Stochastic Lagrangian Modeling of Traffic Dynamics

This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates.The source of uncertainty in the proposed model is parametric. Specifically, the authors assume that drivers vary in free-flow (desired) speeds, minimum preferred safety distances from their leaders (when stationary), and reaction times. Consequently, uncertainty in the model can be interpreted as capturing heterogeneity in the driver population. It also results in smooth trajectories in a stochastic context, which is in agreement with real-world traffic dynamics and, thereby,overcoming issues with aggressive oscillation typically observed in sample paths of stochastic traffic flow models. A stochastic version of Newells car-following model is utilized. The mean dynamics of the model are presented as the limiting dynamics of an ensemble averaged process as the ensemble size goes to infinity. Covariance dynamics are also presented using a Gaussian approximation of the stochastic system. Numerical examples are provided to illustrate convergence of ensemble averaged process to the mean dynamics, as well as to illustrate the behavior of covariance dynamics. A data assimilation example is also given. Results show that the model can be used to estimate aggregated measures of traffic conditions with reasonable accuracy.

• Supplemental Notes:
  • This paper was sponsored by TRB committee AHB45 Standing Committee on Traffic Flow Theory and Characteristics.
• Authors:
  • Jabari, Saif Eddin
  • Zheng, Fangfang
  • Liu, Henry X
  • Filipovska, Monika
• Conference:
  • Transportation Research Board 97th Annual Meeting
  • Location: Washington DC, United States
  • Date: 2018-1-7 to 2018-1-11
• Date: 2018

Language

• English

Media Info

• Media Type: Digital/other
• Features: Figures; References;
• Pagination: 14p

Subject/Index Terms

• TRT Terms: Car following; Lagrangian functions; Stochastic processes; Traffic flow; Traffic speed; Uncertainty
• Subject Areas: Highways; Operations and Traffic Management; Planning and Forecasting;

Filing Info

• Accession Number: 01660535
• Record Type: Publication
• Report/Paper Numbers: 18-04170
• Files: TRIS, TRB, ATRI
• Created Date: Feb 20 2018 9:29AM