# SROR: A Secure and Reliable Opportunistic Routing for VANETs
## 3 System Model and Routing-Related Metrics
### Network Model  
Figure 2 depicts the considered network model, where there are \(N\) vehicles and they are denoted by the set \(\mathcal{N}=\{\theta_{1},\theta_{2},\ldots,\theta_{N}\}\). By means of an On-Board Unit (OBU) that is installed in each vehicle, each vehicle can communicate with adjacent vehicles based on the IEEE 802.11p protocol. We assume that only a small fraction of vehicles are malicious and that they may launch the BHA or GHA. Each vehicle can be a source node, relay node, or destination. If the destination is out of the transmission range of the source node, the source node needs the help of relay node to send packet to the destination. So, multi-hop routing requires multiple relay nodes to participate in. If some relay nodes are malicious, they may launch BHA or GHA, namely deliberately drop packets, resulting in the increase of packet loss ratio, as shown in Figure 1. For example, assume that the \(\theta_{1}\) is a source node, and it needs to transmit a packet toward the relay node \(\theta_{2}\). The arrow represents the direction of transmitting packet. After receiving the packet from \(\theta_{2}\), the attacker \(\theta_{3}\) should forward the packet, but instead of transmitting the packet, it drops the packet. The dotted lines without arrow indicate that the packet does not forward in Figure 2.  
Without loss of generality, assume that all vehicles have the same transmission range, which is denoted by \(\varrho\). Furthermore, \(\varrho\) is commonly much larger than the length of a vehicle, similar to [46], and thus, the length of any vehicle is not taken into consideration. The inter-vehicle distances are independent identically distributed and it is exponentially distributed random variables with mean \(\lambda^{-1}\). Additionally, if the distance between two vehicles is not more than \(\varrho\), they can form a link. Let \(l_{ij}\) represent a link between vehicle pairs \((\theta_{i},\theta_{j})\), where \(\theta_{i}\) represents the sender and \(\theta_{j}\) is the receiver. Moreover, each vehicle needs to maintain a neighbor set. Let \(\mathcal{M}_{i}\) denote the neighbor set of vehicle \(\vartheta_{i}\). The distance between vehicle \(\vartheta_{i}\) and each vehicle in set \(\mathcal{M}_{i}\) is less than \(\varrho\). By receiving the periodical beacon packet, the set \(\mathcal{M}_{i}\) can be updated. \begin{table}
\begin{tabular}{c|c|c} \hline \hline
**Notation** & **Description** & **Unit** \\ \hline \(\hat{\vartheta}_{i}\) & \(i\)-th vehicle & – \\ \hline \(v_{i}\) & Velocity of \(\vartheta_{i}\) & m/s \\ \hline \((x_{i},y_{i})\) & Coordinates of \(\vartheta_{i}\) & m \\ \hline \(D_{ij}\) & Distance between \(\vartheta_{i}\) and \(\hat{\vartheta}_{j}\) & – \\ \hline \(l_{ij}\) & Link between \(\vartheta_{i}\) and \(\vartheta_{j}\) & m \\ \hline \(T_{ij}^{\text{do}}\) & Total delay that a packet is transmitted through link \(l_{ij}\) & s \\ \hline \(v_{i,j}\) & Relative velocity of the \(\hat{\vartheta}_{i}\) with respect to \(\hat{\vartheta}_{j}\) & m/s \\ \hline \(PFR_{j}\) & Packet forwarding ratio of the vehicle \(\hat{\vartheta}_{j}\) & – \\ \hline \(P_{j}\) & Connectivity probability of \(\vartheta_{j}\) connected to \(\hat{\vartheta}_{i}\) & – \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of symbols. Figure 2: System model. Delay is a measure of the efficiency of transmitting packet. The total delay is the times that a packet is transmitted from a sender to a receiver, which included propagation delay as well as transmission delay. Let \(T_{i,j}^{\text{tr}}\) and \(T_{i,j}^{\text{pr}}\) represent the transmission delay and propagation delay, respectively. They can be given as [47]:  
\[T_{i,j}^{\text{tr}}=L^{\text{da}}/R_{i,j},T_{i,j}^{\text{pr}}=D_{i,j}/c, \tag{1}\]  
where \(L^{\text{da}}\) represents the length of transmitted packet, \(R_{i,j}\) represents the transmission rate of link \(l_{i,j}\), \(D_{i,j}\) represents the distance from \(\vartheta_{i}\) to \(\vartheta_{j}\), and \(c\) is the speed of light.