# Biform Game Approach to Strategy Optimization of Autonomous Vehicle Lane Changes on Highway Ramps
## 2 Lane-Change Model for Autonomous Vehicles on Highways
### Analysis of Relevant Parameters
\tag{3}\]  
When the distance between two vehicles is \(\Delta d_{(i-1,i)}>d_{safe}\), the surrounding autonomous vehicles can continue to travel at their current speed without affecting the lane-changing vehicles; when the distance between the two vehicles is \(\Delta d_{(i-1,i)}=d_{safe}\), the distance equals the safe lane-changing distance, and the autonomous vehicles affected by the lane change in the target lane should adjust their speed to improve driving efficiency and provide safe lane-changing space for the lane-changing vehicles, gradually adjusting the speed of each vehicle; and when the distance between the two vehicles is \(\Delta d_{(i-1,i)}<d_{safe}\), the autonomous vehicles affected by the lane change in the target lane should increase their speed to provide safe lane-changing space for the forced lane-changing vehicles and quickly adjust to the traffic flow impact caused by the lane change. Under the influence of lane changes by autonomous vehicles on the target lane, we allocate the speed change values of the lane-changing vehicles, the vehicles ahead, and the vehicles behind, ensuring safe passage through the ramp while adjusting the comfort of the autonomous vehicles and effectively improving driving efficiency. Therefore, the speed update criteria for autonomous vehicles entering the ramp section are as follows [41]:  
1. The vehicles ahead in the target lane \(i-1\)  
The autonomous vehicle \(i-1\) accelerates appropriately at the beginning of the lane change, and after the lane-changing vehicle successfully merges, the speed gradually changes to the optimal speed. The speed changes as follows:  
\[V_{i-1}(t+1)=\left\{ \begin{array}{cl}V_{i-1}(t)+1,&\theta_{0}\leq\theta_{i-1 }\\ V_{i-1}(t),&\theta_{0}>\theta_{i-1}\end{array} \right. \tag{4}\]  
where \(\theta_{0}\) is a random number between (0,1), and \(\theta_{i-1}\) is the probability that the vehicle in the target lane takes acceleration or constant speed measures \(i-1\). 1. The lane-changing vehicle \(i\)  
The lane-changing vehicle adjusts its speed based on the distance to the vehicles in front and behind in the target lane, as described by Equation (5):\[V_{i}(t+1)=\left\{ \begin{array}{ll}\min[V_{i}(t)+1,V_{\max}],&V_{i}(t)<V_{i-1}(t) \\ V_{i}(t),&V_{i}(t)=V_{i-1}(t)\\ \max[V_{i}(t)-1,V_{i-1}(t)],&V_{i}(t)>V_{i-1}(t)\end{array} \right. \tag{5}\]  
When the lane-changing vehicle completes the maneuver, it primarily references the speed and distance provided by the vehicle in front in the target lane to adjust its speed, taking appropriate acceleration, constant speed, or deceleration measures. The speed adjustment of the vehicles behind in the target lane \(\mathrm{i}+1\). Based on the speed and distance of the lane-changing vehicle during the maneuver, the speed adjustment of the vehicles behind in the target lane \(\mathrm{i}+1\) is described by Equation (6):  
\[V_{i+1}(t+1)=\left\{ \begin{array}{ll}\max[V_{i+1}(t)+1,\ V_{\min}],&\theta_{ 0}\leq\theta_{i+1}\\ V_{i+1}(t),&\theta_{0}>\theta_{i+1}\end{array} \right. \tag{6}\]  
where \(\theta_{\mathrm{i}+1}\) is the deceleration probability of the vehicles behind in the target lane \(\mathrm{i}+1\); the first term of the piecewise function indicates that the following vehicle \(\mathrm{i}+1\) takes deceleration measures, and the speed after deceleration does not fall below the minimum driving speed for that segment \(\mathrm{V_{min}}\); and the second term indicates that the vehicle \(\mathrm{i}+1\) maintains its current speed. This study set the rate of change of speed per unit time to 3, which represents the unit change in speed from one moment to the next and can be adjusted according to the actual conditions.