## 3 Model Hypothesis and Construction
### Model Construction
#### 3.2.3 Bus Companies' Exhaust Emission Costs  
The operation of a bus on a route is roughly divided into two parts: one part is the vehicle traveling at a constant speed between stops and the other part is the process of the vehicle stopping at stops. Researches have indicated that car tailpipe pollutant emissions vary depending on driving conditions. Emissions between stops occur during uniform speed, while emissions during stops are associated with acceleration and deceleration. Here, we only consider the size of vehicle emissions between stations to account for lower during-stop emissions. The primary pollutants from public bus exhaust are CO, NOx, PM, and HC. Impact cost modeling is proposed to estimate vehicle exhaust emissions based on pollutants released from public bus exhaust, allowing for the assessment of the social impact cost of these tailpipe emissions [30]. Equations (8) and (9) can be used to estimate the emission of each type of pollutant from public buses. The emission of each type of pollutant is mostly related to the emission factor, the number of departures, and the length of the route. Buses in a city often operate at a speed of 20 to 30 km/h, hence in this study, \(V_{q}\) is set as 30 km/h. \[Z_{ipp}=\lambda_{i}\cdot EF_{iq}\cdot S\cdot n_{p}\cdot V_{q} \tag{8}\]  
\[Z_{inp}=\lambda_{i}\cdot EF_{iq}\cdot S\cdot n_{np}\cdot V_{q} \tag{9}\]  
Bus tailpipe emissions were estimated based on the bus VSP measurement method [34] after collecting the National IV standard emission data regarding operating conditions [35] for a single-deck, single-engine CNG (compressed natural gas) bus and the vehicle's average traveling speed. The emission factor of each type of pollutant for the vehicle is displayed in Table 2, which is derived from a large number of bus emission data and operating condition data. Table 3 displays the weighting factors for each type of pollutant. The method of determining the weight factor is the expert evaluation method. The importance of each index is evaluated and arranged by experts and then converted into a weight coefficient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Forms of Dispatch** & **NO\({}_{\mathbf{x}}\) (g/km)** & **HC (g/km)** & **CO (g/km)** & **PM (g/km)** \\ \hline Full journey bus & 8.2560 & 2.0996 & 5.3981 & 0.1054 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Emission factors for each pollutant. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Pollutant Type** & **Weighting Factor** & **Value** \\ \hline NO\({}_{\mathbf{x}}\) & \(\lambda_{1}\) & 0.3 \\ HC & \(\lambda_{2}\) & 0.1 \\ CO & \(\lambda_{3}\) & 0.3 \\ PM & \(\lambda_{4}\) & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Weighting factors for each type of pollutant. The total cost of tailpipe emissions is:  
\[C_{ep}=\sum_{i=1}^{4}u_{i}Z_{ipp} \tag{10}\]  
\[C_{emp}=\sum_{i=1}^{4}u_{i}Z_{inp} \tag{11}\]  
The World Resources Institute provided a methodological guide for estimating transportation emission inventories and their corresponding social costs in the \"Assessment of Transportation Emission Inventories and Corresponding Social Costs\" project study [36]. The guide covers pollutants and greenhouse gases emitted by 18 different transportation modes. It is designed for use in developing nations and cities with limited statistical systems and poor data availability and quality. According to the guideline, social costs refer to the external expenses linked to transportation emissions, primarily focusing on their effects on public health. The initial assessment of social costs involves utilizing knowledge from various sources such as models, surveys, epidemiology, statistics, and socio-economic analysis, employing IPA (Importance and Performance Analysis) as the framework and adopting a top-down approach through meta-analysis of social impact costs.