## 2 Statement of RSU Deployment in Expressway
### Characteristics Analysis of Vehicle Cluster and Information Transmission  
In the vehicle self-organizing network, a large number of intelligent connected vehicles bear the responsibility of network communication as information transmission nodes in the network. Some scholars have carried out a lot of research on the positioning of vehicles in the road network using vehicles as research units [26; 27; 28]. However, due to the fast-moving speed of vehicles, the difficulty of trajectory prediction and the large number of nodes, it is not feasible to study the mobility attributes of vehicles using vehicle nodes as units. Therefore, this paper adopts vehicle clusters as the research object in vehicle self-organizing networks. As a large number of vehicles are divided into clusters in this paper, the vehicles within the same cluster can realize information transmission by single-hop or multi-hop. Since the expressway has the characteristics of relatively small traffic density, fast vehicle speed, relatively fixed driving direction, and easy prediction of driving trajectory, it is suitable to adopt a Poisson distribution. It is assumed that the vehicles arriving near the roadside sensing unit obey the Poisson distribution which means that the probability of the existence of \(\lambda\) vehicles at the average traffic density \(n\) on an expressway of length \(L\) is as in Equation (1):  
\[P(n,L)=\frac{\left(\lambda L\right)^{n}}{n!}\mathrm{e}^{-\lambda L} \tag{1}\]  
The arrival of the vehicle obeys the Poisson distribution and the arrival time interval obeys the exponential distribution. Assuming that the driving speed of the vehicle is the same, it is deduced that the distance \(x\) between vehicles also obeys the exponential distribution, as shown in Equation (2). Assuming that the communication range of intelligent vehicles is a circle with \(R_{\mathrm{p}}\) as the radius, when \(x<R_{\mathrm{p}}\) and \(x>R_{\mathrm{p}}\), the probability of communication and non-communication between vehicles is shown in Equations (3) and (4),respectively. \[f(x)=\lambda e^{-\lambda x} \tag{2}\]  
\[P(x<R_{\mathrm{p}})=\int\limits_{0}^{R_{\mathrm{p}}}f(x)dx=1-e^{-\alpha\lambda R _{\mathrm{p}}} \tag{3}\]  
\[P(x>R_{\mathrm{p}})=\int\limits_{R_{\mathrm{p}}}^{\infty}f(x)dx=e^{-\alpha \lambda R_{\mathrm{p}}} \tag{4}\]  
\(\alpha\) represents permeability. Within the vehicle cluster, each node has access to the information transmitted by the cluster head, therefore, the vehicle cluster length can be calculated by the number of intervals; then, the probability of having \(n\) intervals in the cluster is as in Equation (5). \[P(n)=\left(e^{-\alpha\lambda R_{\mathrm{p}}}\right)^{2}\left(1-e^{-\alpha \lambda R_{\mathrm{p}}}\right)^{n} \tag{5}\]  
Based on the information flow-traffic flow coupling theory, the transmission of information flow in the traffic flow of connected vehicles is divided into two categories, namely instantaneous transmission and ferry transmission. When the distance between two adjacent vehicles is less than or equal to the radius of information transmission, instantaneous transmission will occur and information will be transmitted directly between vehicles through wireless communication. Ferry transmission occurs when the distance between two adjacent vehicles is greater than the information transmission radius, at which time the information will be attached to the vehicle and continue to move along the traffic flow. The speed of information transmission is equal to the speed of the vehicle until the distance between the next transmission target vehicle is equal to the transmission radius; at this point, after completing the ferry transmission, a new round of transmission will begin. In summary, there is a fixed mode of information flow transmission in traffic flow. Each group of information consists of one or more instantaneous transmissions and one ferry transmission.