## 3 Results and Discussions
### Case Study
#### 3.1.3 Water System  
Table 5 delivers Pittsburgh's City water treatment plants, using public data, including the power consumption for each water treatment facility, as calculated using the Equation (7). Then, Equation (8) is applied for the total weighted value for standalone infrastructure. The table shows that two of the five tested water treatment planets are considered critical: Pittsburgh WTP and Westview WTP.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**eNB ID**} & **Coverage** & **Population** & **Power Consumption** & \\  & **Index** & **Covered** & **(kWh)** & \\ \hline
780206 & 3 & 4475 & 25 & 2.156 \\
780007 & 2 & 16,227 & 20 & 1.848 \\
780165 & 2 & 5338 & 20 & \(-\)0.141 \\
780059 & 3 & 7119 & 25 & 2.639 \\
780213 & 1 & 15,500 & 15 & \(-\)0.739 \\
780108 & 2 & 15,500 & 20 & 1.715 \\
780399 & 1 & 12,915 & 15 & \(-\)1.211 \\
780184 & 1 & 5096 & 15 & \(-\)2.639 \\
780017 & 3 & 843 & 25 & 1.492 \\
780527 & 1 & 8424 & 15 & \(-\)2.032 \\
780037 & 1 & 8424 & 15 & \(-\)2.032 \\
780364 & 1 & 24,080 & 15 & 0.828 \\
780154 & 2 & 6446 & 20 & 0.061 \\
780178 & 2 & 6446 & 20 & 0.061 \\
780560 & 3 & 6446 & 25 & 2.516 \\
780225 & 2 & 2710 & 20 & \(-\)0.621 \\
780163 & 3 & 7622 & 25 & 2.731 \\ \hline \hline \end{tabular}
\end{table}
Table 6: LTE base stations.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Hospital**} & **Power Consumption** & \multirow{2}{*}{**Population**} & **Size** & \\  & **(kWh)** & & **(Beds)** & \\ \hline West Penn Hospital & 9,510,000 & 12,915 & 317 & \(-\)0.034 \\ UPMC Montefiore & 7,500,000 & 24,080 & 250 & 0.976 \\ UPMC Mercy & 14,460,000 & 15,714 & 482 & 2.361 \\ Allegheny Hospital & 11,430,000 & 5949 & 381 & \(-\)0.402 \\ UPMC St. Margaret & 7,470,000 & 5200 & 249 & \(-\)2.078 \\ Children’s Hospital & 8,880,000 & 15,500 & 296 & 0.136 \\ LifeCare Hospitals & 7,080,000 & 9555.00 & 236 & \(-\)1.529 \\ UPMC Presbyterian & 23,850,000 & 24,080.00 & 795 & 7.396 \\ VA Healthcare & 4,380,000 & 14,117 & 146 & \(-\)1.854 \\ UPMC Shadyside & 15,600,000 & 15,916 & 520 & 2.841 \\ Magee’s Hospital & 10,800,000 & 10,850 & 360 & 0.140 \\ St. Clair Hospital & 9,840,000 & 4569 & 328 & \(-\)1.249 \\ Children’s Genetics & 7,500,000 & 10,850 & 250 & \(-\)1.156 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Healthcare.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Facility**} & **Capacity** & **Power Consumption** & \\  & **(Million G/Day)** & **(kWh)** & \\ \hline Pittsburgh WTP & 70,000,000 & 327,600,000 & 3.029 \\ Brush WTP & 1,500,000 & 7,020,000 & \(-\)1.387 \\ Plum Creek WTP & 2,234,669 & 10,458,250.9 & \(-\)1.340 \\ Harmar Twp WTP & 1,500,000 & 7,020,000 & \(-\)1.387 \\ Westview WTP & 39,850,000 & 186,498,000 & 1.085 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Water treatment plants (WTP).  
Given the infrastructure data above in Tables 4-7, we made an initial analysis of the city, considering a grid of 3 km \(\times\) 3 km squares as \(Geo_{i}\). Figure 4 displays heat maps of the top significant nodes in each infrastructures. Figure 5 exhibits the heat map when all four infrastructures are overlain and considered a group. The results present the outputs of applying the proposed heuristic and optimization models to the data.