Macroscopic traffic models from microscopic car-following models

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a momentum equation, and the latter contains a relaxation term, an anticipation term, and a diffusion term. Properties of the resulting macroscopic model are compared with those of the optimal velocity model through numerical simulations, and reasonable agreement is found although there are deviations in the quantitative level. The derivation is also extended to general car-following models.Comment: 12 pages, 4 figures; to appear in Phys. Rev.

Offline reconstruction of missing vehicle trajectory data from 3D LIDAR

LIDAR has become an important part of many autonomous vehicles with its advantages on distance measurement and obstacle detection. LIDAR produces point clouds which have important information about surrounding environment. In this paper, we collected trajectory data on a two lane urban road using a Velodyne VLP-16 Lidar. Due to dynamic nature of data collection and limited range of the sensor, some of these trajectories have missing points or gaps. In this paper, we propose a novel method for recovery of missing vehicle trajectory data points using microscopic traffic flow models. While short gaps (less than 5 seconds) can be recovered with simple linear regression, and longer gaps are recovered with the proposed method that makes use of car following models calibrated by assigning weights to known points based on proximity to the gaps. Newell's, Pipes, IDM and Gipps' car following models are calibrated and tested with the ground truth trajectory data from LIDAR and NGSIM I-80 dataset. Gipps' calibrated model yielded the best result