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Deterioration of Traffic System Through Standard Dynamic Traffic Assignment in Networks

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Breakdown in Traffic Networks

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Abstract

The main objective of this chapter is to show that applications of this standard methodology of the minimization of network travel times deteriorates traffic system basically while provoking heavy traffic congestion in the network.

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Notes

  1. 1.

    In Sect. 12.4 we have mentioned that in the Kerner-Klenov model used for all simulations in this chapter conditions (5.13) are satisfied and, therefore, the threshold for spontaneous traffic breakdown at a bottleneck is determined by the threshold flow rate q th (B,k) of bottleneck k. For this reason, in simulations with the Kerner-Klenov model the network capacity C net is given by formula (12.17). The threshold flow rate q th (B,k) of on-ramp bottleneck k is larger than the minimum capacity C min (k) of the bottleneck. This explains why the minimum possible theoretical value of the network capacity C net (12.14) is considerably smaller than the network capacity C net (12.17) following from simulations with the Kerner-Klenov model.

  2. 2.

    A comparison of the application of congested pattern control approach used in the main text of the book with a step-by-step method for the searching of the Wardrop’s UE can be found in Appendix C.

  3. 3.

    In the case under consideration, the location of bottleneck 1 is x = x on = 15 km. An F → S transition is registered by the feedback control detector when the speed at the detector v ≤ 80 km/h (for two-route network) and v ≤ 70 km/h (for three route network) during 3 min. A return S → F transition is registered by the feedback control detector when the speed at the detector v ≥ 92 km/h during 2 min.

  4. 4.

    The dynamic traffic assignment of the link inflow rates q m (m = 1, 2 in Fig. 12.3a and m = 1, 2, 3 in Fig. 12.4a) under time-dependent flow rate q (o)(t) (Figs. 13.4–13.6) is performed with the use of standard methods [13, 98, 112, 114, 115, 119]: For some flow rates q (o), values q m have been found in accordance with the Wardrop’s UE (points in Figs. 13.4b and 13.5b). Simulations show that these points are well fitted with lines q m (q (o)) given in captions to Figs. 13.4 and 13.5. These lines have further been used for calculations of q m under time-dependent flow rate q (o)(t).

  5. 5.

    It should be noted that a free assignment of the flow rates q 1 and q 2 is only possible as long as free flow is at the origin of the network. Therefore, simulation results presented in Fig. 13.11 has only the sense as long as a contested pattern occurring in the network has not reached the origin (x = 0 in Figs. 13.11b, right and c, left).

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    Boris S. Kerner

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Kerner, B.S. (2017). Deterioration of Traffic System Through Standard Dynamic Traffic Assignment in Networks. In: Breakdown in Traffic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54473-0_13

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