## 4 Numerical Analysis
### Cost of Inter-Domain Handover in PMIPv6 for VANET  
Originally, inter-domain handover was not supported by PMIPv6. For inter-domain handover, the IETF takes into consideration the usage of the previously suggested technique, Mobile IPv6 (MIPv6). The problems in MIPv6, such as duplicate address detection (DAD), Home Agent Binding Update (HA-BU), and Correspond Node-Binding Update (CN-BU), which are transmitted in MIPv6, increase the latency. Our proposed architecture suggests a new approach to facilitating inter-domain handover by using the method of multicasting the authentication information with PMIPv6. By adding the multicast facility to TTPs, the Layer 4 connection is maintained in both the intra-domain and inter-domain handover of vehicles, which was not formerly supported in PMIPv6 mobility management protocols. The cost of inter-domain handoff for VANET for the proposed architecture is expressed by Equation (15). \[TC_{Inter-PMIPv6}^{VANET}=T_{Inter-Authentication}^{VANET}+BUC_{ Inter-PMIPv6}^{VANET}+PDC_{Inter-PMIPv6}^{VANET} \tag{15}\]  
The authentication cost required in authenticating the network entities such as the LMA and MAG is represented as \(\big{(}T_{Inter-Network-Entities}^{VANET}\big{)}\), whereas the cost of mobile entities' authentication is represented by \((T_{Inter-Mobile-Entities}^{VANET}\big{)}\). Therefore, the authentication cost for inter-domain handover for VANET in PMIPv6 is expressed as in Equation (16). \[T_{Inter-Authentication}^{VANET}=T_{Inter-Network-Entities}^{VANET}+T_{ Inter-Mobile-Entities}^{VANET} \tag{16}\]  
Network entities and the TTP server will exchange authentication control messages, \(S_{TTP}\), throughout the course of the authentication procedure. The PMIPv6 domain contains several MAGs, and each MAG will send a control message to the TTP server for authentication, and the TTP server will respond by sending a control message back to the MAG. In the same way, the LMA sends the control message to the TTP, and, in response, the TTPwill send the control message back to the LMA. Hence, the authentication cost of network entities \(T_{Inter-Network-Entities}^{VANET}\) can be expressed as in Equation (17). \[T_{Inter-Network-Entities}^{VANET}=N_{MAG}\times(S_{TTP}\times 2T_{MAG-TTP})+S_{ TTP}\times 2T_{LMA-TTP} \tag{17}\]  
A connection between a vehicle and MAG requires the setup cost, \(T_{Setup}\), for the authentication of every vehicle. The MAG is responsible for generating and forwarding the authentication request to the TTP server utilizing an authentication control message, \(S_{TTP}\), on the vehicle's behalf. Consequently, an authentication control message, \(S_{TTP}\), will be delivered for each vehicle present in the PMIPv6 domain, to the TTP server, via the MAG. After authentication is complete, the TTP will send the authentication control message back to the MAG. During inter-domain handoff, if the TTP of the local PMIPv6 domain has information about the vehicle, then it is authenticated; otherwise, the authentication request from the TTP present in the local PMIPv6 domain is multi-casted to neighboring TTPs and the TTP that has the authentication information will unicast the authentication response back to the requested TTP. The cost of authentication for vehicles includes the minimum cost required to multicast to neighboring TTPs. Hence, the cost of mobile entities' authentication for inter-domain handoff, (\(T_{Inter-Mobile-Entities}^{VANET}\)), can be expressed as in Equation (18). \[ \begin{array}{ll}T_{Mobile-Entities}^{VANET}=&N_{Vch}\times\big{(}T_{Setup}+ Max(S_{TTP}\times 2T_{MAG-TTP},\\ &S_{TTP}\times T_{TTP-LMA})\big{)}+(S_{TTP}\\ &\times Min(2T_{TTP1-TTP2},2T_{TTP1-TTP3},\ldots\ldots 2T_{TTP1-TTPn})\big{)} \end{array}  \tag{18}\]  
Therefore, from Equations (17) and (18), the authentication cost for inter-domain handover in VANET [24; 25; 26; 27] in PMIPv6, \(T_{Inter-Authentication}^{VANET}\), expressed in Equation (16), can be represented by Equation (19). \[