## 5 Numerical Results
We consider a study case in which the number \(R\) of optical rings is varied and chosen equal to 1, 2 and 4 and each of them interconnects \(S=10\) Access Switches. The variation of the number of optical rings leads to changing the number \(D=\frac{T}{RS}\) of sub-areas handled by any AS from 20 to 5 for \(R\) varying from 1 to 4, respectively. From the results reported in Figure 5, we can notice how the proposed dynamic resource allocation solution allows for remarkable saving with respect to the static solution in which the bandwidth resources are not shared and dimensioned according to the worst case, that is in the case in which the installed hardware is operating at full load. As an example, when \(R=1\) and \(\gamma=0.6\)m the static and dynamic solutions need a number of wavelengths equal to 960 and 92 wavelengths, respectively, and consequently the cost saving is in the order of 90%. In Figure 5, we can also observe how the use of fewer rings leads to using fewer wavelengths, which is due to the higher number of sub-area handled by each AS with the consequence of a higher statistical multiplexing gain. For instance, in the case \(\gamma=0.7\), the total number of wavelengths needed equals 130, 210 and 350 for \(R\) equal to 1, 2 and 4, respectively. The problem of fewer rings may lead to solutions that not can be implemented (i.e., ROADMs or transmission systems technology not available due to the high number of wavelengths needed) and for this reason a right trade-off has to be chosen between costs and feasibility. For instance, in our example, in the case in which 128 wavelengths can be supported at 100 Gbps rate, the best solution is the one with two optical rings each one supporting 105 wavelengths as illustrated in Figure 6.  
The impact of the traffic type (business and residential) on the dimensioning is investigated in Figures 7 and 8 where we report the number of wavelengths per optical ring as a function of the probability that any sub-area handles residential user traffic. The results reported in Figure 7 are obtained by varying the used RRU percentage from 0% to 100%. We consider a network organized in two optical rings. The other parameter values are chosen as the ones of Figures 5 and 6. We can observe how the wavelength dimensioning does not depend only on the values of peak average traffic \(A_{o,b}\) and \(A_{o,r}\) but even on the percentage of residential and business sub-area. Because the peak average traffic in the PHI occurs in different stationary intervals for business and residential sub-areas, respectively, then the bandwidth sharing between business and residential users may lead to less severe dimensioning. For instance in the case \(\gamma=1\), the lowest dimensioning occurs for \(p_{r}=0.80\) when 309 wavelengths are needed. That is confirmed in Figure 8 where we have chosen the residential peak traffic \(A_{o,r}\) equal to 16 Gbps and varied the ratio \(\omega=\frac{A_{o,r}}{A_{o,r}}\) from 0.5 to 2. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{S_{1}}\) & \(\mathbf{S_{2}}\) & \(\mathbf{S_{3}}\) & \(\mathbf{S_{4}}\) \\ \hline
**Number of active antennas** & \(1\) & \(2\) & \(4\) & \(8\) \\ \hline
**RRU Capacity** & \(75\) Mbps & \(150\) Mbps & \(300\) Mbps & \(600\) Mbps \\ \hline
**CPRI bit-rate** & \(1.2288\) Gbps & \(2.4576\) Gbps & \(4.9152\) Gbps & \(9.8304\) Gbps \\ \hline
**Number of CPRI flows in one ODU2** & \(8\) & \(4\) & \(2\) & \(1\) \\ \hline \end{tabular}
\end{table} 
Table 3: Number of active antennas, RRU capacities, CPRI bit-rates and maximum number of CPRI flows carried in one ODU2 for the antenna configurations \(S_{1}\), \(S_{2}\), \(S_{3}\) and \(S_{4}\). Figure 5: Comparison of the total number of wavelengths for the static and dynamic scenario cases. The total number of wavelengths is reported as a function of the used RRU percentage in the case of number \(R\) of optical rings equal to 1, 2 and 4.