# The Car-Following Model and Its Applications in the V2X Environment: A Historical Review
## 3 Research on Car-Following Behavior in the V2X Environment
### Applications of the Car-Following Models
#### 3.3.3 Evaluating Energy Consumption and Emission  
It is very hard to directly measure the energy consumption and emission of the transportation system. Thus, the energy consumption and emission were usually estimated based on the car-following and evaluating model along with the numerical simulation approach in previous works. According to vehicle dynamics theory, the energy consumption and emission of the vehicle are determined by the acceleration and its changing rate. Most of the car-following models essentially calculate the object vehicle's acceleration, and are marked as second-order models. The non-second-order models can be derived into the second-order form based on the differential or integral approach. Based on these second-order models, the energy consumption and emission can be conveniently estimated through numerical methods. [PERSON] et al. proposed a model for estimating vehicle energy consumption and its emission [142], and the equation is as follows:  
\[\ln(MOE_{e})=\sum_{i=0}^{3}\sum_{j=0}^{3}\left[K_{i,j}^{e}\times v^{i}\times \left(\frac{dv}{dt}\right)^{j}\right] \tag{2}\]  
where the \(MOE_{e}\) is the instantaneous rate of energy consumption or emission of the vehicle \(n\); \(i\) is the velocity power of the vehicle \(n\); \(j\) is the acceleration power of the vehicle \(n\); and \(K_{i,j}^{e}\) is the regression coefficient. Applying different values of the regression coefficient, Equation (2) can be used to estimate the energy consumption or emission of CO/HC/NO\({}_{\rm x}\). The values of \(K_{i,j}^{e}\) to estimate the above items are given in [142]. This estimation model has been widely used to estimate the energy consumption and emission of vehicles controlled by various car-following models. Among these approaches, [PERSON] and his team contributed much. Based on the field driving experiments conducted with vehicles equipped with the ACC system, [PERSON] et al. explored the fuel consumption and emission characteristics of vehicles with consideration of the headway fluctuation, utilizing [PERSON]'s method and the extended car-following models proposed by themselves [88]. Later, [PERSON] et al. analyzed the fuel consumption and emission characteristics of vehicles affected by the velocity fluctuation of the preceding vehicle with different lengths of time window [143]. In the same period, [PERSON] et al. further analyzed the impacts of relative velocity fluctuation information on the fuel consumption and emission characteristics of vehicles [144]. On the basis of the aforementioned research, [PERSON] et al. discussed the fuel consumption and emission characteristics of vehicles affected by the relative velocity fluctuation information of multiple preceding vehicles equipped with the CACC system [145]. [PERSON] et al. also explored the impacts of headway fluctuation on fuel consumption and emission from a different perspective [90]. Then, [PERSON] et al. analyzed the impacts of relative velocity and its fluctuation on fuel consumption and emission [89]. Besides the above works based on the ACC or CACC systems, [PERSON] et al. explored the impacts of information about traffic accidents that occurred downstream on fuel consumption and emission based on their extended car-following model [20]. [PERSON] et al. also analyzed the impacts of information about the remaining time of green light in the signalized intersection on the fuel consumption and emission of the vehicles approaching the intersection based on their extended car-following model [30]. Later, [PERSON] et al. discussed the fuel consumption and emission characteristics affected by the information about ETOA of multiple preceding vehicles [68]. Based on the extended car-following model, [PERSON] et al. explored the impacts of driver's characteristics on fuel consumption and emission [146]. Recently, [PERSON] et al. discussed the fuel consumption and emission characteristics of a Connected and Automated Vehicle (CAV) based on the improved car-following model for the CAV [147].