The Uncertainty of Drivers’ Gap Selection and its Impact on the Fundamental Diagram

Abstract

Time gap, defined as the time difference between the departure of the leading vehicle and the arrival of the following at the designated test point, is of great importance for both microscopic and macroscopic traffic modeling. In this paper, we report our recent investigation on a large amount of time gap data. By categorizing time gaps according to traffic conditions (indicated by travel speeds) and driving conditions (including no-speed-change, acceleration, and deceleration), we first 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 out, 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 speeds.We further studied the impact of the uncertainty of drivers’ gap selection 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, and then derived the fundamental diagram (FD) based on the count distribution. We found out that the uncertainty of drivers’ gap selection partially contributes to the scatter in the FD; and 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 FD offer a possible explanation for the “capacity drop”.