# Characteristic Analysis and Decision Model of Lane-Changing Game for Intelligent Connected Vehicles
## 5 Simulation Results and Analysis  
In this paper, SUMO (Simulation of Urban Mobility) software is used for simulation validation, simulation control, and decision planning of vehicle game strategies through the Traci interface. SUMO is an open-source and microscopic traffic simulation software for road traffic simulation. It was developed mainly by the staff of the Institute for Transportation Systems at the German Aerospace Center. We are using version sumo-1.17.0, which can be obtained in detail at [[https://sumo.dlr.de/docs/index.html](https://sumo.dlr.de/docs/index.html)]([https://sumo.dlr.de/docs/index.html](https://sumo.dlr.de/docs/index.html)) (accessed on 21 June 2023). These vehicles adopt the CACC following model [30] and use quintic polynomials to plan the horizontal and longitudinal lane-change trajectory, The CACC model is based on vehicle-vehicle communication to obtain information about the surrounding vehicles and has the characteristics of accuracy and smaller time delay. The expression of the CACC model is:  
\[e=x_{i-1}-x_{i}-Tv_{i} \tag{21}\]  
\[v_{i}(t)=v_{i}(t-1)+k_{1}e+k_{2}^{\bullet} \tag{22}\]  
\begin{table}
\begin{tabular}{c c c} \hline
**Equalization Point** & \(|\text{[PERSON]}|\) & \(\text{tr}(\text{[PERSON]})\) & **Stability** \\ \hline (0, 0) & \(4\beta(1-\alpha)P_{eff}^{RV}P_{safe}^{LV}\) & \(-2\Big{(}(1-\alpha)P_{safe}^{LV}+\beta P_{eff}^{RV}\Big{)}\) & Stable point \\ (0, 1) & \(4\alpha\beta P_{eff}^{RV}P_{eff}^{LV}\) & \(2\Big{(}\alpha P_{eff}^{LV}+\beta P_{eff}^{RV}\Big{)}\) & Instability point \\ (1, 0) & \(4(1-\alpha)(1-\beta)P_{safe}^{LV}P_{safe}^{RV}\) & \(2(1-\alpha)P_{safe}^{LV}+2(1-\beta)P_{safe}^{RV}\) & Instability point \\ (1, 1) & \(4\alpha(1-\beta)P_{eff}^{LV}P_{safe}^{RV}\) & \(-2\alpha P_{eff}^{LV}-2(1-\beta)P_{safe}^{RV}\) & Stable point \\ \(\left(\frac{P_{eff}^{RV}}{P_{eff}^{RV}+(1/\beta-1)P_{safe}^{RV}}\right)\) & \(-4\frac{\alpha P_{eff}^{LV}P_{safe}^{LV}}{\alpha(1-\alpha)P_{eff}^{LV}+P_{safe} ^{RV}}\) & \(\frac{\beta P_{eff}^{RV}P_{safe}^{RV}}{\beta(1-\beta)P_{eff}^{RV}+P_{safe}^{LV}}\) & 0 & Saddle point \\ \hline \end{tabular}
\end{table}
Table 3: Stability of each equilibrium point.  
where \(e\) is the difference between the actual following distance and the desired distance; \(x_{i}\) is the displacement of the vehicle \(i\); \(v_{i}\) is the velocity of the vehicle \(i\); \(x_{i-1}\) is the displacement of the vehicle \(i-1\); \(T\) is the minimum safe headway time distance; and \(k_{1}\) and \(k_{2}\) are parameters.  
We turn off the default lane-changing model by [PERSON]'s command and plan the lane-changing trajectory by using quintic polynomials. Quintic polynomials can obtain the minimum jerk value to satisfy the constraints and meet the comfort of a lane change. The quintic polynomials are used to plan the horizontal and vertical directions, respectively, and track the trajectory points by [PERSON]'s command to complete the lane-change process. The lane-change trajectory polynomials are:  
\[x(t)=a_{0}t^{5}+a_{1}t^{4}+a_{2}t^{3}+a_{3}t^{2}+a_{4}t+a_{5} \tag{23}\]  
\[y(t)=b_{0}t^{5}+b_{1}t^{4}+b_{2}t^{3}+b_{3}t^{2}+b_{4}t+b_{5} \tag{24}\]  
where \(a_{i}(i=0,1,2,3,4,5)\) is the polynomial coefficient of the longitudinal trajectory; \(b_{i}(i=0,1,2,3,4,5)\) is the polynomial coefficient of the horizontal trajectory; and the trajectory constraints are determined by the constraint of the starting and ending points of the path.  
To elucidate the strategy evolution process of the vehicle lane-change game and to perform simulation validation, the road geometry characteristics and vehicle characteristics data of the intersection of Renmin Road and Yongzhou Road in Qingdao City, Shandong Province, were statistically collected and the main parameter values were set in SUMO software, as shown in Table 4. The decision response time indicates the minimum time from the beginning of the vehicle decision to the completion of the decision behavior, and the meaning of the other parameters can be obtained from the variable names.