## 4 SD-EAR in Detail
### Optimum Route Selection
#### 4.2.3 Example of Optimum Path Selection  
Table 3 specifies all of the node ids in Figure 10 along with their descriptions. Based on these assumptions, we are about to find out the optimal route from \(n_{\text{b}}\) to \(n_{\text{d}}\) at current timestamp 100. The significance of all of the symbols used in Table 3 have been mentioned earlier in this section. For the purpose of simplicity, we have assumed that all of the links are bi-directional. The latitude and longitudinal positions are given in Table 3. It is seen from Figure 10 that \(n_{\text{a}}\) is directly connected to \(n_{\text{e}}\) only, while \(n_{\text{e}}\) is directly connected to \(n_{\text{a}}\), \(n_{\text{b}}\), \(n_{\text{g}}\), \(n_{\text{u}^{\prime}}\), and \(n_{\text{v}^{\prime}}\). Among them, \(n_{\text{u}^{\prime}}\) and \(n_{\text{v}^{\prime}}\) are out of \(Z_{\text{A}}\). So, EN(a) = {\(n_{\text{e}}\)} and \(\text{pphr}_{\text{a}}\) = 0, since \(n_{\text{e}}\)\(\in Z_{\text{A}}\). On the other hand, EN(a) = {\(n_{\text{a}}\), \(n_{\text{b}}\), \(n_{\text{g}}\), \(n_{\text{u}^{\prime}}\), \(n_{\text{v}^{\prime}}\)} and \(\text{pphr}_{\text{e}}\) = 1, since \(n_{\text{u}^{\prime}}\), \(n_{\text{v}^{\prime}}\
otin Z_{\text{A}}\). Similarly, the EN and pphr of other nodes can be computed. Other attribute values are assumed. The performances of different routes from \(n_{\text{b}}\) to \(n_{\text{d}}\) are calculated in the FUZZ-OPT-ROUTE of SDN controller of \(Z_{\text{A}}\). \begin{table}
\begin{tabular}{c c c c c} \hline
**Ref\(\rightarrow\)** & & & & \\
**Trim \(\downarrow\)** & **L** & **S** & **H** & **VH** \\ \hline L & L & L & L & L \\ S & L & S & S & S \\ H & L & S & H & H \\ VH & L & S & H & VH \\ \hline \end{tabular}
\end{table} 
Table 1: Composition of reft and trim producing temp1. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Temp1 \(\rightarrow\)** & & & & \\
**Neff\(\downarrow\)** & **L** & **S** & **H** & **VH** \\ \hline L & L & L & S & H \\ S & L & S & H & H \\ H & L & S & H & VH \\ VH & L & S & H & VH \\ \hline \end{tabular}
\end{table} 
Table 2: Composition of temp1 and neff producing opt-performance. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Node-id** & **Latitude, Longitude** & **EN** & **m-en** & **r-en** & **dep** & **slp** & **\(\tau\)-slp** & **pphr** & **mrpw** \\ \hline n\({}_{\text{a}}\) & (0,0) & n\({}_{\text{e}}\) & 40 & 25 & 2 & 0 & \(-1\) & 0 & 1 \\ n\({}_{\text{b}}\) & (10,10) & n\({}_{\text{e}}\), \(n_{\text{f}}\) and n\({}_{\text{c}}\) & 15 & 3 & 2 & 0 & \(-1\) & 0 & 1 \\ n\({}_{\text{c}}\) & (11,11) & n\({}_{\text{b}}\), \(n_{\text{f}}\) and n\({}_{\text{b}}\) & 30 & 20 & 4 & 0 & 90 & 0 & 2 \\ n\({}_{\text{d}}\) & (11.5,11.5) & n\({}_{\text{c}}\), \(n_{\text{g}}\) & 80 & 20 & 4 & 0 & \(-1\) & 0 & 1 \\ n\({}_{\text{e}}\) & (3,2) & n\({}_{\text{a}}\), \(n_{\text{b}}\) & 80 & 20 & 10 & 0 & 80 & 1 & 3 \\ n\({}_{\text{f}}\) & (12, 12) & n\({}_{\text{b}}\), n\({}_{\text{c}}\) & 40 & 25 & 3 & 1 & \(-1\) & 0 & 1 \\ n\({}_{\text{g}}\) & (11.75,11.75) & n\({}_{\text{d}}\) & 60 & 30 & 2 & 1 & 85 & 1 & 1 \\ \hline \end{tabular}
\end{table} 
Table 3: Node identifiers and descriptions. The different routes from \(n_{b}\) to \(n_{d}\) obtained through a depth-first traversal of topology of \(Z_{A}\), are as follows:  
(i) \(R_{1}\): \(n_{b}\to n_{c}\to n_{d}\)  
(ii) \(R_{2}\): \(n_{b}\to n_{c}\to n_{d}\)  
(iii) \(R_{3}\): \(n_{b}\to n_{c}\to n_{f}\to n_{d}\)  
(iv) \(R_{4}\): \(n_{b}\to n_{f}\to n_{c}\to n_{d}\)  
(v) \(R_{5}\): \(n_{b}\to n_{e}\to n_{g}\to n_{d}\)  
Performance of \(R_{1}\)  
\[\text{reft}(R_{1})=[\{1-1/(20+2)\}\,\{1-3/(3+20+20+2)\}]^{0.5}=0.9438\]  
\[\text{trim}(R_{1})=[\{1-(2+1)/(3\times 4)\}/\max\{2^{0.5},\,0.5^{0.5}\}]^{0.5}=0.7 282\]  
\[\text{neft}(R_{1})=[\{1-0/3\}\,\{1-1/(1+2)\}]^{0.5}=0.8176\]  
After fuzzification, the fuzzy premise variables corresponding t reft(R\({}_{1}\)), trim(R\({}_{1}\)), andneff(R\({}_{1}\)) become VH, H, and VH, respectively. Their combination, according to Tables 1 and 2, is VH.