Journal of Statistical Physics

, Volume 177, Issue 4, pp 588–607 | Cite as

Interpreting Traffic on a Highway with On/Off Ramps in the Light of TASEP

  • Reihaneh Kouhi Esfahani
  • Norbert KernEmail author


We raise the question whether a simple model for traffic, generic but based on microscopic rules, can provide an additional angle for interpreting flow through a road system. Using the totally simple exclusion process (TASEP) on a road segment with ramps, we show that measuring the flow directly at the road junctions may be a useful setup. We show that the presence of junctions affects the characterisation of traffic, suggesting that interpretations in terms of a 2-phase or a 3-phase description may be complementary, rather than contradictory. We furthermore argue that hysteresis-like features can appear in a system with junctions, which is intriguing as the TASEP dynamics as such do not lead to hysteresis. We discuss our findings in the light of boundary-driven phase transitions.


TASEP dynamics Traffic flow Fundamental diagram Microscopic traffic models Hysteresis effect Traffic phases 



We would like to thank Prof. Meisam Akbarzadeh and Prof. Farhad Shahbazi for encouraging this collaboration. R. K.-I. wishes to thank Isfahan municipality for financial support of her PhD.


  1. 1.
    Knight, F.H.: Cost of production and price over long and short periods. J. Political Econ. 29(4), 304–335 (1921)Google Scholar
  2. 2.
    Knight, F.H.: Some fallacies in the interpretation of social cost. Q. J. Econ. 38(4), 582–606 (1924)Google Scholar
  3. 3.
    Greenshields, B.D., Thompson, J.T., Dickinson, H.C., Swinton, R.S.: The photographic method of studying traffic behavior. In: Highway Research Board Proceedings (Vol. 13) (1934)Google Scholar
  4. 4.
    Kerner, B.S.: Introduction to modern traffic flow theory and control: the long road to three-phase traffic theory. Springer, Berlin (2009)zbMATHGoogle Scholar
  5. 5.
    Lighthill, M.J., Whitham, J.B.: On kinematic waves. I: flow movement in long rivers. 11: a theory of traffic flow on long crowded roads. Proc. R. Soc. A229, 281–345 (1955)ADSzbMATHGoogle Scholar
  6. 6.
    Richards, P.I.: Shockwaves on the highway. Oper. Res. 4, 42–51 (1956)zbMATHGoogle Scholar
  7. 7.
    Daganzo, C.F.: The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transp. Res. Part B 28(4), 269–287 (1994)Google Scholar
  8. 8.
    Smulders, S.: Control of freeway traffic flow by variable speed signs. Transp. Res. Part B 24(2), 111–132 (1990)Google Scholar
  9. 9.
    Daganzo, C.F.: Requiem for second-order fluid approximations of traffic flow. Transp. Res. Part B 29(4), 277–286 (1995)Google Scholar
  10. 10.
    Pipes, L.A.: Car following models and the fundamental diagram of road traffic. Transp. Res. 1(1), 21–29 (1967)Google Scholar
  11. 11.
    Chandler, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Oper. Res. 6(2), 165–184 (1958)MathSciNetGoogle Scholar
  12. 12.
    Chandler, R.E., Herman, R., Montroll, E.W.: Car following theory of steady-state traffic flow. Oper. Res. 7(4), 499–505 (1959)MathSciNetGoogle Scholar
  13. 13.
    Brackstone, M., McDonald, M.: Car-following: a historical review. Transp. Res. Part F 2(4), 181–196 (1999)Google Scholar
  14. 14.
    Hoogendoorn, S.P., Bovy, P.H.: State-of-the-art of vehicular traffic flow modelling. J. Syst. Control Eng. 215(4), 283–303 (2001)Google Scholar
  15. 15.
    Wilson, R.E.: Mechanisms for spatio-temporal pattern formation in highway traffic models. Philos. Trans. R. Soc. Lond. A 366(1872), 2017–2032 (2008)ADSMathSciNetzbMATHGoogle Scholar
  16. 16.
    Wilson, R.E., Ward, J.A.: Car-following models: fifty years of linear stability analysisa mathematical perspective. Transp. Plan. Technol. 34(1), 3–18 (2011)Google Scholar
  17. 17.
    Bando, M., Hasebe, K., Nakanishi, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Phenomenological study of dynamical model of traffic flow. J. Phy. I 5(11), 1389–1399 (1995)ADSGoogle Scholar
  18. 18.
    Bando, M., Hasebe, K., Nakanishi, K., Nakayama, A.: Analysis of optimal velocity model with explicit delay. Phys. Rev. E 58(5), 5429 (1998)ADSGoogle Scholar
  19. 19.
    Popkov, V., Santen, L., Schadschneider, A., Schütz, G.M.: Empirical evidence for a boundary-induced nonequilibrium phase transition. J. Phys. A 34(6), L45 (2001)ADSzbMATHGoogle Scholar
  20. 20.
    Jiang, R., Wu, Q.S., Wang, B.H.: Cellular automata model simulating traffic interactions between on-ramp and main road. Phys. Rev. E 66(3), 036104 (2002)ADSGoogle Scholar
  21. 21.
    Buckley, D.J.: A semi-poisson model of traffic flow. Transp. Sci. 2(2), 107–133 (1968)Google Scholar
  22. 22.
    Branston, D.: Link capacity functions: a review. Transp. Res. 10(4), 223–236 (1976)Google Scholar
  23. 23.
    Treiterer, J., Myers, J.: The hysteresis phenomenon in traffic flow. Transp. Traffic Theory 6, 13–38 (1974)Google Scholar
  24. 24.
    Gayah, V.V., Daganzo, C.F.: Clockwise hysteresis loops in the macroscopic fundamental diagram: an effect of network instability. Transp. Res. Part B 45(4), 643–655 (2011)Google Scholar
  25. 25.
    Blase, J.H.: Hysteresis and catastrophe theory: empirical identification in transportation modelling. Environ. Plan. A 11(6), 675–688 (1979)Google Scholar
  26. 26.
    Kerner, B.S., Klenov, S.L.: Deterministic microscopic three-phase traffic flow models. J. Phys. A 39(8), 1775 (2006)ADSMathSciNetzbMATHGoogle Scholar
  27. 27.
    Kerner, B.S.: The physics of traffic. Phys. World Mag. 12, 25–30 (1999)Google Scholar
  28. 28.
    Kerner, B.S.: Congested traffic flow: observations and theory. Transp. Res. Rec. 1678, 160–167 (1999)Google Scholar
  29. 29.
    Kerner, B.S.: The Physics of Traffic. Springer, Berlin, New York (2004)Google Scholar
  30. 30.
    Kouhi Esfahani, R., Shahbazi, F., Akbarzadeh, M.: Three-phase classification of an uninterrupted traffic flow: a k-means clustering study. Transportmetrica B 7(1), 546–558 (2018)Google Scholar
  31. 31.
    Wagner, P., Nagel, K.: Comparing traffic flow models with different number of ’phases’. Eur. Phys. J. B 63, 315–320 (2008)ADSMathSciNetzbMATHGoogle Scholar
  32. 32.
    Schönhof, M., Helbing, D.: Criticism of three-phase traffic theory. Transp. Res. Part B 43(7), 784–797 (2009)Google Scholar
  33. 33.
    Krauss, S., Wagner, P., Gawron, C.: Metastable states in a microscopic model of traffic flow. Phys. Rev. E 55(5), 5597–5602 (1997)ADSGoogle Scholar
  34. 34.
    Barlovic, R., Santen, L., Schadschneider, A., Schreckenberg, M.: Metastable states in cellular automata for traffic flow. Eur. Phys. J. B 5(3), 793–800 (1998)ADSGoogle Scholar
  35. 35.
    Deng, H., Zhang, H.M.: Positive-negative loops (clockwise or unti-clockwise): on traffic relaxation, anticipation, and hysteresis. Transp. Res. Rec. 2491, 90–97 (2015)Google Scholar
  36. 36.
    Saifuzzaman, M., Zheng, Z., Haque, M.M., Washington, S.: Understanding the mechanism of traffic hysteresis and traffic oscillations through the change in task difficulty level. Transp. Res. Part B 105, 523–538 (2017)Google Scholar
  37. 37.
    Huang, D.W.: Ramp Effects in Asymmetric Simple Exclusion Processes. In: Schadschneider, A., Pöschel, T., Kühne, R., Schreckenberg, M., Wolf, D.E. (eds.) Traffic and Granular Flow05, pp. 509–514. Springer, Berlin, Heidelberg (2007)Google Scholar
  38. 38.
    Popkov, V., Hager, J., Krug, J., Schütz, G.M.: Minimal current phase and boundary layers in driven diffusive systems. Phys. Rev. E 63, 056110 (2001)ADSGoogle Scholar
  39. 39.
    MacDonald, C.T., Gibbs, J.H., Pipkin, A.C.: Kinetics of biopolymerization on nucleic acid templates. Biopolymers 6(1), 1–25 (1968)Google Scholar
  40. 40.
    Embley, B., Parmeggiani, A., Kern, N.: Understanding totally asymmetric simple-exclusion-process transport on networks: generic analysis via effective rates and explicit vertices. Phys. Rev. E 80(4), 041128 (2009)ADSGoogle Scholar
  41. 41.
    Neri, I., Kern, N., Parmeggiani, A.: Totally asymmetric simple exclusion process on networks. Phys. Rev. Lett. 107(6), 068702 (2011)ADSGoogle Scholar
  42. 42.
    Schütz, G., Domany, E.: Phase transitions in an exactly solube one-dimensiaonal exclusion process. J. Stat. Phys. 72(1/2), 277 (1993)ADSzbMATHGoogle Scholar
  43. 43.
    Hilhorst, H.J., Appert-Rolland, C.: A multi-lane TASEP model for crossing pedestrian traffic flows. J. Stat. Mech. 2012(06), P06009 (2012)Google Scholar
  44. 44.
    Appert-Rolland, C., Cividini, J., Hilhorst, H.J.: Intersection of two TASEP traffic lanes with frozen shuffle update. J. Stat. Mech. 2011(10), P10014 (2011)Google Scholar
  45. 45.
    Schadschneider, A.: Statistical physics of traffic flow. Physica A 285(1), 101–120 (2000)ADSMathSciNetzbMATHGoogle Scholar
  46. 46.
    Srinivasa, S., Haenggi, M.: The TASEP: A Statistical Mechanics Tool to Study the Performance of Wireless Line Networks. In ICCCN (pp. 1-6) (2010, August)Google Scholar
  47. 47.
    Chou, T., Mallick, K., Zia, R.K.P.: Synchronous totally asymmetric exclusion process with a dial-input-single-output junction. J. Res. Phys. 35(1), 75 (2011)Google Scholar
  48. 48.
    Rajewsky, N., Santen, L., Schadschneider, A., Schreckenberg, M.: The asymmetric exclusion process: comparison of update procedures. J. Stat. Phys. 92(1–2), 151–194 (1998)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Appert-Rolland, C., Ebbinghaus, M., Santen, L.: Intracellular transport driven by cytoskeletal motors: general mechanisms and defects. Phys. Rep. 593, 159 (2015)MathSciNetGoogle Scholar
  50. 50.
    Appert-Rolland, C., Cividini, J., Hilhorst, H.J.: Random shuffle update for an asymmetric exclusion process on a ring. J. Stat. Mech. 7(07), 07009 (2011)Google Scholar
  51. 51.
    Kerner, B.S.: Introduction to modern traffic flow theory and control: the long road to three-phase traffic theory. Springer, Berlin (2009)zbMATHGoogle Scholar
  52. 52.
    Knospe, W., Santen, L., Schadschneider, A., Schreckenberg, M.: Empirical test for cellular automaton models of traffic flow. Phys. Rev. E 70(1), 016115 (2004)ADSGoogle Scholar
  53. 53.
    Xiao, S., Wu, S., Zheng, D.: Synchronous totally asymmetric exclusion process with a dial-input-single-output junction. J. Res. Phys. 35(1), 75 (2011)Google Scholar
  54. 54.
    Brankov, J. G., Pesheva, N. C., Bunzarova, N.Z.: One-Dimensional Traffic Flow Models: Theory and Computer Simulations. arXiv preprint arXiv:0803.2625 (2008)
  55. 55.
    Raguin, A., Parmeggiani, A., Kern, N.: Role of network junctions for the totally asymmetric simple exclusion process. Phys. Rev. E 88(4), 042104 (2013)ADSGoogle Scholar
  56. 56.
    Kolomeisky, A.B., Schütz, G.M., Kolomeisky, E.B., Straley, J.P.: Phase diagram of one-dimensional driven lattice gases with open boundaries. J. Phys. A 31(33), 6911 (1998)ADSzbMATHGoogle Scholar
  57. 57.
    Kraub, S., Wagner, P., Gawon, C.: Metastable states in a microscopic model of traffic flow. Phys. Rev. E 55(5), 5597 (1997)ADSGoogle Scholar
  58. 58.
    Buisson, C., Ladier, C.: Exploring the impact of homogeneity of traffic measurements on the existence of macroscopic fundamental diagrams. Transp. Res. Rec. 2124, 127–136 (2009)Google Scholar
  59. 59.
    Geroliminis, N., Sun, J.: Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transp. Res. Part B 45(3), 605–617 (2011)Google Scholar
  60. 60.
    Chen, D., Laval, J.A., Ahn, S., Zheng, Z.: Microscopic traffic hysteresis in traffic oscillations: a behavioral perspective. Transp. Res. Part B 46(10), 1440–1453 (2012)Google Scholar
  61. 61.
    Helbing, D., Treiber, M.: Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Phys. Rev. Lett. 81(14), 3042 (1998)ADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsIsfahan University of TechnologyIsfahanIran
  2. 2.Laboratoire Charles Coulomb (L2C)University of Montpellier, CNRSMontpellierFrance

Personalised recommendations