# 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
#### 2.2.3 Delay Model of Road Vehicle  
In practice, road vehicles, vehicles leaving the parking lot, and vehicles arriving at the parking lot do not fully follow the principle of main road priority, and road vehicles will also be delayed. The delay of road vehicles can be analyzed according to the number of lanes. The number of lanes refers to the total number of lanes conforming to the right-in and right-out organization mode at the entrance and exit of the parking lot. Through the field investigation of parking lots with more than 300 parking spaces and more than two entrances and exits in Nanjing. The results showed that the entrance and exit connecting roads of the parking lot are mainly two lanes, three lanes, and four lanes on the same side. Because the first and the second lane close to the entrance and exit are often selected for vehicles arriving and leaving the parking lot, the third and the fourth lanes on the same side have less impact on dynamic and static traffic [18; 19; 20; 21]. Therefore, this paper mainly studied the roads with two and three lanes on the same side. In the case of three lanes on the same side, vehicles in the second lane can continue to pass through the third lane by changing lanes, so only vehicles in the first lane will delay. The delays in the first lane are as follows. (1) Delay in the first lane affected by vehicles leaving the parking lot \(d_{r1c}\). \[d_{r1c}=3600\times\frac{1-e^{-((q_{1}!t_{r1c}+q_{r1c}t_{r1 cf})/3600)}}{3600 \times q_{r1c}\times\frac{1}{t_{r1f}}e^{-(q_{1}!t_{r1c}/3600)}-q_{r1}} \tag{7}\]  
where \(d_{r1c}\) is the average delay of vehicles in the first lane affected by vehicles leaving the parking lot, and \(q_{l}\) is the number of vehicles leaving the parking lot, and \(q_{r1c}\) is the number of vehicles in the first lane affected by vehicles leaving the parking lot, and \(t_{r1f}\) is the following time of road vehicles in the first lane, and \(t_{r1 cc}\) is the critical gap between the entry and exit conflict zone of vehicles in the first lane, and \(t_{r1 cf}\) is the following time of vehicles in the first lane entering and exiting the conflict zone, and \(q_{r1c}\) is the capacity correction factor for the first lane entering and exiting the conflict zone. (2) Delay in the first lane affected by passage vehicles of the second lane \(d_{r1r}\)  
\[d_{r1r}=3600\times\frac{1-e^{-((q_{2}!t_{r1c}+q_{r1c}t_{r1 cf})/3600)}}{3600 \times q_{r1r}\times\frac{1}{t_{r1f}}e^{-(q_{2}!t_{r1c}/3600)}-q_{r1}} \tag{8}\]  
where \(d_{r1r}\) is the average delay of vehicles in the first lane affected by the passage vehicles of the second lane, and \(q_{r1}\) is the traffic volume of the first lane, and \(q_{r1r}\) is the number of vehicles in the first lane affected by vehicles in the second lane, and \(q_{\alpha 2}\) is the number of vehicles entering the parking lot in the second lane, and \(t_{r1 rc}\) is the critical gap between the vehicles in the first lane and the conflict zone passed by the vehicles in the second lane, and \(t_{r1 rf}\) is the following time when the vehicle in the first lane enters the conflict zone passed by the vehicle in the second lane, and \(t_{r1f}\) is the following time of road vehicles in the first lane, and \(q_{r1r}\) is the capacity correction factor of the conflict zone between the first lane and the second lane. The delay caused by road vehicles in three lanes on the same side was shown in Figure 3.  
In the case of two lanes on the same side, the vehicles in the first lane are still affected by the vehicles leaving the parking lot and the vehicles passing through the second lane. However, vehicles in the second lane cannot change lanes, so they need to queue up for vehicles in front of the same lane to enter the parking lot, which will lead to queue delays. The queuing delay of the second lane \(d_{r2r}\) is about equal to the average delay of the second lane vehicles entering the parking lot, as shown in Equation (9).