# Coordination of Macro Base Stations for 5G Network with User Clustering
## 4 Case Study
### Simulation on 3 \(\times\) 3 5G Macro BSs Network
#### 4.1.3 Computational Efficiency of the User Clustering Method and Benders Decomposition  
To demonstrate the computational efficiency of the proposed user clustering method and Benders decomposition, the following three cases were tested for comparison.  
Case 1: In the original model proposed in Section 2 for the 5G macro BS network, neither the proposed user clustering methods and Benders decomposition were applied.  
Case 2: In the two-step energy management model for the 5G macro BS network, the proposed user clustering method was applied to reduce the computational burden of the first-step problem. Benders decomposition was not applied to the second step problem.  
Case 3: In the reformulated model proposed in Section 3 for the 5G macro BS network, both the proposed user clustering method and Benders decomposition were applied to the first and the second step problems, respectively.  
Table 1 lists the comparative results for the three cases.  
Based on the comparison between Cases 1 and 2 in Table 1, the objective values of (**P\({}_{1}\)**) and (**P\({}_{2}\)**) based on the use of the proposed user clustering method (Case 2) are 0.442% and 0.436% larger than that of Case 1, respectively, validating the achievement of approximately optimal performance. In addition, the user clustering method (Case 2) outperforms Case 1 in terms of calculation time because it can reduce a large number of integer variables, and the solving time of (**P\({}_{1}\)**) is reduced by approximately 80%. However, the long calculation time of (**P\({}_{2}\)**) remains a problem that needs to be solved.  
By comparing Cases 2 and 3 in Table 1, the reformulated model (Case 3) combines the advantages of the user clustering method and Benders decomposition. The objective values of (**P\({}_{1}\)**) and (**P\({}_{2}\)**) of Case 3 are the same as those of Case 2, which is also shown to reach approximately optimal performance. It can also be observed that the application of Benders  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Objective Value of** & **Optimality** & **Calculation** & **Objective Value of** & **Optimality** & **Calculation** \\  & **(P\({}_{1}\)) (kWh)** & **Gap** & **Time (s)** & **(P\({}_{2}\)) (S)** & **Gap** & **Time (s)** \\ \hline Case 1 & 588.3 & 0 & 5.3518 & 48.21 & 0 & 582.7 \\ Case 2 & 590.9 & 0.442\% & 1.1317 & 48.42 & 0.436\% & 469.5 \\ Case 3 & 590.9 & 0.442\% & 0.7798 & 48.42 & 0.436\% & 40.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparative results for the three tested cases.  
Figure 9: Energy storage of backup batteries in the 5G macro BS network.  
decomposition does not reduce optimality. In addition, the reformulated model (Case 3) outperforms the other two cases in terms of the total calculation time because it reduces the number of integer variables in (\(\mathbf{P}_{1}\)) and the size of (\(\mathbf{P}_{2}\)) by the decomposition method.  
In summary, with the proposed user clustering method and Benders decomposition, the proposed dispatching scheme can achieve approximately optimal performance, while the solution time is reduced considerably.