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Time-Delayed Breakdown at Traffic Signal in City Traffic

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Breakdown in Traffic Networks

Abstract

In this Chapter, we present a theory of time-delayed traffic breakdown (transition from under-saturated to over-saturated traffic) at traffic signal in city traffic. A detailed comparison of the theory of time-delayed traffic breakdown at the signal with the classical theory of traffic at the signal is made. The analysis of traffic at the signal allows us to find conditions at which classical traffic flow theories can be considered special cases of the three-phase traffic theory.

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Notes

  1. 1.

    The queue length and the jam width should be considerably larger than the lengths of the upstream and downstream fronts of the moving queue and the wide moving jam, respectively.

  2. 2.

    The cycle time of traffic signal and the durations of the green, yellow, and red phases of traffic signal are often called signal parameters or signal control settings.

  3. 3.

    Different simulation realizations (runs) are made at the same chosen q in and signal parameters (signal control settings). The only difference between these runs is different initial conditions for model fluctuations in the different runs. To reach this goal, initial values for random function rand() in the Kerner-Klenov model (Appendix A) have been different ones for different simulation realizations.

  4. 4.

    Note that in Sec. 5.2.7 of the book [24] we have explained that the flow rate q out (MSP) determines the threshold flow rate q in = q th for the F → S transition (traffic breakdown) on a hypothetical homogeneous road without bottlenecks: q th = q out (MSP).

  5. 5.

    For the calculation of the probability of GW breakdown we have used N R = 40 different simulation realizations (runs) at the same chosen q in(t) and the same signal parameters. The only difference between these runs is different initial conditions for random function rand() used in the Kerner-Klenov stochastic microscopic model at time t = 0 (see Appendix A).

  6. 6.

    It should be noted that due to fluctuations in the outflow from a moving queue, there are very narrow ranges of the average arrival flow rate within which either dissolving over-saturated traffic occurs (when condition (9.28) is satisfied) or a random time-delayed breakdown is observed (when condition (9.21) is satisfied).

References

  1. M.S. Chaudhry, P. Ranjitkar, in TRB 92nd Annual Meeting Compendium of Papers, TRB Paper 13-3396 (Transportation Research Board, Washington D.C., 2013)

    Google Scholar 

  2. F. Dion, H. Rakha, Y.S. Kang, Transp. Rec. B 38, 99–122 (2004)

    Article  Google Scholar 

  3. N.H. Gartner, Transp. Sci. 6, 88–93 (1972)

    Article  Google Scholar 

  4. N.H. Gartner, Transp. Res. Rec. 906, 75–81 (1983)

    Google Scholar 

  5. N.H. Gartner, Transp. Res. A 19, 369–373 (1985)

    Article  Google Scholar 

  6. N.H. Gartner, M. Al-Malik, Transp. Res. Rec. 1554, 27–35 (1996)

    Article  Google Scholar 

  7. N.H. Gartner, S.F. Assmann, F. Lasaga, D.L. Hou, Transp. Res. Rec. 1287, 212–222 (1990)

    Google Scholar 

  8. N.H. Gartner, S.F. Assmann, F. Lasaga, D.L. Hou, Transp. Res. B 25, 55–74 (1991)

    Article  Google Scholar 

  9. N.H. Gartner, J.D.C. Little, Transp. Res. Rec. 531, 58–69 (1975)

    Google Scholar 

  10. N.H. Gartner, J.D.C. Little, H. Gabbay, Transp. Sci. 9, 321–343 (1975)

    Article  Google Scholar 

  11. N.H. Gartner, J.D.C. Little, H. Gabbay, Transp. Res. Rec. 596, 6–15 (1976)

    Google Scholar 

  12. N.H. Gartner, Ch. Stamatiadis, Math. Comp. Model. 35, 657–671 (2002)

    Article  Google Scholar 

  13. N.H. Gartner, Ch. Stamatiadis, J. Intel. Transp. Sys. 8, 77–86 (2004)

    Google Scholar 

  14. N.H. Gartner, Ch. Stamatiadis, in Encyclopedia of Complexity and System Science, ed. by R.A. Meyers (Springer, Berlin, 2009), pp. 9470–9500

    Chapter  Google Scholar 

  15. N.H. Gartner, Ch. Stamatiadis, P.J. Tarnoff, Transp. Res. Rec. 1494, 98–105 (1995)

    Google Scholar 

  16. N.H. Gartner, P.J. Tarnoff, C.M. Andrews, Transp. Res. Rec. 1324, 105–114 (1991)

    Google Scholar 

  17. D.L. Gerlough, M.J. Huber, Traffic Flow Theory Special Report 165 (Transp. Res. Board, Washington D.C., 1975)

    Google Scholar 

  18. R.B. Grafton, G.F. Newell, in Vehicular Traffic Science, ed. by L.C. Edie, R. Herman, R. Rothery (Elsevier, New York, 1967), pp. 239–257

    Google Scholar 

  19. B.D. Greenshields, D. Schapiro, E.L. Ericksen, Technical Report No.1 (Yale Bureau of Highway Traffic, Yale University, 1947)

    Google Scholar 

  20. P. Hemmerle, M. Koller, H. Rehborn, B.S. Kerner, M. Schreckenberg, IET Intell. Transp. Syst. 10, 122–129 (2016)

    Article  Google Scholar 

  21. G. Hermanns, P. Hemmerle, H. Rehborn, M. Koller, B.S. Kerner, M. Schreckenberg, Transp. Res. Rec. 2490, 47–55 (2015)

    Article  Google Scholar 

  22. P.B. Hunt, D.I. Robertson, R.D. Bretherton, R.I. Winton, TRRL Report No. LR 1014 (Transp. and Road Res. Lab., Crowthorne, UK, 1981)

    Google Scholar 

  23. R. Jiang, M.-B. Hu, B. Jia, Z.-Y. Gao, Comp. Phys. Comm. 185, 1439 (2014)

    Article  Google Scholar 

  24. B.S. Kerner, The Physics of Traffic (Springer, Berlin, New York, 2004)

    Book  Google Scholar 

  25. B.S. Kerner, Introduction to Modern Traffic Flow Theory and Control (Springer, Berlin, New York, 2009)

    Book  MATH  Google Scholar 

  26. B.S. Kerner, Phys. Rev. E 84, 045102(R) (2011)

    Google Scholar 

  27. B.S. Kerner, Europhys. Lett. 102, 28010 (2013)

    Article  Google Scholar 

  28. B.S. Kerner, Physica A 397, 76–110 (2014)

    Article  MathSciNet  Google Scholar 

  29. B.S. Kerner, P. Hemmerle, M. Koller, G. Hermanns, S.L. Klenov, H. Rehborn, M. Schreckenberg, Phys. Rev. E 90, 032810 (2014)

    Article  Google Scholar 

  30. B.S. Kerner, S.L. Klenov, M. Schreckenberg, J. Stat. Mech. P03001 (2014)

    Google Scholar 

  31. B.S. Kerner, S.L. Klenov, G. Hermanns, P. Hemmerle, H. Rehborn, M. Schreckenberg, Phys. Rev. E 88, 054801 (2013)

    Article  Google Scholar 

  32. W.R. McShane, R.P. Roess, Traffic Engineering (Prentice Hall, Englewood Cliffs, NJ, 1990)

    Google Scholar 

  33. T.S. Kuhn, in The Structure of Scientific Revolutions, 4th edn. (The University of Chicago Press, Chicago, London, 2012)

    Google Scholar 

  34. M.J. Lighthill, G.B. Whitham, Proc. Roy. Soc. A 229, 281–345 (1955)

    Article  Google Scholar 

  35. J.D.C. Little, Oper. Res. 14, 568–594 (1966)

    Article  Google Scholar 

  36. J.D.C. Little, M.D. Kelson, N.H. Gartner, Transp. Res. Rec. 795, 40–46 (1981)

    Google Scholar 

  37. P.G. Michalopoulos, G. Stephanopoulos, V.B. Pisharody, Transp. Sci. 14, 9–41 (1980)

    Article  Google Scholar 

  38. P.G. Michalopoulos, G. Stephanopoulos, G., Stephanopoulos, Transp. Res. B 15, 35–51 (1981)

    Google Scholar 

  39. J.T. Morgan, J.D.C. Little, Oper. Res. 12, 896–912 (1964)

    Article  Google Scholar 

  40. G.F. Newell, Ann. Math. Stat. 31, 589–597 (1960)

    Article  Google Scholar 

  41. G.F. Newell, SIAM Rev. 575, 223–240 (1965)

    Article  Google Scholar 

  42. G.F. Newell, Applications of Queuing Theory (Chapman Hall, London, 1982)

    Book  MATH  Google Scholar 

  43. P.I. Richards, Oper. Res. 4, 42–51 (1956)

    Article  Google Scholar 

  44. D.I. Robertson, TRRL Report No. LR 253 (Transportation and Road Research Laboratory, Crowthorne, UK, 1969)

    Google Scholar 

  45. D.I. Robertson, in Proceedings of the International Symposium on Traffic Control Systems, pp. 262–288 (1979)

    Google Scholar 

  46. Ch. Stamatiadis, N.H. Gartner, Transp. Res. Rec. 1554, 9–17 (1996)

    Article  Google Scholar 

  47. G. Stephanopoulos, P.G. Michalopoulos, Transp. Res. A 13, 295–307 (1979)

    Article  Google Scholar 

  48. Y. Wang, Y.-Y. Chen, Physica A 463, 12–24 (2016)

    Article  MathSciNet  Google Scholar 

  49. F.V. Webster, Road Research Technical Paper No. 39 (Road Research Laboratory, London, UK, 1958)

    Google Scholar 

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Authors and Affiliations

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

    Boris S. Kerner

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Kerner, B.S. (2017). Time-Delayed Breakdown at Traffic Signal in City Traffic. In: Breakdown in Traffic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54473-0_9

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  • DOI: https://doi.org/10.1007/978-3-662-54473-0_9

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