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Failure of Generally Accepted Classical Traffic Flow Theories

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Breakdown in Traffic Networks

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Abstract

Traffic researchers have developed a huge number of traffic theories for optimization and control of traffic and transportation networks. In particular, to generally accepted fundamentals and methodologies of traffic and transportation theory belong to the Lighthill-Whitham-Richards (LWR) model and the General Motors (GM) model class. These classical theories explain many real traffic flow phenomena. In this Chapter, we show that although these classical traffic flow models exhibit many important achievements, the classical models are inconsistent with the empirical nucleation nature of traffic breakdown at highway bottlenecks. Because the classical models and theories have failed in the explanation of the empirical fundamental of transportation science, the use of the classical approaches for a study of the reliability of applications of intelligent transportation systems (ITS) leads usually to invalid conclusions for real traffic. Moreover, ITS based on these classical traffic flow theories and models cannot also be used for reliable traffic control and dynamic optimization of traffic and transportation networks.

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Notes

  1. 1.

    There is a huge number of publications devoted to measurements of flow–density (fundamental diagram), speed-density, speed–space-gap, and link-travel-time–flow relationships (see, e.g., a review by Hall in [163]).

  2. 2.

    While propagating though the bottleneck, the wide moving jam can cause a variety of diverse effects of congested pattern formation at the bottleneck found out in 1999–2001 in the models of the GM model class by Helbing, Treiber et al. [222, 507]. This is because the free flow at the bottleneck is in a metastable state with respect to an F → J transition. These diverse effects of congested pattern formation, which are considered in details in papers of Helbing and Treiber et al. [464, 465, 511], in the review by Helbing [213] and the book by Treiber and Kesting [508, 509], are out of scope of the book under consideration. The reason of this is as follows. All the effects of the congested pattern formation at road bottlenecks found with the simulations of the models of the GM model class are associated with the metastability of free flow at the bottleneck with respect to the F → J transition. Contrarily, in real traffic as proven in Chap. 3, rather than the F → J transition, the metastability of free flow at the bottleneck with respect to the F → S transition is responsible for traffic breakdown at a highway bottleneck in real traffic (see Sect. 4.5.1). For this reason, all theoretical results of the congested pattern formation at road bottlenecks found by Helbing, Treiber, Kesting et al. as well as by other authors in many different traffic flow models of the GM model class (see e.g. [206–222, 224–231, 464, 465, 504, 505, 507–509, 511]) are invalid for real traffic. This critical conclusion has been considered in more detailed in Sec. 10.3.10 and 10.3.11 of the book [269] (see also Sects. 4.7,  4.9.1, and 4.11.4 below).

  3. 3.

    Some of the models belonging to the GM model class like the OV model [28–30] and IDM (intelligent driving model) [213, 507–509] have a unique speed–density relationship, whereas the initial GM model of Herman, Montroll, Potts, and Rothery does not have [233]. Rather than a relation between steady speed and density in a model, the common feature of any traffic flow model belonging to the GM model is a free flow instability that causes a growing wave of vehicle speed reduction propagating upstream in traffic flow. Note that to describe traffic beyond of instabilities, Gazis, Herman and Rothery made a further development of the GM model in which steady-state solutions lie on a one-dimensional curve in the flow-density plane (fundamental diagram) [171] (see the review by Nagel et al. [380] for more details).

  4. 4.

    Empirical characteristic parameters of wide moving jam propagation will be considered in more details in Sect. 8.3.1

  5. 5.

    In simulations, this broad spread of traffic data is usually associated with different driver behavioral characteristics (heterogeneous flow of different drivers and vehicles) used in a traffic flow model as well as with complex dynamics of moving jams and other dynamic spatiotemporal effects in congested traffic, rather than with steady states of a traffic flow model.

  6. 6.

    Recall that in Sect. 1.12 to distinguish classical traffic flow models from three-phase traffic flow models, we have called traffic flow models in the frameworks of the LWR model, Daganzo’s cell-transmission model, traffic flow models of the GM model class as well as any other traffic flow models that can be considered a combination of these classical approaches to traffic flow modeling as “two-phase traffic flow models”. In other words, in the book the term a two-phase traffic flow model is a synonym of the term a classical traffic flow model and the term a classical traffic flow theory.

  7. 7.

    In the books [268, 269], for two-phase traffic flow models we have used the term traffic flow models in the framework of the “fundamental diagram approach”. We do not use the term the fundamental diagram approach any more. It occurs that the use of the term the fundamental diagram approach leads to confusions for many authors that have begun to work in the framework of the three-phase theory. One of the reasons for this confusion is as follows. As shown in Sec. 12.1 of the book [269], there can be derived three-phase traffic flow models that exhibit a fundamental diagram for steady state model solutions. Therefore, instead of the term the fundamental diagram approach, as mentioned in footnote 6, in this book for classical traffic flow models and theories we use the term two-phase traffic flow models.

  8. 8.

    The exclusion is Chap. 8, in which we will explain why the three-phase theory is incommensurable with classical traffic flow theories.

  9. 9.

    See the explanation of the term two-phase traffic flow model in Sect. 1.12.

  10. 10.

    There are many theoretical works in which rather than a flow-rate drop observed during traffic breakdown at a highway bottleneck (Sect. 2.2.2) as “capacity drop” another flow-rate drop q cr (J) − q out shown in Fig. 4.9 is considered. This application of the term “capacity drop” is incorrect for another reason. To explain this critical statement, we should recall that traffic breakdown occurs at the effective location of a highway bottleneck (see explanations of the effective location of the bottleneck in Sect. 3.4.4). In Fig. 4.9, free flow states together with the line J that characterizes some features of wide moving jams have been presented. As explained in details in Sec. 15.4 of the book [268], rather than traffic breakdown at the bottleneck, the free flow states together with the line J shown in Fig. 4.9 explain the Koshi’s reverse-λ fundamental diagram found by Koshi et al. in empirical data [298]. In Sec. 15.4 of the book [268], it has also been shown that the Koshi’s reverse-λ fundamental diagram can be measured at road locations at which wide moving jams have already been formed within a congested pattern localized at a highway bottleneck. The road locations are several kilometers upstream of the effective bottleneck location at which traffic breakdown has initially occurred. In the empirical example of a congested pattern shown in Fig. 4.2a, these road locations at which the Koshi’s reverse-λ fundamental diagram can be measured (locations x = 0 and x = 1. 5 km in Fig. 4.2b) are about 5 km upstream of the effective location of the bottleneck at which traffic breakdown has been observed (location x = 6. 4 km in Fig. 4.2b). Thus, the flow-rate drop between the maximum flow rate that is reachable in free flow and the outflow rate in the wide moving jam outflow (Figs. 4.2b (x = 0 and x = 1. 5 km) and 4.9) has in general no relation to a flow-rate drop observed [33, 191] during traffic breakdown at the effective location of traffic breakdown at a highway bottleneck (Sect. 2.2.2).

  11. 11.

    This can be seen on Fig. 7.7 (b, c) of the book [269] in which the same empirical data as that studied in [464, 465] have been presented.

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    Boris S. Kerner

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Kerner, B.S. (2017). Failure of Generally Accepted Classical Traffic Flow Theories. In: Breakdown in Traffic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54473-0_4

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