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Traffic Breakdown, Mathematical Probabilistic Approaches to

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Bibliography

  • 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 

  • 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 

  • 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 

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

    Book  Google Scholar 

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

    Book  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 

  • Gardiner CW (1994) Handbook of stochastic methods for physics, chemistry, and the natural sciences. Springer, Berlin

    MATH  Google Scholar 

  • Gartner NH, Messer CJ, Rathi A (eds) (2001) Traffic flow theory. A state-of-the-art report. 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 

  • Greenshields BD (1935) A study of traffic capacity. In: Highway Research Board proceedings, 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. Transp Res Rec 1320:91–98

    Google Scholar 

  • Hall FL, Hurdle VF, Banks JH (1992) Synthesis of recent work on the nature of speedflow 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 

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

    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 

  • 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 – Denmark, 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 (1999a) Congested traffic flow: observations and theory. Transp 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 (2000a) Theory of breakdown phenomenon at highway bottlenecks. Transp Res Rec 1710:136–144

    Article  Google Scholar 

  • Kerner BS (2000b) Experimental features of the emergence of moving jams in free traffic flow. J Phys A Math Gen 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 (2004) The physics of traffic. Springer, Berlin/New York

    Book  Google Scholar 

  • 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. Phys A 392:5261–5282

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Book  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 spatial-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 non-homogeneous traffic. Phys A 364:473–492

    Article  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 (2009) Phase transitions in traffic flow on multilane roads. Phys Rev E 80:056101

    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 

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

    Book  Google Scholar 

  • Kühne R, Mahnke R, Lubashevsky I, Kaupužs J (2002) Probabilistic description of traffic breakdown. Phys Rev E 65:066125

    Article  ADS  Google Scholar 

  • Kühne R, Mahnke R, Lubashevsky I, Kaupužs J (2004) Probabilistic description of traffic breakdown caused by on-ramp. E-print arXiv: cond-mat/0405163

    Google Scholar 

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

    Book  Google Scholar 

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

    Google Scholar 

  • Mahnke R, Kaupužs J (1999) Stochastic theory of freeway traffic. Phys Rev E 59:117–125

    Article  ADS  MATH  Google Scholar 

  • Mahnke R, Pieret N (1997) Stochastic master-equation approach to aggregation in freeway traffic. Phys Rev E 56:2666–2671

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Mahnke R, Kaupužs J, Lubashevsky I (2009) Physics of stochastic processes. Wiley-VCH, Darmstadt

    MATH  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    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 

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

    Article  Google Scholar 

  • Piccoli B, Tosin A (2009) In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9727–9749

    Chapter  Google Scholar 

  • Rakha H, Wang W (2009) Procedure for calibrating Gipps car-following model. Transp Res Rec 2124:113–124

    Article  Google Scholar 

  • Rakha H, Pasumarthy P, Adjerid S (2009) A simplified behavioral vehicle longitudinal motion model. Transp Lett 1:95–110

    Article  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. IEEE Intelligent Veh Symp:186–191. http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4607789&filter%3DAND(p_IS_Number%3A4621124)&pageNumber=3

  • 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. Phys A 390:4466–4485

    Article  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. IEEE Intelligent Veh Symp IV:19–24

    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, Rio de Janeiro, Brazil, November 1–4. 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 

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

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  • 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. Phys A 263:438–451

    Article  MathSciNet  Google Scholar 

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Acknowledgments

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.

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Correspondence to Boris S. Kerner .

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Kerner, B.S., Klenov, S.L. (2018). Traffic Breakdown, Mathematical Probabilistic 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_558-3

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_558-3

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