# Tunnel-Free Distributed Mobility Management (DMM) Support Protocol for Future Mobile Networks
## 3 Analytical Modeling and Performance Evaluation
### Modeling the Handover Latency
#### 3.2.5 Handover Latency of Proposed Approach  
The handover latency for MIPv6 is found using Equation (1). For our proposed approach, as shown in the handover timing diagram in Figure 4, the handover latency is comprised of the handover delay of link layer depending on the chipset implementation for a wireless interface (\(d_{L2}\)), the link layer authentication latency (\(d_{AU}\)), the movement detection process delay (\(d_{MD}\)), the duplicate address detection delay (\(d_{DAD}\)), the new binding update and acknowledgement process delay (\(d_{N}\)), the delay of the proposed protocol's handover registration (\(d_{R}\)), and the arrival delay of the first packet of the previous session from the current BMA to the MN (\(d_{S}\)). The delay in the movement detection process (\(d_{MD}\)) is comprised of the time required for sending the RS notification and receiving the RA notification. If \(t_{RS}\) denotes the time required for the RS notification, and \(t_{RA}\) denotes the time required for the RA notification, then movement detection process delay \(d_{MD}\) can be calculated using:  
\[d_{MD}=T_{RS}+T_{R}. \tag{6}\]  
where \(T_{RS}\) is the time required for sending the RS notification and receiving the RA notification and \(T_{R}\) is the handover registration delay. The factors involved in the delay in the RS/RA notification are the message size of RS/RA, the bandwidth and propagation time of the wireless link, and the link failure probability of the wireless link. The RS/RA delay has been calculated according to the AR involved [9; 30]. We derived \(t_{RS}\) and \(t_{RA}\) for our proposed approach focusing on the factors involved as mentioned above. \(t_{RS}\) and \(t_{RA}\) can then be calculated using:  
\[t_{RS}=\left(\frac{m_{BU}}{b_{WD}}+t_{WD}\right)+\left(\frac{m_{BU}}{b_{WL}}+t _{WL}\right)\times\frac{pf}{1-pf} \tag{7}\]  
\[t_{RA}=\left(\frac{m_{RA}}{b_{WD}}+t_{WD}\right)+\left(\frac{m_{RA}}{b_{WL}}+t _{WL}\right)\times\frac{pf}{1-pf} \tag{8}\]  
In Figure 4, \(d_{R}\) specifies the proposed protocol's handover registration delay. It begins with the BU notification. For the proposed approach we derived \(d_{R}\) as follows:  
\[d_{R}=\left(\frac{m_{BU}}{b_{WD}}+t_{WD}\right)+\left(\frac{m_{BU}}{b_{WL}}+t _{WL}\right)\times\frac{pf}{1-pf}. \tag{9}\]  
Figure 4: Handover timing diagram for the proposed approach. The proposed approach eliminates the need for tunneling by anchoring the sessions via a new BMA using the MBB approach. Let \(d_{N}\) represent the new binding update and acknowledgement latency caused while sending a signaling message. Then, \(d_{N}\) consists of a new binding update represented by \(d_{NBU}\) and a new binding acknowledgement represented by \(d_{NBAck}\). We can calculate \(d_{N}\) using:  
\[d_{N}=d_{NBU}+d_{NBAck}. \tag{10}\]  
The proposed approach also provides a mobility option for an address bound to the MN. It is represented by \(m_{M}\). Adding this factor to \(d_{N}\), \(d_{NBU}\) and \(d_{NBAck}\) can be calculated as follows:  
\[d_{NBU}=\left(\frac{m_{NBU}+m_{M}}{b_{WD}}+t_{WD}\right)+\left(\frac{m_{NBU}+ m_{M}}{b_{WL}}+t_{WL}\right)\times\frac{pf}{1-pf}, \tag{11}\]  
\[d_{NBAck}=\left(\frac{m_{NBAck}+m_{M}}{b_{WD}}+t_{WD}\right)+\left(\frac{m_{NBA ck}+m_{M}}{b_{WL}}+t_{WL}\right)\times\frac{pf}{1-pf}. \tag{12}\]  
The arrival delay of the first packet of the previous session from the current BMA to the MN is represented by \(d_{S}\). It involves a BA and the data packet represented by \(m_{D}\). We calculated \(d_{S}\) as follows:  
\[d_{S}=\left(\frac{m_{BA}+m_{D}}{b_{WD}}+t_{WD}\right)+\left(\frac{m_{BA}+m_{D} }{b_{WL}}+t_{WL}\right)\times\frac{pf}{1-pf}. \tag{13}\]  
As can be seen in Figure 4, the overall registration delay is represented by \(d_{REG}\).