A car-following model with real-time road conditions and numerical tests
Introduction
To date, car-following behaviors have significantly influenced traffic performance (e.g., congestion, jam), safety, fuel consumption and exhaust emissions and attracted researchers to propose various traffic flow models to study the complex traffic phenomena [1], [2], [3].
As for traffic performance, researchers proposed many car-following models to study the traffic situations (where the following vehicle reacts to its leading vehicle’s actions) and found that studying driving behavior can help us understand the formation mechanisms, evolution laws and propagation properties of the micro traffic phenomena (e.g., stop-and-go, congestion, etc.) [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. As for traffic safety, each driver should consider the safety factors in car-following model to avoid collision, so researchers have been attracted to explore the relationship between traffic safety and driving behavior. For example, researchers found that rear-end collision is one of the most frequently occurring types of collision [20], [21], [22]; one quarter of all police-reported collisions in US [23] and more than 13% of all casualties from road accidents in Europe [24] are relevant to the rear-end collisions. As for the vehicle’s fuel consumption and exhaust emissions, Ahn and his coauthors [25], [26] applied the testing data to prove that the vehicle’s fuel consumption and exhaust emissions are related to its current velocity and acceleration and developed VT-Micro Model (the Virginia Tech Microscopic energy and emission model); Rakha et al. [27], [28] incorporated the VT-Micro model into the simulation tool INTEGRATION to explore the effects of traffic light on the vehicle’s fuel consumption and emissions; Wu et al. [29] studied the vehicle’s fuel consumption in the mixed traffic system with the human driver and the autonomous vehicle; Tang et al. [30] studied the vehicle’s fuel consumption of car-following models.
The above studies focus on studying the traffic phenomena from the analytical and numerical perspectives, so it is necessary to testify whether the results obtained by the above models are quantitatively accordant with the real traffic phenomena. To explore the real traffic phenomena, Sarvi et al. [31] used empirical data to undertake a comprehensive investigation of traffic behavior and its characteristics in the freeway ramp merging under congested traffic conditions; Ndoguy [32], [33] used observed data to study the flow-density relationship; Castillo [34] constructed three traffic flow models and applied empirical data to calibrate four main parameters; Pei et al. [35] used the GPS data to develop a speed model for traffic flow.
However, the above models cannot be used to explore the effects of road condition on traffic flow since this factor is not explicitly considered. To describe road condition, Delitala and Tosin [36] constructed a discrete velocity model for traffic flow and Bellouquid and Delita [37] extended it and developed a traffic flow model with road condition [38]; Li et al. [39] constructed a car-following model with the driving resistance; Tang et al. [40], [41] developed two traffic flow models to study the influences of road condition on the stability of traffic flow, traffic waves and the starting and braking processes. However, the above models cannot be used to explore the effects of real-time road condition on each vehicle’s driving behavior, fuel consumption and exhaust emissions. In this paper, we propose a new car-following model to explore the impacts of real-time road condition on the vehicle’s driving behavior, fuel consumption and exhaust emissions.
Section snippets
Empirical results
Here, we used electronic loop detectors and digital video cameras to collect the speed-density data on the Weizikeng segment of the Badaling freeway, where the traffic data are the average values during the daytime in June, 2006 and the traffic data of every 5 min are collected as a group (see Fig. 1). From Fig. 1, we find that the average speed may be different under the same density due to the real-time road condition which varies with the traffic state and affects the average speed, which
Car-following model accounting for real-time road condition
The existing car-following models can be formulated as follows:where are the nth vehicle’s speed, headway and relative velocity (xn is the nth vehicle’s position), respectively. Eq. (7) shows that the nth vehicle’s acceleration is determined by its own current speed, headway, relative speed and other related factors [18], [19].
However, Eq. (7) and its extensions cannot be directly used to study the impacts of road condition on traffic
Numerical tests
Before exploring the influences of real-time road condition on each vehicle’s velocity, acceleration, headway, fuel consumption and CO, HC, NOX, we should define the numerical scheme of Eq. (9). Eq. (9) has many numerical schemes but the schemes have no qualitative influences on the numerical results, so we here use the Euler difference to discretize Eq. (9), i.e.,where Δt = 0.005s is the time-step length.
First, we explore the
Conclusions
Although many traffic flow models have been developed to explore various complex traffic behavior (e.g., car-following, lane-changing, etc.), little effort has been made to study the effects of real-time road condition on driving behavior. In this paper, we develop a car-following model to study the effects of real-time road condition on each vehicle’s speed, acceleration, headway, fuel consumption, CO, HC and NOX under uniform flow. Numerical results indicate that the proposed model can
Acknowledgments
This work has been supported by the National Natural Science Foundation of China (71271016) and the National Basic Research Program of China (2012CB725401). The authors would like to thank the four anonymous referees for their helpful comments and valuable suggestions which have improved the paper substantially.
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