## 2 Description of Highway Vehicle Clustering
### Analysis of Vehicle Mobility in Heterogeneous Traffic Flow  
The Poisson distribution is suitable for low-density traffic flow scenarios where external interference factors are essentially absent and vehicle arrivals occur randomly [33]. Figure 1: Highway V2X communications network diagram. Therefore, based on the low density and randomness of highways, it is assumed that the number of vehicles from the heterogeneous traffic flow arriving near an RSU follows a Poisson distribution, and the CAV permeability is \(p\); then, the probability of \(n\) vehicles arriving on a highway segment with a length of \(L\) can be expressed as follows:  
\[P_{n}=\frac{(\lambda L)^{n}}{n!}e^{-\lambda L},n=0,1,2,\ldots. \tag{1}\]  
In Equation (1), \(\lambda\) represents the traffic flow density of the heterogeneous traffic. Then the CAV vehicle density \(\lambda^{\prime}=\lambda p\), the average number of CAV vehicle nodes \(N\) can be calculated as \(N=L\lambda\), and the number of CAV vehicle nodes \(N^{\prime}=L\lambda p=L\lambda^{\prime}\). Drivers generally keep their vehicle speeds close to the speed limit on highways. Therefore, we can assume that the vehicle speeds are the same, and the distance \(x\) between vehicles in mixed traffic flows follows an exponential distribution. Since vehicle-to-vehicle communication is carried out between intelligent connected vehicles, the distance \(x^{\prime}\) between these vehicles follows an exponential distribution:  
\[f(x^{\prime})=\lambda^{\prime}e^{-\lambda^{\prime}x}=\lambda pe^{-\lambda x^{ \prime}} \tag{2}\]  
Since the communication range of vehicles is much larger than the width of a lane, the influence of lane width on the system analysis can be neglected. We assume that the vehicle communication range is circular with a communication radius of \(R\); therefore, the probability of vehicles being able to communicate is given by the condition that the distance \(x^{\prime}\) between intelligent connected vehicles is smaller than the vehicle communication radius \(R\), that is, \(x^{\prime}<R\), expressed as follows:  
\[P(x^{\prime}<R)=\int\limits_{0}^{R}f(x^{\prime})dx^{\prime}=1-e^{-\lambda pR} \tag{3}\]  
Similarly, when the distance \(x^{\prime}\) between intelligent connected vehicles is greater than the vehicle communication radius \(R\), that is, \(x^{\prime}>R\), the probability of vehicles being unable to communicate can be expressed as follows:  
\[P(x^{\prime}>R)=\int\limits_{R}^{\infty}f(x^{\prime})dx^{\prime}=e^{-\lambda pR} \tag{4}\]  
Since the distance distribution between any two vehicles is independent, the communication can be generated via multi-hop links between two intelligent connected vehicles when the distance \(x^{\prime}\) between them is greater than the vehicle communication radius \(R\). This probability can be expressed as:  
\[P_{h}(x^{\prime}>R)=\int\limits_{R}^{\infty}f(x^{\prime})dx^{\prime}=(1-e^{- \lambda pR})^{h} \tag{5}\]  
In Equation (5), \(h\) represents the number of hops required for vehicle-to-vehicle communication within the cluster. After vehicles gather into clusters near the RSU, the length of the vehicle cluster can be determined by counting the number of vehicle intervals within the cluster where the distance between adjacent vehicles is less than the vehicle communication radius. Suppose there is a cluster of intelligent connected vehicles with a permeability of \(p\), and there are \(z\) mixed vehicles within the cluster, then there are \(zp\) intelligent connected vehicles within the cluster, that is, \(n=zp\). The clustering of mixed vehicles implies that the first and last intelligent connected vehicles within the cluster have distances greater than the vehicle communication radius from adjacent intelligent connected vehicles outside the cluster. Additionally, the distances between any two vehicles among the \(n\) intelligent connected vehicles within the cluster are all smaller than the vehicle communication radius.