Estimation of Link Travel Time Distribution With Limited Traffic Detectors

Motivated by the network tomography, in this paper, we present a novel methodology to estimate link travel time distributions (TTDs) using end-to-end (E2E) measurements detected by the limited traffic detectors at or near the road intersections. As it is not necessary to monitor the traffic in each link, the proposed estimator can be readily implemented in real life. The technical contributions of this paper are as follows: First, we employ the kernel density estimator (KDE) to model link travel times instead of parametric models, e.g., Gaussian distribution. It is able to capture the dynamic of link travel times that vary with the change of road conditions. The model parameters are estimated with the proposed <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula>-shortest path algorithm, <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-means-based algorithm, as well as expectation maximization (EM) algorithm. Second, to reduce the complexity of parameter estimation, we further propose a <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-opt and an <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>-means -based algorithm. Finally, we validate our proposed method using a dataset consisting of 3.0e +07 GPS trajectories collected by the taxicabs in Xi’an, China. With the metrics of Kullback Leibler and Kolmogorov–Smirnov test, the experimental results show that the link TTDs obtained from our proposed model are in excellent agreement with the empirical distributions, provided that ∼ 70% of the intersections are equipped with traffic detectors.