# Performance Analysis of Internet of Vehicles Mesh Networks Based on Actual Switch Models
## 3 Network Architecture and System Model
### Network Model  
In order to analyze network performance, this subsection constructs the IoV mesh network dynamic topology. Since the topology depends on link construction, the IoV mesh network channel model is initially established by abstracting the network architecture into a mathematical model. The scenario involves multiple vehicles and RSUs distributed at an intersection with bi-directional traffic flow. To determine the boundaries of the network model, we refer to the urban case described in 3 GPP TR 36.885 [31]. The size of the four grids included is 866 m \(\times\) 500 m, which has four lanes (two lanes in both forward and reverse directions), and the lane width is 3.5 m. The scenario model diagram is shown in Figure 2.  
To facilitate the modeling, a spatial right-angled coordinate system is established with the center of the road as the coordinate origin, the _xoy_ plane parallel to the ground, and the z-axis perpendicular to the ground. \(U=\{u_{1},\cdots,u_{p}\}\) is defined as the set of vehicles and \(S=\{s_{1},\cdots,s_{q}\}\) represents the set of RSUs, where \(p\) is the total number of vehicles and \(q\) is the total number of RSUs. The IoV mesh network model is shown in Figure 3.  
Figure 3: IoV mesh network model. Figure 2: Simulation scenario. \((x_{i},y_{i},z_{i})\) and \((x_{j},y_{j},z_{j})\) are the coordinates of any two nodes \(i\) and \(j\) in the network, respectively. Therefore, the Euclidean distance \(d_{ij}\) between any two nodes at moment \(t\) can be given by:  
\[d_{ij}(t)=\sqrt{\left(x_{i}(t)-x_{j}(t)\right)^{2}+\left(y_{i}(t)-y_{j}(t) \right)^{2}+\left(z_{i}(t)-z_{j}(t)\right)^{2}} \tag{1}\]  
According to the destination, the network has two ways of transmitting data, which are V2I and V2V. When V2V communication is performed, based on existing communication protocols, each vehicle can exchange information with other vehicles located within its maximum access range denoted by \(D\). From this, the condition that defines the existence of a link between vehicles is shown below, where \(g_{ij}(t)=1\) indicates that the link is connected and, vice versa, interrupted. \[g_{ij}^{v22v}(t)=\left\{ \begin{array}{ll}1,&d_{ij}^{v2v}(t)\leq D_{j}\\ 0,&otherwise\end{array} \right. \tag{2}\]  
Therefore, the link capacity at moment \(t\) is shown below, where \(B_{ij}^{v2v}\) and \(h_{ij}^{v2v}\) are the channel bandwidth and the channel gain between vehicle \(i\) and vehicle \(j\), respectively, and \(\sigma^{2}\) denotes the background noise power. Moreover, \(P_{i}^{v2v}\) denotes the transmit power of vehicle \(i\), and \(A_{0}=-17.8\) dB is a constant parameter. \[R_{ij}^{v2v}(t)=g_{ij}^{v2v}(t)\cdot B_{ij}^{v2v}\text{log}_{2}(1+\frac{P_{i}^ {v2v}\cdot h_{ij}^{v2v}}{\sigma^{2}+A_{0}(d_{ij}^{v2v}(t))^{-2}}) \tag{3}\]  
Similarly, when V2I communication is performed, each RSU can exchange information with vehicles located within its maximum access range. Assuming that the network has been pre-allocated with orthogonal spectrum resources and there is no interference, at this time, the link capacity at moment \(t\) of V2I is shown in Equation (4). \(B_{ij}^{v2I}\) and \(h_{ij}^{v2I}\) are the channel bandwidth and the channel gain between vehicle \(i\) and RSU \(j\), respectively [32]. \[R_{ij}^{v2I}(t)=g_{ij}^{v2I}(t)\cdot B_{ij}^{v2I}\text{log}_{2}(1+\frac{P_{i}^ {v2I}\cdot h_{ij}^{v2I}}{\sigma^{2}}) \tag{4}\]  
Since this paper focuses on network traffic analysis, assuming all vehicles move in a uniform linear motion for modeling simplicity. A given time interval \(T\) is divided into \(n\) time slots, and the length of the time slot is \(\Delta t=T/n\). The network topology remains unchanged within each time slot. However, as vehicles move, connections between vehicles, in different time slots change. The weighted adjacency matrix of the network of the \(k\) th time slot is defined by Equation (5), where \(\pi_{ij}^{k}\) represents the link rate. \(\pi_{ij}^{k}=0\) indicates not connectivity.