## 4 Performance Analysis and Evaluation
### Energy Consumption Analysis of IP-WSN  
For energy consumption analysis, we consider an IP-WSN with densely deployed IP sensing devices. The network consists of two types of IP sensing device: fully functional IP sensing devices (IP-FFDs) and reduced functional IP sensing devices (IP-RFDs). IP-FFDs hold the complete 6 LoWPAN protocol stack and perform the routing functions. IP-RFDs perform the sensing functions and forward the data to the IP-FFDs. We have followed the energy consumption model used in [7,19-23]. Table 2 represents the used parameter values in the energy consumption model. Here, \(E^{\alpha}\) and \(E^{\pi x}\) is the distance-independent amount of energy consumed by the transmitter and receiver electronics and the digital processing of each:  
\[E=E^{\alpha}+\beta*d^{\alpha}+E^{\alpha} \tag{12a}\]  
Since same type of transmitting and receiving device is concerned in IP-WSN:  
\[E^{\alpha}=E^{\alpha}=E_{\mathit{dec}} \tag{12b}\] \[E=2*E_{\mathit{dec}}+\beta*d^{\alpha} \tag{12c}\]  
For a particular fully functional device or a SMAG node \(i\), control packet transmission cost can be calculated as follows:  
\[C_{i}^{\mathit{cnt}}(r)=[L_{\mathit{cnt}}*\beta*r^{\alpha}+(nrf\hat{d}_{i}(r)+ 1)*L_{\mathit{cnt}}*L_{E}]\frac{1}{T} \tag{13}\]  
Here \(\alpha\) is path loss exponent (\(2<\alpha<5\)) and \(\beta\) is a constant [J/bit m\({}^{2}\)], \(r\) is a transmission range. \(nrf\hat{d}(r)\) is the average number of reduced functional device nodes in the neighborhood of the fully  
\begin{table}
\begin{tabular}{l l} \hline Parameter & Value \\ \hline No of IP-WSN Node (N) & 25–120 \\ Network Area (A) & 120 \(\times\) 120 M \\ Node density (\(\rho\)) & 0.00173–0.00833 \\ Initial Energy & 2 J \\ Transmit/Receive electronics (\(\rm{L_{E}}\)) & 50 nJ bit\({}^{-1}\) m\({}^{2}\) \\ Transmission Power & \(5.85\times 10^{-5}\) W \\ Number of SMAG & 1–10 \\ Transmission range (r) & 25 m \\ Packet size & 2 KB \\ \hline \end{tabular}
\end{table}
Table 2: Parameter values.  
functional node \(i\) within the range \(r\). \(L_{ctrl}\) is the length of control packets in bits, \(L_{E}\) is the energy consumed by the transmitter device to transmit or receive a packet, and \(T\) is the time period between two consecutive topological changes of the IP-WSN.  
Now for a particular path \(p\), cost for information transmission from a source to the fully functional SMAG node \(i\) is calculated as follows:  
\[C_{i}^{\inf}(p)=[\sum_{i=1,j=2}^{N}\left(n\!f\!fd_{p}(d_{i})+1\right)*L_{data}* \beta d_{i,j}^{\alpha}+\left(n\!r\!fd_{p}(d_{i})+1\right)*L_{data}]*L_{E} \tag{14}\]  
Here \(n\!f\!fd_{p}(d_{i})\) indicates the number of fully functional node for a path \(p\) and within the range \(d\). \(n\!r\!fd_{p}(d_{i})\) indicates the number of reduced functional device for path \(p\) and range \(d\).  
Total communication cost for transmitting data packet from a source to SMAG node \(i\) can be calculated from Equations (13) and (14):  
\[C_{i}^{total}(p)=\sum_{i=1}^{N}\left[C_{i}^{ctrl}(r)\right]+C_{i}^{\inf}(p) \tag{15}\]  
Now let us calculate the energy consumption in terms of MIPv6, PMIPv6 and the proposed global IP-WSN scheme based on SPMIPv6 with the help of Equations (9) to (15). Energy consumed by MIPv6 scheme can be calculated by the following mathematical derivation. Here \(E_{i}^{mipv6}\) indicates energy consumption by MIPv6 scheme:  
\[E_{i}^{mipv6}=SigCost_{i}^{mipv6}*C_{i}^{total}(p) \tag{16}\]  
Energy consumed by PMIPv6 scheme can be calculated by the following mathematical derivation. Here \(E_{i}^{mipv6}\) indicates energy consumption by PMIPv6 scheme:  
\[E_{i}^{mipv6}=SigCost_{i}^{mipv6}*C_{i}^{total}(p) \tag{17}\]  
Finally energy consumed by the proposed IP-WSN based on SPMIPv6 scheme can be calculated in the same way. Here \(E_{i}^{spmipv6}\) indicates energy consumption by IP-WSN based on SPMIPv6 scheme:  
\[E_{i}^{spmipv6}=SigCost_{i}^{spmipv6}*C_{i}^{total}(p) \tag{18}\]