Denoising, deconvolving, and decomposing photon observations

Abstract

Attempts to investigate the inherent complexities in traffic have gained more attentions, especially with better quality traffic data available now. In this paper, we report our recent investigation on a large amount of time gap (the time difference between the rear of the leading vehicle and the front of the following vehicle) data. By categorizing time gaps according to traffic conditions (i.e. speeds) and driving conditions (including no-speed-change, acceleration, and deceleration), we studied the uncertainty in drivers' gap selection, which is determined by drivers' perception of selecting a comfortable and safe distance to the front vehicle. As we found, under congested conditions, the average time gaps selected by drivers display little variation when drivers do not accelerate or decelerate; but when drivers are accelerating or decelerating, on average, they choose different time gaps with different speed. We further studied the impact of the uncertainty on the macroscopic traffic variables by considering the road traffic as a stochastic process. We derived a shifted Gamma traffic count distribution to describe the randomness of traffic flow caused by the uncertainty of drivers' gap selection. The count distribution is used to derive the fundamental diagram. We found that the uncertainty of drivers' gap selection partially contributes to the scatter in the FDs. We also found that the shape of the FD changes with driving conditions: the right-hand-side of the FD most likely is a linear line for no-speed-change condition; but it becomes a convex curve when vehicles are accelerating and a concave curve when decelerating. The different capacity values shown in the FDs offer a possible explanation for the " capacity drop " .