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Minimization of Traffic Congestion in Networks

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Breakdown in Traffic Networks

Abstract

In chapter “Maximization of Network Throughput Ensuring Free Flow Conditions in Network”, we have considered the application of the BM principle called the network throughput maximization approach. This approach allows us to prevent traffic breakdown in the whole network while keeping condition that the probability of traffic breakdown in the network remains to be equal to zero. The objective of this chapter is to study the case of larger values of the total network inflow rate related to rush hours in urban networks at which under application of the BM principle the probability that traffic breakdown occurs in the network becomes larger than zero.

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Notes

  1. 1.

    This means that applications of the BM principle under condition (12.1) for the case of non-isolated traffic networks (Sect. 11.6.6) will not be studied in this book.

  2. 2.

    It should be noted that in some networks the on-ramp inflow rate q on (k) can be equal to the inflow rate for another network link; in this case, q sum (k) depends on the inflow rates for two different network links.

  3. 3.

    Recall that as mentioned in Sect. 11.1, when network bottleneck k is due to traffic signal, for this bottleneck k the flow rate q sum (k) in all formulas should be replaced by the average arrival flow rate at the approach \(\bar{q}_{\mathrm{in}}^{(k)}\) (see Sect. 9.3).

  4. 4.

    Two-route network models are often used for studies of other traffic phenomena (e.g., [1–8, 38–43]).

  5. 5.

    In [17] it has been found that the closer the feedback detector location to the effective location of the bottleneck, the more efficient is ANCONA application. However, in any case the feedback detector location in ANCONA must be upstream of the effective bottleneck location. For simplicity, we study here only a case [14, 15] in which a feedback detector location in ANCONA is upstream of the bottleneck as shown in Fig. 12.17.

  6. 6.

    In simulations presented in Fig. 12.18, the location of detectors for feedback control is upstream of the effective bottleneck location (Fig. 12.17). On-ramp inflow bottleneck control starts only after traffic breakdown (F → S transition) is registered by the detectors for feedback control installed on the main road 100 m upstream of bottleneck location x on = 15 km. Additionally to the detectors for feedback control installed on the main road, there is a detector in the on-ramp lane. Due to the detector in the on-ramp lane, the queue length of vehicles at traffic signals in the on-ramp lane is measured.

References

  1. B. Chen, W. Tong, W. Zhang, X. Sun, B. Wang, EPL 97, 14001 (2012)

    Article  Google Scholar 

  2. B. Chen, W. Tong, W. Zhang, X. Sun, B. Wang, Comput. Phys. Comm. 183, 2081–2088 (2012)

    Article  Google Scholar 

  3. R. Claes, T. Holvoet, and D. Weyns, IEEE Trans. ITS 12, 364–373 (2011)

    Google Scholar 

  4. L.C. Davis, Physica A 388, 4459 (2009)

    Article  Google Scholar 

  5. L.C. Davis, Physica A 389, 3588 (2010)

    Article  Google Scholar 

  6. C. Dong, X. Ma, B. Wang, Phys. Lett. A 374, 1326–1331 (2010)

    Article  Google Scholar 

  7. C. Dong, X. Ma, B. Wang, Sci. China-Infor. Sci. 53, 2265–2271 (2010)

    Article  Google Scholar 

  8. C. Dong, X. Ma, G. Wang, B. Wang, X. Sun, Physica A 389, 3274–3281 (2010)

    Article  Google Scholar 

  9. Ch.M. Grinstead, J.L. Snell Introduction to Probability, 2nd edn. (American Mathematical Society, Rhode Island, 1997)

    Google Scholar 

  10. H. Guo, Z. Cao, J. Zhang, D. Niyato, U. Fastenrath, in 17th Inter. IEEE Conference on ITS (ITSC), (China, Qingdao, 2014), pp. 2180–2187

    Google Scholar 

  11. H. Guo, Z. Cao, J. Zhang, D. Niyato, M. Seshadri, U. Fastenrath, IEEE Trans. Emerg. Top. Comp. Intell. (2017). doi:10.1109/TETCI.2017.2665592

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Book  Google Scholar 

  15. B.S. Kerner, Physica A 355, 565–601 (2005)

    Article  Google Scholar 

  16. B.S. Kerner, in Traffic and Transportation Theory, ed. by H.S. Mahmassani (Elsevier Science, Amsterdam, 2005), pp. 181–203

    Google Scholar 

  17. B.S. Kerner, IEEE Trans. ITS 8, 308–320 (2007)

    Google Scholar 

  18. B.S. Kerner, Transp. Res. Rec. 1999, 30–39 (2007)

    Article  Google Scholar 

  19. B.S. Kerner, J. Phys. A Math. Theor. 41, 215101 (2008)

    Article  Google Scholar 

  20. B.S. Kerner, Introduction to Modern Traffic Flow Theory and Control (Springer, Heidelberg, Dordrecht, London, New York, 2009)

    Book  MATH  Google Scholar 

  21. B.S. Kerner, J. Phys. A Math. Theor. 44, 092001 (2011)

    Article  Google Scholar 

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

    Google Scholar 

  23. B.S. Kerner, Traffic Eng. Contr. 52, 379–386 (2011)

    Google Scholar 

  24. B.S. Kerner, in Proc. of 2011 IEEE Forum on Integrated and Sustainable Transp. Systems (Austria, Vienna, 2011), pp. 196–201

    Google Scholar 

  25. B.S. Kerner, in Proc. of the 19th ITS World Congress (Austria, Vienna, 2012), Paper No. EU-00190

    Google Scholar 

  26. B.S. Kerner, Phys. Rev. E 85, 036110 (2012)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  28. B.S. Kerner, Phys. Rev. E 92, 062827 (2015)

    Article  Google Scholar 

  29. B.S. Kerner, Elektrotechnik Informationstechnik 132, 417–433 (2015)

    Article  Google Scholar 

  30. B.S. Kerner, Physica A 450, 700–747 (2016)

    Article  MathSciNet  Google Scholar 

  31. B.S. Kerner, Eur. Phys. J. B 89, 199 (2016)

    Article  Google Scholar 

  32. B.S. Kerner, Physica A 466, 626–662 (2017)

    Article  MathSciNet  Google Scholar 

  33. B.S. Kerner, S.L. Klenov, J. Phys. A Math. Gen. 35, L31–L43 (2002)

    Article  Google Scholar 

  34. B.S. Kerner, S.L. Klenov, Phys. Rev. E 80, 056101 (2009)

    Article  Google Scholar 

  35. B.S. Kerner, S.L. Klenov, D.E. Wolf, J. Phys. A Math. Gen. 35, 9971–10013 (2002)

    Article  Google Scholar 

  36. B.S. Kerner, M. Koller, S.L. Klenov, H. Rehborn, M. Leibel, Physica A 438, 365–397 (2015)

    Article  Google Scholar 

  37. B.S. Kerner, H. Rehborn, R.-P. Schäfer, S.L. Klenov, J. Palmer, S. Lorkowski, N. Witte, Physica A 392, 221–251 (2013)

    Article  Google Scholar 

  38. K. Lee, P. Hui, B. Wang, N. Johnson, J. Phys. Soc. Jpn. 70, 3507–3510 (2001)

    Article  Google Scholar 

  39. K. Tobita, T. Nagatani, Physica A 391, 6137–6145 (2012)

    Article  Google Scholar 

  40. J. Wahle, A.L.C. Bazzan, F. Klugl, M. Schreckenberg, Physica A 287, 669 (2000)

    Article  Google Scholar 

  41. J. Wahle, A. Bazzan, F. Klugl, M. Schreckenberg, Transp. Res. C 10, 399–417 (2002)

    Article  Google Scholar 

  42. W. Wang, B. Wang, W. Zheng, C. Yin, T. Zhou, Phys. Rev. E 72, 066702 (2005)

    Article  Google Scholar 

  43. X.-m. Zhao, D.-f. Xie, Q. Li, Comput. Phys. Comm. 187, 106–114 (2015)

    Article  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). Minimization of Traffic Congestion in Networks. In: Breakdown in Traffic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54473-0_12

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  • DOI: https://doi.org/10.1007/978-3-662-54473-0_12

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