# Vehicle Delay Model Applied to Dynamic and Static Traffic Impact Analysis of Large Parking Lots
## 2 Establishment of Vehicle Delay Model
### Establishment of Delay Model
#### 2.2.1 Delay Model of Arriving Vehicle  
The driving process of vehicles arriving at the parking lot is as follows. First, the vehicle waits for an acceptable gap from the second lane to decelerate into the entrance channel or decelerates from the first lane to enter the entrance channel, and then the vehicle decelerates in front of the gate and stops, waiting for the rod to be lifted and accelerated through. The delay of arriving vehicles is shown in Figure 1.  
It can be seen from the above driving process that the delay of arriving vehicles mainly includes the following. (1) Fixed delay \(d_{af}\). It is the acceleration and deceleration delays caused by the geometric size of the entrance channel and the channelization method at the connection between the entrance and the connecting road. Figure 1: Delay of Arriving Vehicles. (2) Delay of entrance gates \(d_{ag}\). It is the acceleration, deceleration, and queue delay when passing through the parking lot gate. Because the entrance and exit of the parking lot is a single channel queuing system, the M/M/1 queuing model is adopted. According to the model [16], it can be deduced that the time of vehicles in the queuing system is the average delay time of vehicles, as shown in Equation (1). \[d_{ag}=\frac{1}{\mu_{a}-q_{a}}\times 3600 \tag{1}\]  
where \(d_{a}\) is the average delay of vehicles arriving at the parking lot, and \(q_{a}\) is the number of vehicles arriving at the parking lot, and \(\mu_{a}\) is the service rate of the entrance gate. (3) Delay of second lane vehicles entering the parking lot \(d_{a2c}\). It is the acceleration and deceleration delay and queuing delay caused by vehicles in the second lane (starting from the right) passing through the first lane (close to the entrance channel) to enter the entrance channel. The first lane is regarded as the main road and the second lane is regarded as the secondary road. Only when the headway of the vehicles on the main road is greater than the critical gap, the vehicles on the secondary road are allowed to enter the conflict area. Based on the above assumptions, [PERSON] [17] gave a formula for calculating the average delay of secondary road vehicles. Since the capacity of the second lane is affected by the width of the first lane, the geometric characteristics of the entrance, and other factors, it is necessary to correct the capacity of vehicles in the second lane when crossing the first lane. Finally, the average delay of vehicles in the second lane when entering the parking lot can be obtained. As shown in Equation (2). \[d_{a2c}=3600\times\frac{1-e^{-(((q_{\tau 1}+q_{a1})t_{a2c}+q_{a2}t_{a2f})/3600)}}{360 0\times q_{a2c}\times\frac{1}{t_{a2f}}e^{-((q_{\tau 1}+q_{a1})t_{a2c}/3600)}-q_{a2}} \tag{2}\]  
where \(d_{a2c}\) is the average delay of vehicles entering the parking lot in the second lane, and \(q_{a1}\) is the number of vehicles entering the parking lot in the first lane, and \(q_{a2c}\) is the number of vehicles entering the parking lot in the second lane, and \(q_{\tau 1}\) is the traffic volume of the first lane, and \(t_{a2c}\) is the critical gap for arriving vehicles in the second lane, and \(t_{a2f}\) is the following time of the arriving vehicle in the second lane, and \(q_{a2c}\) is the correction factor for the capacity of vehicles in the second lane when crossing the first lane. Therefore, the average delay of arriving vehicles in the parking lot is shown in Equation (3). \[d_{a}=\left\{ \begin{array}{c}d_{af}+d_{ag}+\frac{q_{a2}}{q_{a}}\times d_{a2c },n\geq 2\\ d_{af}+d_{ag},n=1\end{array} \right.