## 3 Model Hypothesis and Construction
### Model Construction
#### 3.2.2 Bus Companies' Operating Costs  
Bus companies' operational costs are influenced by a variety of factors, including the cost of hiring drivers and the cost of buying and maintaining buses. In this paper, we only  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Definition** \\ \hline \(K_{np}\) & Number of total nonpeak hours \\ \(K_{p}\) & Number of total peak hours \\ \(T_{p}\) & The length of bus operating time during the \(k\)-th peak hour \\ \(T_{np}\) & The length of bus operating time during the \(k\)-th nonpeak hour \\ \(\mu_{kj}\) & The arrival rate of passengers at the station \(j\) during peak hours \\ \(v_{kj}\) & The arrival rate of passengers at the station \(j\) during nonpeak hours \\ \(J\) & The total number of bus stops along the route \\ \(\Delta t_{p}\) & The interval between bus departures during peak hours \\ \(\Delta t_{np}\) & The interval between bus departures during nonpeak hours \\ \(C_{pp}\) & The total waiting time cost for passengers during peak hours \\ \(C_{pp}\) & The total waiting time cost for passengers during nonpeak hours \\ \(y\) & The amount that passengers are paid per minute, EUR/min \\ \(D_{p}\) & The cost loss weighting factor for passengers waiting for buses during peak hours \\ \(D_{np}\) & The cost loss weighting factor for passengers waiting for buses during nonpeak hours \\ \(n_{p}\) & The departure number during peak hours \\ \(n_{np}\) & The departure number during nonpeak hours \\ \(T_{i}\) & The traveling time of the vehicle in the \(i\) period \\ \(C_{bp}\) & The operating costs of bus companies during peak hours \\ \(C_{php}\) & The operating costs of bus companies during nonpeak hours \\ \(S\) & The total length of the route, km \\ \(m\) & The cost per kilometer on the route, yuan \\ \(Z_{ipp}\) & The mass of pollutant \(i\) emitted from the exhaust of buses during peak hours \\ \(Z_{inp}\) & The mass of pollutant \(i\) emitted from the exhaust of buses during nonpeak hours \\ \(EF_{iq}\) & The emission factor corresponding to pollutant \(i\) emitted by buses, g/km \\ \(\lambda_{i}\) & The weighting factor of pollutant \(i\) emitted by buses \\ \(V_{q}\) & The planned running speed of the vehicle, m/s. \\ \(u_{i}\) & The impact cost of emitted pollutant \(i\), yuan/g \\ \(\alpha_{p}\) & Weighting factor assigned to passenger waiting time cost during peak hours \\ \(\alpha_{np}\) & Weighting factor assigned to public transportation enterprises operating cost during peak hours \\ \(\beta_{p}\) & Weighting factor assigned to public transportation enterprises operating cost during nonpeak hours \\ \(\gamma_{p}\) & Weighting factor assigned to public transportation tailpipe emission cost during peak hours \\ \(\gamma_{np}\) & Weighting factor assigned to public transportation tailpipe emission cost during nonpeak hours \\ \(\omega_{1}\) & Weighting factor assigned to the total cost of the passenger during peak hours \\ \(\omega_{2}\) & Weighting factor assigned to the total cost of the passenger during nonpeak hours \\ \hline \end{tabular}
\end{table}
Table 1: Definition of variables for models.  
take into account the variable costs of buses operating on the entire route [33]. For buses, the cost of gasoline used per kilometer is 4 yuan.  
Equations (4)-(7) are used to determine the overall operating costs of the bus company, as well as the number of departures in a trip cycle.  
\[n_{p}=\frac{T_{i}}{\Delta t_{p}} \tag{4}\]  
\[n_{np}=\frac{T_{i}}{\Delta t_{np}} \tag{5}\]  
\[C_{bp}=\mathrm{S}\times\mathrm{m}\times n_{p} \tag{6}\]  
\[C_{bnp}=\mathrm{S}\times\mathrm{m}\times n_{np} \tag{7}\]