys Rev E 50:54–83

    Article  ADS  Google Scholar 

  • Kerner BS, Rehborn H (1996a) Experimental features and characteristics of traffic jams. Phys Rev E 53:R1297–R1300

    Article  ADS  Google Scholar 

  • Kerner BS, Rehborn H (1996b) Experimental properties of complexity in traffic flow. Phys Rev E 53:R4275–R4278

    Article  ADS  Google Scholar 

  • Kerner BS, Rehborn H (1997) Experimental properties of phase transitions in traffic flow. Phys Rev Lett 79:4030–4033

    Article  ADS  Google Scholar 

  • Kerner BS, Konhäuser P, Schilke M (1995) Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow. Phys Rev E 51:6243–6246

    Article  ADS  Google Scholar 

  • Kerner BS, Konhäuser P, Schilke M (1996) “Dipole-layer” effect in dense traffic flow. Phys Lett A 215:45–56

    Article  ADS  Google Scholar 

  • Kerner BS, Klenov SL, Wolf DE (2002) Cellular automata approach to three-phase traffic theory. J Phys A Math Gen 35:9971–10013

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • 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 39:2001–2020

    Article  ADS  MATH  Google Scholar 

  • Kerner BS, Klenov SL, Hiller A, Rehborn H (2006b) Microscopic features of moving traffic jams. Phys Rev E 73:046107

    Article  ADS  Google Scholar 

  • Kerner BS, Klenov SL, Hiller A (2007) Empirical test of a microscopic three-phase traffic theory. Non Dyn 49:525–553

    Article  MATH  Google Scholar 

  • Kerner BS, Klenov SL, Schreckenberg M (2011) Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow. Phys Rev E 84:046110

    Article  ADS  Google Scholar 

  • 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 392:4083–4105

    Article  ADS  MathSciNet  Google Scholar 

  • 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 392:221–251

    Article  ADS  Google Scholar 

  • 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 89:052807

    Article  ADS  Google Scholar 

  • 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 438:365–397

    Article  ADS  Google Scholar 

  • Knospe W, Santen L, Schadschneider A, Schreckenberg M (2000) Towards a realistic microscopic description of highway traffic. J Phys A Math Gen 33:L477–L485

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Knospe W, Santen L, Schadschneider A, Schreckenberg M (2002) Single-vehicle data of highway traffic: microscopic description of traffic phases. Phys Rev E 65:056133

    Article  ADS  MATH  Google Scholar 

  • Knospe W, Santen L, Schadschneider A, Schreckenberg M (2004) Empirical test for cellular automaton models of traffic flow. Phys Rev E 70:016115

    Article  ADS  Google Scholar 

  • 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 390:561–568

    Article  ADS  Google Scholar 

  • Kometani E, Sasaki T (1958) On the stability of traffic flow. J Oper Res Soc Jpn 2:11–26

    MathSciNet  Google Scholar 

  • Kometani E, Sasaki T (1959) A safety index for traffic with linear spacing. Oper Res 7:704–720

    Article  Google Scholar 

  • 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 199–210

    Chapter  Google Scholar 

  • 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 403

    Google Scholar 

  • Krauß S, Wagner P, Gawron C (1997) Metastable states in a microscopic model of traffic flow. Phys Rev E 55:5597–5602

    Article  ADS  Google Scholar 

  • Kuhn TS (2012) The structure of scientific revolutions, 4th edn. The University of Chicago Press, Chicago

    Book  Google Scholar 

  • 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 211–223

    Google Scholar 

  • 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 521–526

    Google Scholar 

  • Lee HY, Lee H-W, Kim D (1999) Dynamic states of a continuum traffic equation with on-ramp. Phys Rev E 59:5101–5111

    Article  ADS  Google Scholar 

  • Lee HK, Barlović R, Schreckenberg M, Kim D (2004) Mechanical restriction versus human overreaction triggering congested traffic states. Phys Rev Lett 92:238702

    Article  ADS  Google Scholar 

  • Lesort J-B (ed) (1996) Transportation and traffic theory. In: Proceedings of the 13th international symposium on transportation and traffic theory. Elsevier Science Ltd, Oxford

    Google Scholar 

  • Leutzbach W (1988) Introduction to the theory of traffic flow. Springer, Berlin

    Book  Google Scholar 

  • Li XG, Gao ZY, Li KP, Zhao XM (2007) Relationship between microscopic dynamics in traffic flow and complexity in networks. Phys Rev E 76:016110

    Article  ADS  Google Scholar 

  • 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 229:281–345

    Article  ADS  MATH  Google Scholar 

  • Lorenz M, Elefteriadou L (2000) A probabilistic approach to defining freeway capacity and breakdown. Trans Res Cir E-C018, pp 84–95

    Google Scholar 

  • Maerivoet S, De Moor B (2005) Cellular automata models of road traffic. Phys Rep 419:1–64

    Article  ADS  MathSciNet  Google Scholar 

  • Mahmassani HS (ed) (2005) Transportation and traffic theory. In: Proceedings of the 16th international symposium on transportation and traffic theory. Elsevier, Amsterdam

    Google Scholar 

  • Mahnke R, Kaupuzˇs J, Lubashevsky I (2005) Probabilistic description of traffic flow. Phys Rep 408:1–130

    Article  ADS  Google Scholar 

  • Mahnke R, Kaupuzˇs J, Lubashevsky I (2009) Physics of stochastic processes: how randomness acts in time. Wiley-VCH, Weinheim

    MATH  Google Scholar 

  • May AD (1990) Traffic flow fundamentals. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Nagatani T (1998) Modified KdV equation for jamming transition in the continuum models of traffic. Physica A 261:599–607

    Article  ADS  MathSciNet  Google Scholar 

  • Nagatani T (1999) Jamming transition in a two-dimensional traffic flow model. Phys Rev E 59:4857–4864

    Article  ADS  Google Scholar 

  • Nagatani T (2002) The physics of traffic jams. Rep Prog Phys 65:1331–1386

    Article  ADS  Google Scholar 

  • Nagatani T, Nakanishi K (1998) Delay effect on phase transitions in traffic dynamics. Phys Rev E 57:6415–6421

    Article  ADS  Google Scholar 

  • Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J Phys (France) I 2:2221–2229

    Article  ADS  Google Scholar 

  • Nagel K, Wolf DE, Wagner P, Simon P (1998) Two-lane traffic rules for cellular automata: a systematic approach. Phys Rev E 58:1425–1437

    Article  ADS  Google Scholar 

  • Nagel K, Wagner P, Woesler R (2003) Still flowing: approaches to traffic flow and traffic jam modeling. Oper Res 51:681–716

    Article  MathSciNet  MATH  Google Scholar 

  • Newell GF (1961) Nonlinear effects in the dynamics of car following. Oper Res 9:209–229

    Article  MATH  Google Scholar 

  • Newell GF (1982) Applications of queuing theory. Chapman Hall, London

    Book  MATH  Google Scholar 

  • Newell GF (2002) A simplified car-following theory: a lower order model. Transp Res B 36:195–205

    Article  Google Scholar 

  • Papageorgiou M (1983) Application of automatic control concepts in traffic flow modeling and control. Springer, Berlin/New York

    Book  MATH  Google Scholar 

  • 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 228–239

    Google Scholar 

  • Papageorgiou M, Kotsialos A (2002) Freeway ramp metering: an overview. IEEE Trans Intell Transp Syst 3(4):271–280

    Article  Google Scholar 

  • Papageorgiou M, Papamichail I (2008) Overview of traffic signal operation policies for ramp metering. Transp Res Rec 2047:28–36

    Article  Google Scholar 

  • 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):345–359

    Article  Google Scholar 

  • 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):361–370

    Article  Google Scholar 

  • Papageorgiou M, Hadj-Salem H, Blosseville J-M (1991) ALINEA: a local feedback control law for on-ramp metering. Transp Res Rec 1320:58–64

    Google Scholar 

  • Papageorgiou M, Hadj-Salem H, Middelham F (1997) ALINEA local ramp metering summary of field results. Transp Res Rec 1603:90–98

    Article  Google Scholar 

  • 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 2043–2067

    Google Scholar 

  • Papageorgiou M, Wang Y, Kosmatopoulos E, Papamichail I (2007) ALINEA maximizes motorway throughput – an answer to flawed criticism. Traffic Eng Control 48(6):271–276

    Google Scholar 

  • Payne HJ (1971) Models of freeway traffic and control. In: Bekey GA (ed) Mathematical models of public systems, vol 1. Simulation council, La Jolla

    Google Scholar 

  • Payne HJ (1979) FREEFLO: a macroscopic simulation model of freeway traffic. Transp Res Rec 772:68–75

    Google Scholar 

  • Persaud BN, Yagar S, Brownlee R (1998) Exploration of the breakdown phenomenon in freeway traffic. Trans Res Rec 1634:64–69

    Article  Google Scholar 

  • Pipes LA (1953) An operational analysis of traffic dynamics. J Appl Phys 24:274–287

    Article  ADS  MathSciNet  Google Scholar 

  • 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 503–508

    Google Scholar 

  • Prigogine I, Herman R (1971) Kinetic theory of vehicular traffic. American Elsevier, New York

    MATH  Google Scholar 

  • Qian Y-S, Feng X, Jun-Wei Zeng J-W (2017) A cellular automata traffic flow model for three-phase theory. Physica A 479:509–526

    Article  ADS  MathSciNet  Google Scholar 

  • 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 9429–9470

    Chapter  Google Scholar 

  • Rehborn H, Klenov SL (2009) Traffic prediction of congested patterns. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9500–9536

    Chapter  Google Scholar 

  • Rehborn H, Koller M (2014) A study of the influence of severe environmental conditions on common traffic congestion features. J Adv Transp 48:1107–1120

    Article  Google Scholar 

  • 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 186–191

    Google Scholar 

  • 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 390:4466–4485

    Article  ADS  Google Scholar 

  • 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 19–24

    Google Scholar 

  • 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 LLC

    Google Scholar 

  • 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 1838–1843

    Google Scholar 

  • 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 85:644–663

    Article  Google Scholar 

  • Richards PI (1956) Shockwaves on the highway. Oper Res 4:42–51

    Article  Google Scholar 

  • Saifuzzaman M, Zheng Z (2014) Incorporating human-factors in car-following models: a review of recent developments and research needs. Transp Res C 48:379–403

    Article  Google Scholar 

  • 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, Berlin

    Google Scholar 

  • Schadschneider A, Chowdhury D, Nishinari K (2011) Stochastic transport in complex systems. Elsevier Science, New York

    MATH  Google Scholar 

  • Schönhof M, Helbing D (2007) Empirical features of congested traffic states and their implications for traffic modelling. Transp Sc 41:135–166

    Article  Google Scholar 

  • Schönhof M, Helbing D (2009) Transp Res B 43:784–797

    Article  Google Scholar 

  • Schreckenberg M, Wolf DE (eds) (1998) Traffic and granular flow’97. In: Proceedings of the international workshop on traffic and granular flow. Springer, Singapore

    Google Scholar 

  • Siebel F, Mauser W (2006) Synchronized flow and wide moving jams from balanced vehicular traffic. Phys Rev E 73:066108

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Smaragdis E, Papageorgiou M (2003, 1856) Series of new local ramp metering strategies. Transp Res Rec:74–86

    Google Scholar 

  • Takayasu M, Takayasu H (1993) Phase transition and 1/f type noise in one dimensional asymmetric particle dynamics. Fractals 1:860–866

    Article  MATH  Google Scholar 

  • Tanga CF, Jiang R, Wu QS (2007) Phase diagram of speed gradient model with an on-ramp. Physica A 377:641–650

    Article  ADS  Google Scholar 

  • 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, Amsterdam

    Google Scholar 

  • 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 71:138–157

    Article  Google Scholar 

  • 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 93:338–354

    Article  Google Scholar 

  • 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 41:55–65

    Article  Google Scholar 

  • 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 93:560–575

    Article  Google Scholar 

  • Tomer E, Safonov L, Havlin S (2000) Presence of many stable nonhomogeneous states in an inertial car-following model. Phys Rev Lett 84:382–385

    Article  ADS  Google Scholar 

  • Treiber M, Kesting A (2013) Traffic flow dynamics. Springer, Berlin

    Book  MATH  Google Scholar 

  • Treiber M, Hennecke A, Helbing D (2000) Congested traffic states in empirical observations and microscopic simulations. Phys Rev E 62:1805–1824

    Article  ADS  MATH  Google Scholar 

  • 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 44:983–1000

    Article  Google Scholar 

  • Treiterer J (1967) Improvement of traffic flow and safety by longitudinal control. Transp Res 1:231–251

    Article  Google Scholar 

  • Treiterer J (1975) Investigation of traffic dynamics by aerial photogrammetry techniques. Ohio State University technical report PB 246 094, Columbus

    Google Scholar 

  • 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 13–38

    Google Scholar 

  • Treiterer J, Taylor JI (1966) Traffic flow investigations by photogrammetric techniques. Highway Res Rec 142:1–12

    Google Scholar 

  • Wang R, Jiang R, Wu QS, Liu M (2007) Synchronized flow and phase separations in single-lane mixed traffic flow. Physica A 378:475–484

    Article  ADS  Google Scholar 

  • 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

  • Whitham GB (1974) Linear and nonlinear waves. Wiley, New York

    MATH  Google Scholar 

  • Wiedemann R (1974) Simulation des Verkehrsflusses. University of Karlsruhe, Karlsruhe

    Google Scholar 

  • Wolf DE (1999) Cellular automata for traffic simulations. Physica A 263:438–451

    Article  ADS  MathSciNet  Google Scholar 

  • 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 392:5399–5413

    Article  ADS  Google Scholar 

  • 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 392:4009–4018

    Article  ADS  MathSciNet  Google Scholar 

  • Zurlinden H (2003) Ganzjahresanalyse des Verkehrsflusses auf Straßen. Schriftenreihe des Lehrstuhls für Verkehrswesen der Ruhr-Universität Bochum, Heft 26, Bochum

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Physics of Transport and Traffic, University Duisburg-Essen, Duisburg, Germany

    Boris S. Kerner

Authors
  1. Boris S. Kerner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boris S. Kerner .

Editor information

Editors and Affiliations

  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media LLC

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Kerner, B.S. (2018). Traffic Breakdown, Modeling Approaches to. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_559-2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27737-5_559-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics

Search

Navigation