# The Impact of Automated Vehicles on Road and Intersection Capacity
## 2 Methods  
### U.S. Highway Capacity Manual Method  
There are many calculation methods of traffic capacity at home and abroad, and the principles of each are quite different. Among them, the most widely used is the U.S. HCM method [26; 27; 28]. For the calculation of capacity at signal-controlled intersections, the American HCM method is obtained by reducing the basic saturated flow rate. Basic saturated flow rate refers to the maximum road traffic flow at the entrance of an intersection, under the conditions of good weather, good road condition, traffic flow consisting only of cars, and good visual distance of drivers, generally using 1800 pcu/h. When using this method, the basic saturation flow rate is selected first. Then, it is reduced, in order to obtain the revised saturated flow rate of each lane, as shown in Formula (1). Then the traffic capacity of each lane is calculated using the green signal ratio, as shown in Formulas (2) and (3). Finally, the total capacity of signal-controlled intersections can be obtained by summing the capacity of each inlet lane. \[S_{i}=S_{0}\times N\times f_{w}\times f_{HV}\times f_{g}\times f_{p}\times f_{ bb}\times f_{a}\times f_{LI}\times f_{LT}\times f_{RT}\times f_{Lpb}\times f_{Rpb}, \tag{1}\]  
where \(S_{i}\) is the lane group \(i\) saturation flow rate, \(S_{0}\) is the saturation flow rate of the lane group under ideal conditions (the basic saturation flow rate), \(N\) is the number of lanes in this lane group, \(f_{w}\) is the lane width correction factor, and \(f_{HV}\) is the heavy vehicle correction factor, which satisfies the following formula: \(f_{HV}=\frac{1}{1+P_{T}(E_{T}-1)}\), where \(P_{T}\) is the proportion of heavy vehicles, \(E_{T}\) is the passenger car equivalent value of heavy vehicles, \(f_{g}\) is the approach slope correction factor, \(f_{p}\) is the parking in the adjacent lane and the correction factor for the number of stops in that lane (i.e., it illustrates the impact of parking on the nearby lanes and the occasional blocking effect of traffic access to the adjacent lanes), \(f_{bb}\) is the correction factor for the effect of obstruction within the intersection where the bus is parked (i.e., the impacts of having the bus stop located before the intersection and after the intersection are illustrated), \(f_{a}\) is the area type correction factor in the business district, and \(f_{LU}\) is the lane utilization correction factor (lane utilization correction mainly considers the uneven distribution of traffic volume in several lanes of a certain lane group with multiple lanes). The correction coefficient mainly considers the highest flow lane, where: \(f_{LT}\) is the lane group left turn correction factor, in situations where there is a special phase for left turns and a special lane; \(f_{RT}\) is the lane group right turn correction factor; special lane \(f_{RT}=0.85\); shared lane \(f_{RT}=1.0-0.5P_{RT}\); single lane \(f_{RT}=1.0-0.135P_{RT}\); \(P_{RT}\) is the right turn ratio; \(f_{Lpb}\) is the correction factor for left-turning pedestrians; and \(f_{Rpb}\) is the correction factor for right turns of pedestrians and bicycles. \[C_{i}=S_{i}\lambda_{i}, \tag{2}\]  
\[\lambda_{i}=\frac{g_{i}}{T}, \tag{3}\]  
where \(C_{i}\) is the capacity of lane group \(i\); \(\lambda_{i}\) is the green ratio of the lane group \(i\) (it refers to the proportional time that traffic lights can be used for vehicles to pass within a cycle, that is, the ratio of the effective green time of a certain phase, to the duration of the cycle); and \(g_{i}\) is the effective green time of lane group \(i\), i.e., the effective green time of this phase is the time actually used for vehicle passing, after subtracting the total loss time of this phase from the sum of the actual green time and interval time displayed at a certain phase. The effective green time of a cycle is defined as the cycle time minus the total loss time within the cycle. \(T\) is the signal period length.