Glossary
- Effectual Bottleneck:
-
An effectual bottleneck is a highway bottleneck at which an F → S transition (traffic breakdown) occurs during many days and years of empirical observations. Because only effectual bottlenecks are considered in the entry, the term bottleneck is used below for an effectual bottleneck.
- Traffic Breakdown:
-
Traffic breakdown is the onset of congested traffic in an initial free traffic flow. In highway traffic, traffic breakdown occurs mostly at effectual highway bottlenecks like on and off-ramps, roadworks, road gradients, reduction of road lanes, a slow moving vehicle (moving bottleneck), etc. Traffic breakdown results in the emergence of the synchronized flow phase of congested traffic, i.e., traffic breakdown is a phase transition from the free flow traffic phase to synchronized flow traffic phase at a bottleneck (F → S transition for short; F – free flow, S – synchronized flow). Thus, the terms traffic breakdown and an F → S transitionare synonyms...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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
Brilon W, Zurlinden H (2004) Kapazität von Straßen als Zufallsgröße. Straßenverkehrstechnik (4): 164
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
Brilon W, Regler M, Geistefeld J (2005b) Zufallscharakter der Kapazität von Autobahnen und praktische Konsequenzen – Teil 1. Straßenverkehrstechnik (3): 136
Chandler RE, Herman R, Montroll EW (1958) Traffic dynamics: studies in car following. Oper Res 6:165–184
Chowdhury D, Santen L, Schadschneider A (2000) Statistical physics of vehicular traffic and some related systems. Phys Rep 329:199
Cremer M (1979) Der Verkehrsfluss auf Schnellstrassen. Springer, Berlin
Daganzo CF (1997) Fundamentals of transportation and traffic operations. Elsevier Science Inc, New York
Elefteriadou L (2014) An introduction to traffic flow theory. Springer optimization and its applications, vol 84. Springer, Berlin
Elefteriadou L, Roess RP, McShane WR (1995) Probabilistic nature of breakdown at freeway merge junctions. Transp Res Rec 1484:80–89
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
Gardiner CW (1994) Handbook of stochastic methods for physics, chemistry, and the natural sciences. Springer, Berlin
Gartner NH, Messer CJ, Rathi A (eds) (2001) Traffic flow theory. A state-of-the-art report. Transportation Research Board, Washington, DC
Gazis DC (2002) Traffic theory. Springer, Berlin
Gazis DC, Herman R, Potts RB (1959) Car-following theory of steady-state traffic flow. Oper Res 7:499–505
Gazis DC, Herman R, Rothery RW (1961) Nonlinear follow-the-leader models of traffic flow. Oper Res 9:545–567
Greenshields BD, Bibbins JR, Channing WS, Miller HH (1935) A study of traffic capacity. Highw Res Board Proc 14:448–477
Haight FA (1963) Mathematical theories of traffic flow. Academic, New York
Hall FL, Agyemang-Duah K (1991) Freeway capacity drop and the definition of capacity. Transp Res Rec 1320:91–98
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
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
Helbing D (2001) Traffic and related self-driven many-particle systems. Rev Mod Phys 73:1067–1141
Herman R, Montroll EW, Potts RB, Rothery RW (1959) Traffic dynamics: analysis of stability in car following. Oper Res 7:86–106
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
Kerner BS (1998b) Empirical features of self-organization in traffic flow. Phys Rev Lett 81:3797–3400
Kerner BS (1999a) Congested traffic flow: observations and theory. Transp Res Rec 1678:160–167
Kerner BS (1999b) The physics of traffic. Phys World 12:25–30
Kerner BS (2000a) Theory of breakdown phenomenon at highway bottlenecks. Transp Res Rec 1710:136–144
Kerner BS (2000b) Experimental features of the emergence of moving jams in free traffic flow. J Phys A Math Gen 33:L221–L228
Kerner BS (2001) Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories. Netw Spat Econ 1:35–76
Kerner BS (2002a) Synchronized flow as a new traffic phase and related problems for traffic flow modelling. Math Comput Model 35:481–508
Kerner BS (2002b) Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks. Phys Rev E 65:046138
Kerner BS (2004) The physics of traffic. Springer, Berlin/New York
Kerner BS (2009a) Traffic congestion, modelling approaches to. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9302–9355
Kerner BS (2009b) Traffic congestion, spatiotemporal features of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9355–9411
Kerner BS (2009c) Introduction to modern traffic flow theory and control. Springer, Berlin/New York
Kerner BS (2013) Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: a brief review. Phys A 392:5261–5282
Kerner BS (2015) Failure of classical traffic flow theories: a critical review. Elektrotechn Informationstech 132:417–433
Kerner BS (2016) Failure of classical traffic flow theories: stochastic highway capacity and automatic driving. Phys A 450:700–747
Kerner BS (2017a) Breakdown in traffic networks: fundamentals of transportation science. Springer, Berlin/New York
Kerner BS, Klenov SL (2002) A microscopic model for phase transitions in traffic flow. J Phys A Math Gen 35:L31–L43
Kerner BS, Klenov SL (2003) Microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks. Phys Rev E 68:036130
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
Kerner BS, Klenov SL (2006b) Probabilistic breakdown phenomenon at on-ramp bottlenecks in three-phase traffic theory. Transp Res Rec 1965:70–78
Kerner BS, Klenov SL (2009) Phase transitions in traffic flow on multilane roads. Phys Rev E 80:056101
Kerner BS, Klenov SL, Wolf DE (2002) Cellular automata approach to three-phase traffic theory. J Phys A Math Gen 35:9971–10013
Kuhn TS (2012) The structure of scientific revolutions, 4th edn. The University of Chicago Press, Chicago/London
Kühne R, Mahnke R, Lubashevsky I, Kaupužs J (2002) Probabilistic description of traffic breakdown. Phys Rev E 65:066125
Kühne R, Mahnke R, Lubashevsky I, Kaupužs J (2004) Probabilistic description of traffic breakdown caused by on-ramp. E-print arXiv: cond-mat/0405163
Leutzbach W (1988) Introduction to the theory of traffic flow. Springer, Berlin
Lorenz M, Elefteriadou L (2000) A probabilistic approach to defining freeway capacity and breakdown. Trans Res C E-C018:84–95
Mahnke R, Kaupužs J (1999) Stochastic theory of freeway traffic. Phys Rev E 59:117–125
Mahnke R, Pieret N (1997) Stochastic master-equation approach to aggregation in freeway traffic. Phys Rev E 56:2666–2671
Mahnke R, Kaupužs J, Lubashevsky I (2005) Probabilistic description of traffic flow. Phys Rep 408:1–130
Mahnke R, Kaupužs J, Lubashevsky I (2009) Physics of stochastic processes. Wiley-VCH, Darmstadt
May AD (1990) Traffic flow fundamentals. Prentice-Hall, Englewood Cliffs
Nagatani T (2002) The physics of traffic jams. Rep Prog Phys 65:1331–1386
Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J Phys (France) I 2: 2221–2229
Nagel K, Wagner P, Woesler R (2003) Still flowing: approaches to traffic flow and traffic jam Modeling. Oper Res 51:681–716
Persaud BN, Yagar S, Brownlee R (1998) Exploration of the breakdown phenomenon in freeway traffic. Transp Res Rec 1634:64–69
Piccoli B, Tosin A (2009) In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9727–9749
Rakha H, Wang W (2009) Procedure for calibrating Gipps car-following model. Transp Res Rec 2124:113–124
Rakha H, Pasumarthy P, Adjerid S (2009) A simplified behavioral vehicle longitudinal motion model. Transp Lett 1:95–110
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
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
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
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
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
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
Schadschneider A, Chowdhury D, Nishinari K (2011) Stochastic transport in complex systems. Elsevier Science, New York
Treiber M, Kesting A (2013) Traffic flow dynamics. Springer, Berlin
Whitham GB (1974) Linear and nonlinear waves. Wiley, New York
Wiedemann R (1974) Simulation des Verkehrsflusses. University of Karlsruhe, Karlsruhe
Wolf DE (1999) Cellular automata for traffic simulations. Phys A 263:438–451
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Science+Business Media, LLC, part of Springer Nature
About this entry
Cite this entry
Kerner, B.S., Klenov, S.L. (2019). Mathematical Probabilistic Approaches to Traffic Breakdown. In: Kerner, B. (eds) Complex Dynamics of Traffic Management. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8763-4_558
Download citation
DOI: https://doi.org/10.1007/978-1-4939-8763-4_558
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-8762-7
Online ISBN: 978-1-4939-8763-4
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics