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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We present an advanced interpolation method for estimating smooth spatiotemporal profiles for local highway traffic variables such as flow, speed and density. The method is based on stationary detector data as typically collected by traffic control centres, and may be augmented by floating car data or other traffic information. The resulting profiles display transitions between free and congested traffic in great detail, as well as fine structures such as stop-and-go waves. We establish the accuracy and robustness of the method and demonstrate three potential applications: 1. compensation for gaps in data caused by detector failure; 2. separation of noise from dynamic traffic information; and 3. the fusion of floating car data with stationary detector data.Comment: For more information see http://www.mtreiber.de or http://www.akesting.d

A key qualitative requirement for highway traffic models is the ability to replicate a type of traffic jam popularly referred to as a phantom jam, shock wave or stop-and-go wave. Despite over 50 years of modelling, the precise mechanisms for the generation and propagation of stop-and-go waves and the associated spatio-temporal patterns are in dispute. However, the increasing availability of empirical datasets, such as those collected from motorway incident detection and automatic signalling system (MIDAS) inductance loops in the UK or the next-generation simulation trajectory data (NGSIM) project in the USA, means that we can expect to resolve these questions definitively in the next few years. This paper will survey the essence of the competing explanations of highway traffic pattern formation and introduce and analyse a new mechanism, based on dynamical systems theory and bistability, which can help resolve the conflict.

A nonlinear car-following model is studied with driver reaction time delay by using state-of-the-art numerical continuations techniques. These allow us to unveil the detailed microscopic dynamics as well as to extract macroscopic properties of traffic flow. Parameter domains are determined where the uniform flow equilibrium is stable but sufficiently large excitations may trigger traffic jams. This behavior becomes more robust as the reaction time delay is increased.