Traffic jams: dynamics and control

Abstract

This introductory paper reviews the current state-of-the-art scientific methods used for modelling, analysing and controlling the dynamics of vehicular traffic. Possible mechanisms underlying traffic jam formation and propagation are presented from a dynamical viewpoint. Stable and unstable motions are described that may give the skeleton of traffic dynamics, and the effects of driver behaviour are emphasized in determining the emergent state in a vehicular system. At appropriate points, references are provided to the papers published in the corresponding Theme Issue.Keywords: vehicular traffic; congestion; stop-and-go waves; Hopf bifurcation; driver reaction time; unstable waves I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, 'How many arbitrary parameters did you use for your calculations?' I thought for a moment about our cut-off procedures and said, 'Four'. He said, 'I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk '. (Dyson 2004, p. 297) Background and challengesThe introduction of the assembly line in the automotive industry about a century ago allowed the mass production of automobiles, which, in turn, revolutionized land transportation. At the same time, a problem was also generated that has not yet been resolved: traffic congestion. Since then, researchers from many different disciplines (mathematics, physics and engineering) have targeted this problem, *Author for correspondence (gabor@engineering.ucsb.edu).One contribution of 10 to a Theme Issue 'Traffic jams: dynamics and control'.This journal is © 2010 The Royal Society 4455 on May 10, 2018 http://rsta.royalsocietypublishing.org/ Downloaded from 4456 G. Orosz et al. often using sophisticated mathematical tools brought from their own area of expertise. Also, analogies between traffic flow and other flows (fluid flow, gas flow and granular flow) were established. Although such analogies may help scientists to gain understanding of vehicular systems, it is becoming more and more obvious that traffic flows like no other flow in the Newtonian universe.To date, a vast number of different models have been constructed, but still no first principles have been established to guide the modelling procedure (if such principles exist at all). In many cases, authors claimed that the developed model described traffic better than models prior to that point, and such claims were often justified by fitting the models to empirical data. The quote at the beginning of this paper tries to illustrate, without questioning the importance of any specific model, that the above approach may easily lead to research capturing, but also missing, some essential characteristics. We believe that another way to conduct research in traffic can be by studying general classes of models and classifying their qualitative dynamical features (including 'hidden' unstable motions) when varying model parameters. To...

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“…2(b). Note that other control strategies also exist; see Orosz et al (2010) for more details. When v L ≤ v max , the system (1,2) with control law (5) possesses the uniform flow equilibrium…”

“…The fact that human drivers have large reaction times (0.5 − 1 [s]) and that they are only able to monitor the motion of the vehicle immediately in front makes it difficult to attenuate congestion waves traveling upstream. This so-called string instability was introduced in Swaroop and Hedrick (1996) and it typically leads to the formation of stop-and-go traffic jams as shown in Orosz et al (2010).…”

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“…For the OVM with delays, [18] performed an initial numerical study of the bifurcation phenomenon before supplying an analytical proof in [9]. The theme issue on "Traffic jams: dynamics and control" [19] highlights the growing interest in a dynamical systems viewpoint of transportation networks. A recent exposition of linear stability analysis in the context of car-following models can be found in [20].…”

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“…Similarly, the nervous system of humans is subjected to delay [3,4,5], which affects balancing abilities and may cause movement disorders. Reflex delay of the human nervous system is the main reason for the development of stop-and-go traffic jams [6,7]. Time delay also plays an important role in contact problems such as the "shimmy motion" of wheels [8].…”