Fundamentals of Traffic Dynamics

  • Antonella Ferrara
  • Simona Sacone
  • Silvia Siri
Part of the Advances in Industrial Control book series (AIC)


Traffic flow theory is devoted to study the interactions between vehicles (or drivers) and the infrastructure, which is given by many components, such as the roadways, the road signs and the traffic control actuators. Traffic phenomena are very complex, since they depend on the interactions of a large number of inhomogeneous vehicles and on many external factors. The first attempts to develop a mathematical theory of traffic flow date back to about one century ago, and the technology advancement of the last decades (in computer processing capabilities, as well as in measurement devices) has further enabled the evolution of traffic flow theory. Nevertheless, the research in traffic flow modelling is still very active and different types of traffic models are nowadays available, both based on theoretical approaches and on empirical observations. Such models can be used by traffic managers to forecast traffic conditions, and consequently to properly inform users about the forthcoming traffic state they can encounter in their travel, or to adequately design the traffic control frameworks to be applied in freeway networks.


  1. 1.
    Greenshields BD, Bibbins JR, Channing WS, Miller HH (1935) A study of traffic capacity. Highw Res Board 14:448–477Google Scholar
  2. 2.
    Greenberg H (1959) An analysis of traffic flow. Oper Res 7:79–85MathSciNetCrossRefGoogle Scholar
  3. 3.
    Underwood RT (1961) Speed, volume and density relationships: quality and theory of traffic flow. Yale Bureau of Highway Traffic, Connecticut, pp 141–188Google Scholar
  4. 4.
    Newell GF (1961) Nonlinear effects in the dynamics of car following. Oper Res 9:209–229CrossRefGoogle Scholar
  5. 5.
    Drake JS, Schofer JL, May AD (1967) A statistical analysis of speed-density hypotheses in vehicular traffic science. Highw Res Rec Proc 154:112–117Google Scholar
  6. 6.
    Chiabaut N, Buisson C, Leclercq L (2009) Fundamental diagram estimation through passing rate measurements in congestion. IEEE Trans Intell Transp Syst 10:355–359CrossRefGoogle Scholar
  7. 7.
    Ji Y, Daamen W, Hoogendoorn S, Hoogendoorn-Lanser S, Qian X (2010) Investigating the shape of the macroscopic fundamental diagram using simulation data. Transp Res Rec 2161:40–48Google Scholar
  8. 8.
    Wang H, Li J, Chen QY, Ni D (2011) Logistic modeling of the equilibrium speed-density relationship. Transp Res Part A 45:554–566Google Scholar
  9. 9.
    Carey M, Bowers M (2012) A review of properties of flow-density functions. Transp Rev 32:49–73CrossRefGoogle Scholar
  10. 10.
    Newell GF (1962) Theories of instability in dense highway traffic. J Oper Res Soc Jpn 5:9–54MathSciNetGoogle Scholar
  11. 11.
    Zhang HM (1999) A mathematical theory of traffic hysteresis. Transp Res Part B 33:1–23MathSciNetCrossRefGoogle Scholar
  12. 12.
    Laval JA (2011) Hysteresis in traffic flow revisited: an improved measurement method. Transp Res Part B 45:385–391CrossRefGoogle Scholar
  13. 13.
    Kerner BS (2004) The physics of traffic. Springer, HeidelbergCrossRefGoogle Scholar
  14. 14.
    Kerner BS (2004) Three-phase traffic theory and highway capacity. Phys A 333:379–440MathSciNetCrossRefGoogle Scholar
  15. 15.
    Schönhof M, Helbing D (2009) Criticism of three-phase traffic theory. Transp Res Part B 43:784–797CrossRefGoogle Scholar
  16. 16.
    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 Part B 44:983–1000CrossRefGoogle Scholar
  17. 17.
    Banks JH (1990) Flow processes at a freeway bottleneck. Transp Res Rec 1287:20–28Google Scholar
  18. 18.
    Cassidy MJ, Bertini RL (1999) Some traffic features at freeway bottlenecks. Transp Res Part B 33:25–42CrossRefGoogle Scholar
  19. 19.
    Geroliminis N, Daganzo CF (2008) Existence of Urban-scale macroscopic fundamental diagrams: some experimental findings. Transp Res Part B 42:759–770CrossRefGoogle Scholar
  20. 20.
    Geroliminis N, Sun J (2011) Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transp Res Part B 45:605–617CrossRefGoogle Scholar
  21. 21.
    Geroliminis N, Sun J (2011) Hysteresis phenomena of a macroscopic fundamental diagram in freeway networks. Transp Res Part A 45:966–979Google Scholar
  22. 22.
    Gayah VV, Daganzo CF (2011) Clockwise hysteresis loops in the macroscopic fundamental diagram: an effect of network instability. Transp Res Part B 45:643–655CrossRefGoogle Scholar
  23. 23.
    Elefteriadou L (2014) An introduction to traffic flow theory. Springer, BerlinCrossRefGoogle Scholar
  24. 24.
    HCM 2010 - Highway capacity manual. Transportation Research Board of the National Academy of Sciences, Washington D.C., 2010Google Scholar
  25. 25.
    Elefteriadou L (2003) Defining, measuring and estimating freeway capacity. In: Proceedings of the 82nd annual meeting of the transportation research boardGoogle Scholar
  26. 26.
    Lorenz M, Elefteriadou L (2000) A probabilistic approach to defining freeway capacity and breakdown. In: Proceedings of the fourth international symposium on highway capacity, pp 84–95Google Scholar
  27. 27.
    Shiomi Y, Yoshii T, Kitamura R (2011) Platoon-based traffic flow model for estimating breakdown probability at single-lane expressway bottlenecks. Procedia Soc Behav Sci 17:591–610CrossRefGoogle Scholar
  28. 28.
    Zhang L, Levinson D (2010) Ramp metering and freeway bottleneck capacity. Transp Res Part A 44:218–235Google Scholar
  29. 29.
    Daganzo CF (1997) Fundamentals of transportation and traffic operations. Elsevier Science New YorkGoogle Scholar
  30. 30.
    Bertini RL, Leal MT (2005) Empirical study of traffic features at a freeway lane drop. J Transp Eng 131:397–407CrossRefGoogle Scholar
  31. 31.
    May AD (1990) Traffic flow fundamentals. Prenctice-Hall, Englewood CliffsGoogle Scholar
  32. 32.
    Richards PI (1956) Shock waves on the highway. Oper Res 4:42–51MathSciNetCrossRefGoogle Scholar
  33. 33.
    Sugiyama Y, Fukui M, Kikuchi M, Hasebe K, Nakayama A, Nishinari K, Tadaki S-I, Yukawa S (2008) Traffic jams without bottlenecks - experimental evidence for the physical mechanism of the formation of a jam. New J Phys 10:033001CrossRefGoogle Scholar
  34. 34.
    Stern RE, Cui S, Delle Monache ML, Bhadani R, Bunting M, Churchill M, Hamilton N, Haulcy R, Pohlmann H, Wu F, Piccoli B, Seibold B, Sprinkle J, Work DB (2017) Dissipation of stop-and-go waves via control of autonomous vehicles: field experiments. arXiv:1705.01693
  35. 35.
    Cassidy MJ, Ahn S (1934) Driver turn-taking behavior in congested freeway merges. Transp Res Rec 2005:140–147Google Scholar
  36. 36.
    Treiber M, Kesting A, Helbing D (2006) Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps. Phys Rev E 74:1–10CrossRefGoogle Scholar
  37. 37.
    Banks JH (1991) The two-capacity phenomenon: some theoretical issues. Transp Res Rec 1320:234–241Google Scholar
  38. 38.
    Hall F-L, Agyemang-Duah K (1991) Freeway capacity drop and the definition of capacity. Transp Res Rec 1320:91–98Google Scholar
  39. 39.
    Chung K, Rudjanakanoknad J, Cassidy MJ (2007) Relation between traffic density and capacity drop at three freeway bottlenecks. Transp Res Part B 41:82–95CrossRefGoogle Scholar
  40. 40.
    Banks JH (1990) The two-capacity phenomenon at freeway bottlenecks: a basis for ramp metering? Transp Res Rec 1320:83–90Google Scholar
  41. 41.
    Srivastava A, Geroliminis N (2013) Empirical observations of capacity drop in freeway merges with ramp control and integration in a first-order model. Transp Res Part C 30:161–177CrossRefGoogle Scholar
  42. 42.
    Laval JA (1988) Stochastic processes of moving bottlenecks: approximate formulas for highway capacity. Transp Res Rec 2006:86–91Google Scholar
  43. 43.
    Leclercq L, Laval JA, Chiabaut N (2011) Capacity drops at merges: an endogenous model. Transp Res Part B 45:1302–1313CrossRefGoogle Scholar
  44. 44.
    Leclercq L, Laval JA, Chiabaut N (2016) Capacity drops at merges: new analytical investigations. Transp Res Part C 62:171–181CrossRefGoogle Scholar
  45. 45.
    Lighthill MJ, Whitham GB (1955) On kinematic waves II: a theory of traffic flow on long crowded roads. Proc Royal Soc A 229:317–345Google Scholar
  46. 46.
    Hoogendoorn SP, Bovy PHL (2001) State-of-the-art of vehicular traffic flow modelling. Proc Inst Mech Eng Part I: J Syst Control Eng 215:283–303CrossRefGoogle Scholar
  47. 47.
    van Wageningen-Kessels F, van Lint H, Vuik K, Hoogendoorn SP (2015) Genealogy of traffic flow models. EURO J Transp Logist 4:445–473CrossRefGoogle Scholar
  48. 48.
    Papageorgiou M (1998) Some remarks on macroscopic traffic flow modelling. Transp Res Part A 32:323–329Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical, Computer and Biomedical EngineeringUniversity of PaviaPaviaItaly
  2. 2.Department of Informatics, Bioengineering, Robotics and Systems EngineeringUniversity of GenoaGenoaItaly

Personalised recommendations