Traffic Flow

Simulation of traffic instability on circular road.

Vehicular traffic flow is a fascinating real-world system, in which large-scale features emerge from the collective driving behavior of the individual human agents in the roadway. Of particular interest is the phantom traffic jam phenomenon: in certain density regimes, uniform flow become unstable, and small perturbations amplify into large-scale nonlinear waves, so-called stop-and-go traffic waves, or jamitons (a play on the term soliton).

Compared to a uniform flow of traffic, unsteady flow with traffic waves is less safe (higher accident risk), less economic and ecological (increased fuel consumption and emissions), and frequently also less efficient (decreased total throughput). Our research focuses on (a) developing new and improved traffic models that can capture non-equilibrium features such as phantom jams and jamitons; and (b) devising new methodologies that could disperse or even prevent these undesirable features of traffic flow.

A particular research focus lies on macroscopic second-order traffic models. A macroscopic description models traffic like a fluid, and rather than tracking individual vehicles, it captures the evolution of the traffic density and velocity fields. Such a model framework is warranted when state estimation and prediction on large scales is required, particularly under real-time conditions and with sparse Lagrangian data (GPS sensors). Second-order models generalize the classical first-order Lighthill-Whitham-Richards (LWR) model, and can capture flow heterogeneities, and instabilities and jamitons.

One key technology that can help dissipate or prevent traffic waves is given by autonomous vehicles. In the far future we will have roadways on which all vehicles are self-driving and connected. Our research focuses on the near future, in which a small percentage of vehicles on the road will be autonomous (or have adaptive cruise control systems). We devise methodologies that can leverage the presence of just a few autonomous vehicles to control the whole (human-driver-dominated) flow into a more safe and efficient uniform flow regime.

Second-Order Models and Jamitons

Please visit this specific traffic modeling web site to learn more about how phantom traffic jams and traffic waves are mathematical analogs of detonation waves.

• M. R. Flynn, A. R. Kasimov, J.-C. Nave, R. R. Rosales, B. Seibold
  Self-sustained nonlinear waves in traffic flow
  Phys. Rev. E, Vol. 79, No. 5, 2009, pp. 056113.
• B. Seibold, M. R. Flynn, A. R. Kasimov, R. R. Rosales
  Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
  Netw. Heterog. Media., Vol. 8, No. 3, 2013, pp. 745-772.

Data-Fitted Second-Order Models

• S. Fan, M. Herty, B. Seibold
  Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model
  Netw. Heterog. Media., Vol. 9, No. 2, 2014, pp. 239-268
• S. Fan, B. Seibold
  Data-fitted first-order traffic models and their second-order generalizations: Comparison by trajectory and sensor data
  Transportat. Res. Rec., Vol. 2391, 2013, pp. 32-43.

Traffic Control via Autonomous Vehicles

Experiments show that a few self-driving cars can dramatically improve traffic flow

Images

Related Publications

• B. Seibold, M. R. Flynn, A. R. Kasimov, R. R. Rosales, Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models, Netw. Heterog. Media., Vol. 8, No. 3, 2013, pp. 745-772.
• M. R. Flynn, A. R. Kasimov, J.-C. Nave, R. R. Rosales, B. Seibold, Self-sustained nonlinear waves in traffic flow, Phys. Rev. E, Vol. 79, No. 5, 2009.

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