# CoMP-Aware BBU Placements for 5G Radio Access Networks over Optical Aggregation Networks
## 4 CoMP Aware BBU Placement Algorithm
### Computational Complexity  
We evaluate the problem complexity for ILP optimization problem, it explained as the following steps. First, we evaluate the total number of variables for objective function, it is expressed as the following:  
\[N_{v}=|N|(1+S_{v}S_{p}) \tag{11}\]  
We can neglect the constant, so it becomes as following:  
\[N_{v}=|N|(|S_{v}|.|S_{p}|) \tag{12}\]  
Second, we evaluate the number of constraints, it expressed as the following:  
\[N_{xconst}=|N|(6+S_{v})+S_{p}+S_{v} \tag{13}\]  
users from inter-CoMP to intra-CoMP for the different six cases are nearly equal. This is due to the fact that each case checks the same criteria. Figure 5 shows the number of BBU pools and the number of physical links versus different maximum allowable latency values (\(D_{max}\)) at W = 4. At 25 usec and 35 usec, there is no change in the number of BBUs and the number of physical links after the reconfigurable placement algorithm. As all BBUs are located at the cell sites, the maximum delay is not sufficient to reconfigure the RRH to be served by any other BBU. At delays equal to 50 usec, 60 usec, and 70 usec, the number of BBUs does not change after reconfiguration, while the number of physical links increased by 41%, 35%, and 29% of the optimal solution, respectively. As the maximum allowable delay increases, the probability that the adjacent sites are served by the same BBU increases, leading to a higher number of intra-CoMP. Therefore, the number of migrated users decreases, and the number of sites that need  
Figure 4: Percentage of transferred users from Inter-BBU CoMP to Intra-BBU CoMP (for each Cases, W = 4). Figure 3: Network topology. to change their served BBU decreases. At delays equaling 80 usec, the number of BBUs decreased to two BBUs instead of three in the previous delays. This increases the number of intra-CoMP as the probability of sites being served by different BBUs decreased. Therefore, the physical links increased by 24%. At delays of 100 usec and 200 usec, all sites in the area are served by one BBU; thus, there is no inter-CoMP. Therefore, there is no reconfiguration and the number of phvsical links remains constant. Table 4 shows the number of BBU pools and the number of physical links versus different maximum allowable latencies (\(D_{max}\)) = 50, 60, 70, and 80 usec at \(W=4\) and \(W=6\), considering cases 2, 3, 4, 5, and 6. Figure 6 shows the percentage of users migrated from Inter-BBU CoMP to Intra-BBU CoMP at W = 6. The figure shows the same performance explained in Figure 4 except for an increased number of migrated users from inter-CoMP to intra-CoMP in each case. This can be explained as follows; increasing the capacities of the links allow a change in serving BBUs for more RRHs andm hence, increases the number of migrated users. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**50 usec**} & \multicolumn{4}{c}{**60 usec**} & \multicolumn{4}{c}{**70 usec**} & \multicolumn{4}{c}{**80 usec**} \\ \cline{2-13}  & \multicolumn{2}{c}{**Before**} & \multicolumn{2}{c}{**After**} & \multicolumn{2}{c}{**Before**} & \multicolumn{2}{c}{**After**} & \multicolumn{2}{c}{**Before**} & \multicolumn{2}{c}{**After**} & \multicolumn{2}{c}{**Before**} & \multicolumn{2}{c}{**After**} \\ \cline{2-13}  & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} & \multicolumn{2}{c}{**BBU Ph. Links**} \\ \cline{2-13}
**2 nd** & 3 & 17 & 3 & 25 & 3 & 17 & 3 & 24 & 3 & 17 & 3 & 23 & 2 & 25 & 2 & 30 \\ \cline{2-13}
**3 rd** & 3 & 17 & 3 & 23 & 3 & 17 & 3 & 22 & 3 & 17 &  
Figure 7 shows the number of BBU pools and the number of physical links versus different maximum allowable latency values (\(D_{max}\)) at W = 6.