## 2 Single Conversion Standard Delay Calculation Method
### Single Conversion Standard  
For the mixed traffic flow of buses and cars, when calculating the delays of two vehicles, it is the car that is usually used as the conversion standard, and the buses are converted into cars. According to this method, the total delays of all vehicles are calculated first, and then the delays of two vehicles are calculated simultaneously according to the ratio of the number of cars to the number of buses after conversion. The specific calculation process is as follows.  
1. Taking the car as the conversion standard, convert the bus into a car to determine the input parameters of the total delay calculation, and calculate the total delay of all vehicles. The input parameters for the total delay calculation take the following values.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Definition** \\ \hline \(l\) & Adjacent intersection spacing (m) \\ \(C\) & Intersection common signal period (s) \\ \(\lambda^{m}\) & Downstream intersection arterial direction (coordinated control phase) green-signal ratio \\ \(O^{m}\) & Relative phase difference of the downstream intersection to the upstream intersection (s) \\ \({N_{c}}^{m}\) & Number of cars in the direction of the downstream intersection \\ \({N_{b}}^{m}\) & Number of buses in the direction of downstream intersection \\ \({N_{b}}^{m}\) & arterials (vehicles) \\ \({N_{bi}}^{m}\) & Number of vehicles of each bus line in the direction of the downstream intersection artery (vehicles) \\ \({v_{c}}^{m}\) & Speed of the car (m/s) \\ \({v_{bi}}^{m}\) & Speed of each bus line vehicle (m/s) \\ \({v_{bi}}^{m}\) & Speed of all buses (m/s) \\ \(s\) & Saturated flow rate in the direction of the intersection arterial (pcu/hour) \\ \(q^{m}\) & Vehicle arrival rate at downstream intersections (pcu/hour) \\ \(E_{b}\) & Conversion factor for public transport vehicles \\ \hline \end{tabular}
\end{table}
Table 1: Parameter definition.  
The number of vehicles is:  
\[N^{m}=({N_{c}}^{m}+E_{b}\times{N_{b}}^{m}) \tag{1}\]  
The speed is:  
\[v^{m}=\frac{({v_{c}}^{m}\times{N_{c}}^{m}+E_{b}\times{v_{b}}^{m}\times{N_{b}}^{m })}{({N_{c}}^{m}+E_{b}\times{N_{b}}^{m})} \tag{2}\]  
Vehicle arrival rate is derived based on the relationship between the three parameters of traffic flow, as the arterial coordination control is not applicable to intersections with high traffic flow, and there is generally not few vehicles on arterial roads. A single-segment linear relationship model between vehicle density and speed can be used to derive the expression of the relationship between vehicle arrival rate and speed [19], the specific formula is as follows:  
\[q^{m}=k^{m}\times v^{m} \tag{3}\]  
\[k^{m}=k_{jc}\times(1-\frac{v^{m}}{v_{f}}) \tag{4}\]  
\[q^{m}=k_{jc}\times v^{m}\times(1-\frac{v^{m}}{v_{f}}) \tag{5}\]  
where  
\(k^{m}\) is the vehicle density (vehicle/km);  
\(k_{jc}\) is the blocking density of cars (vehicle/km);  
\(v_{f}\) is the free flow velocity (m/s);  
After determining the values of the input parameters, the total delay \(D^{m}\) of all vehicles is calculated by referring to the total delay calculation method in Ref. [1].  
2. Based on the ratio of the number of cars to the converted number of buses, the delays of both vehicles are calculated simultaneously, and thus the average vehicle delay is determined.  
The average car delay is:  
\[{d_{c}}^{m}=\frac{D^{m}}{({N_{c}}^{m}+E_{b}\times{N_{b}}^{m})} \tag{6}\]  
The average bus delay is:  
\[{d_{b}}^{m}=\frac{E_{b}\times D^{m}}{({N_{c}}^{m}+E_{b}\times{N_{b}}^{m})} \tag{7}\]