## 3 Multi-Conversion Standard Delay Calculation Method
### By-Vehicle Type  
The characteristics of buses and cars differ greatly, resulting in different arrival and departure situations of the two types of vehicles at downstream intersections, and the  
Figure 1: Average speed of cars and buses during peak hours in Shenzhen from 2011 to 2019.  
Figure 2: Number of bus stops per kilometer included in arterial roads.  
generations of delays are different. Therefore, this paper regards buses and cars as two fleets and proposes a delay calculation method with multiple conversion standards. On the basis of considering the impact of mixed vehicles, the delays of the two types of vehicles are calculated separately.  
When calculating the delay of cars, buses are converted into cars, considering their influence, and the arrival rate of vehicles at downstream intersections is calculated first. As the distribution of buses and cars in mixed traffic is relatively uniform, then the arrival rate and maximum departure rate of cars at downstream intersections are calculated based on the ratio of the number of input cars to the total number of converted cars. Finally, car delays are calculated.  
When calculating bus delays, cars are converted into buses, considering their influence, and the vehicle arrival rate of downstream intersections is first calculated. Then, the bus arrival rate and maximum departure rate of downstream intersections are calculated based on the ratio of the number of input buses to the total number of converted buses. Finally, bus delays are calculated.  
The detailed processes for calculating the delays of the two vehicles are as follows.  
1. Calculate the average car delay 1 Taking the car as the conversion standard, buses are converted into cars to calculate the vehicle arrival rate \(q^{m}\).  
\[v^{m}=\frac{({v_{c}}^{m}\times{N_{c}}^{m}+{E_{b}}\times{v_{b}}^{m}\times{N_{b}} ^{m})}{({N_{c}}^{m}+{E_{b}}\times{N_{b}}^{m})} \tag{8}\]  
\[q^{m}={k_{jc}}\times{v^{m}}\times(1-\frac{v^{m}}{v_{f}}) \tag{9}\]
2. Calculate the arrival rate and maximum departure rate of cars based on the ratio of the input number of cars entered to the total number of cars converted.  
The car arrival rate is:  
\[{q_{c}}^{m}=q^{m}\times\frac{{N_{c}}^{m}}{{N_{c}}^{m}+{E_{b}}\times{N_{b}}^{m}} \tag{10}\]  
The maximum car departure rate is:  
\[{s_{c}}^{m}=s\times\frac{{N_{c}}^{m}}{{N_{c}}^{m}+{E_{b}}\times{N_{b}}^{m}} \tag{11}\]
3. Taking the number of cars \({N_{c}}^{m}\), speed \({v_{c}}^{m}\), arrival rate \({q_{c}}^{m}\), and maximum departure rate \({s_{c}}^{m}\) as input parameters, the total delay of cars \({D_{c}}^{m}\) is calculated, and then the average delay of cars \({d_{c}}^{m}\) is obtained.  
\[{d_{c}}^{m}=\frac{{D_{c}}^{m}}{{N_{c}}^{m}} \tag{12}\]
2. Calculate the average bus delay 1 Taking the bus as the conversion standard, cars are converted into buses to calculate the vehicle arrival rate \(q^{m}\).  
\[v^{m}=\frac{({v_{c}}^{m}\times\frac{{N_{c}}^{m}}{{E_{b}}}+{v_{b}}^{m}\times{N_ {b}}^{m})}{(\frac{{N_{c}}^{m}}{{E_{b}}}+{N_{b}}^{m})} \tag{13}\]  
\[q^{m}={k_{jb}}\times{v^{m}}\times(1-\frac{v^{m}}{v_{f}}) \tag{14}\]
2. Calculate the arrival and maximum departure rates of buses based on the ratio of the number of buses entered to the total number of buses converted.  
The bus arrival rate is:  
\[{q_{b}}^{m}=q^{m}\times\frac{{N_{b}}^{m}}{\frac{{N_{b}}^{m}}{{E_{b}}}+{N_{b}}^{m}} \tag{15}\]  
The maximum bus departure rate is:  
\[{s_{b}}^{m}=s\times\frac{{N_{b}}^{m}}{\frac{{N_{c}}^{m}}{{E_{b}}}+{N_{b}}^{m}} \tag{16}\]  
3 Taking the number of bus vehicles \({N_{b}}^{m}\), speed \({v_{b}}^{m}\), arrival rate \({q_{b}}^{m}\), and maximum departure rate \({s_{b}}^{m}\) as input parameters, the total delay of buses delay \({D_{b}}^{m}\) is calculated, and then the average delay of buses \({d_{b}}^{m}\) is obtained.  
\[{d_{b}}^{m}=\frac{{D_{b}}^{m}}{{N_{b}}^{m}} \tag{17}\]