On the Distribution of Probe Traffic Volume Estimated from Their Footprints

Collecting traffic volume data is a vital but costly piece of transportation engineering and urban planning. In recent years, efforts have been made to estimate traffic volumes using passively collected probe data that contain spatiotemporal information. However, the feasibility and underlying principles of traffic volume estimation based on probe data without pseudonyms have not been examined thoroughly. In this paper, we present the exact distribution of the estimated probe traffic volume passing through a road segment based on probe point data without trajectory reconstruction. The distribution of the estimated probe traffic volume can exhibit multimodality, without necessarily being line-symmetric with respect to the actual probe traffic volume. As more probes are present, the distribution approaches a normal distribution. The conformity of the distribution was demonstrated through numerical and microscopic traffic simulations. Theoretically, with a well-calibrated probe penetration rate, traffic volumes in a road segment can be estimated using probe point data with high precision even at a low probe penetration rate. Furthermore, sometimes there is a local optimum cordon length that maximises estimation precision. The theoretical variance of the estimated probe traffic volume can address heteroscedasticity in the modelling of traffic volume estimates.