# SDN-Based Survivability Analysis for V2I Communications
## 5 Verification and Analysis of V2I Networks Survivability Model
### Analysis of Maximum Survival Probability of V2I Networks
In addition, with an increased vehicle node repair rate \(\mu_{2}\) from 0.1 to 0.9, the V2I network survivability probability \(P_{sur\_max2}\) also increases. The validation results meet the property definition requirements. Figure 6: The maximum probability of V2I network survivability with respect to the time (corresponding to \(\mu_{1}\) and \(\mu_{2}\)). Figure 7: The maximum survival probability of the V2I network with vehicle failure number \(n\) (corresponding to \(\mu_{2}\)). For the survivability model of the SDN-based V2I vehicle network, we consider the occurrence of various anomalies leading to network link failure. Thus, the V2I link failure rate \(\lambda_{1}\) and vehicle node failure rate \(\lambda_{2}\) are introduced into this model. All of these factors will directly and indirectly affect the connectivity of the vehicle network communication links. Hence, the change of \(\lambda_{1}\) or \(\lambda_{2}\) has a certain influence on the survival probability of the V2I networks. We discuss the survival probability of the V2I network in detail for different values of the parameter \(\lambda_{1}\), as shown in Figure 8. The number \(N\) of vehicles is set at 10, and \(\lambda_{2}\) remains 0.1. It is observed from Figure 8, with an increased repair rate \(\mu_{1}\) and \(\mu_{2}\), that the V2I link failure rate \(\lambda_{1}\) increases, especially when the repair rate of the two situations is greater than 0.4, the corresponding single curve (such as pink) shows a slight decreasing trend. The overall survival probability \(P_{sur\_max3}\) of the V2I network increases with the increased repair rate \(\mu_{1}\) and \(\mu_{2}\), due to the effect of MPTCP, where the repair rate \(\mu_{1}\) dominates the repair degree of each link. Moreover, it is also shown that with an increased \(\mu_{1}\), each V2I link still switches to each other to transfer information according to the link idle situation. Therefore, one can see that the V2I network can maintain a certain survival ability and continue to provide services for the transmission task. Finally, due to the failure of the vehicle node affecting the survivability of the V2I network, we discuss the V2I of the network survival probability \(P_{sur\_max4}\) under the change of the failure rate \(\lambda_{2}\) with the vehicle node, as shown in Figure 9. Failures of vehicle nodes will lead to interruptions of V2I network communication links. The single curve shown in Figure 9 shows that the survival probability \(P_{sur\_max4}\) of the V2I network decreases with an increased failure rate \(\lambda_{2}\) of the vehicle node. However, the overall survival probability of the V2I network increases with the increased repair rate \(\mu_{2}\). Moreover, in Figure 9, one can see that the entire V2I network has a certain survivability even at a minimum repair rate of 0.1. Although the survival probability \(P_{sur\_max4}\) is relatively low, the network still has a certain survivability. Therefore, the MPTCP technology for vehicle network nodes in the SDN-based V2I network has advantages in maintaining network survival performance. Figure 8: The maximum survival probability of the V2I network with link failure rate \(\lambda_{1}\) (corresponding to \(\mu_{1}\) and \(\mu_{2}\)).