## 5 Numerical Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(Q\)} & Number of MIMO & \multirow{2}{*}{\(n_{i}\)} & Number of active antennas \\  & Configurations for & & for the MIMO Configuration \\  & each RRU & & \(S_{i}\) (\(i=0,\cdots,Q-1\)) \\ \hline \multirow{2}{*}{\(C_{i}^{RRU}\)} & RRU User Capacity (Mbps) & \multirow{2}{*}{\(f_{i}^{CPRI}\)} & CPRI hit rate (Qpss) for \\  & for the MIMO Configuration & & the MIMO Configuration \\  & \(S_{i}\) (\(i=0,\cdots,Q-1\)) & & \(S_{i}\) (\(i=0,\cdots,Q-1\)) \\ \hline \multirow{2}{*}{\(C_{RBS}\)} & RRU User Capacity (Mbps) & \multirow{2}{*}{\(n_{RRU}^{R}\)} & Number of RRUs in a \\  & & & business sub-area \\ \hline \multirow{2}{*}{\(n_{RBS}^{b}\)} & Number of RBSs in a & \multirow{2}{*}{\(n_{RRU}^{R}\)} & Number of RRUs in a \\  & business sub-area & & residential sub-area \\ \hline \multirow{2}{*}{\(n_{RBS}^{t}\)} & Number of RBS in a & \multirow{2}{*}{\(D\)} & Number of sub-areas \\  & residential sub-area & & handled by each AS \\ \hline \multirow{2}{*}{\(R\) } & \multirow{2}{*}{Number of Optical Rings} & \multirow{2}{*}{\(S\)} & Number of Access Switches \\  & & & in each Optical Ring \\ \hline \multirow{2}{*}{\(L^{i}\)} & Set of the links in the & \multirow{2}{*}{\(\eta_{i}^{CPRI}\)} & Maximum number of CPRI flows \\  & \(i\)-th Optical Ring & & carried in one ODUZ for the MIMO \\  & & & Configuration \(S_{i}\) (\(i=0,\cdots,Q-1\)) \\ \hline \multirow{2}{*}{\(\eta^{\lambda}\)} & Number of ODU2s & \multirow{2}{*}{\(\eta_{EH}\)} & Number of Ethernet flows \\  & in a wavelength & & carried on any wavelength \\ \hline \(N\) & Number of Stationary Intervals (SI) & \(p_{b}\) & Probability of a business sub-area \\ \hline \multirow{2}{*}{\(p_{r}\)} & Probability of a residential sub-area & \multirow{2}{*}{\((\mu_{k}^{x,b},\sigma_{k}^{x,b})\)} & Log-normal distribution \\  & & & parameters for the upstream \\  & & traffic in a business sub-area \\ \hline \multirow{2}{*}{\((\mu_{k}^{x,b},\sigma_{k}^{x,b})\)} & Log-normal distribution & Log-normal distribution \\  & parameters for the downstream & \multirow{2}{*}{\((\mu_{k}^{x,b},\sigma_{k}^{x,b})\)} & parameters for the upstream \\  & traffic in a business sub-area & & traffic in a residential sub-area \\ \hline \multirow{2}{*}{\((\mu_{k}^{x,b},\sigma_{k}^{x,b})\)} & Log-normal distribution & Peak average traffic in the PHI \\  & parameters for the downstream & \multirow{2}{*}{\(A_{u,b}\)} & \multirow{2}{*}{\(\text{Peak average traffic}\)} \\  & traffic in a residential sub-area & & in a business sub-area \\ \hline \multirow{2}{*}{\(A_{u,r}\)} & Peak average traffic in the PHI & \multirow{2}{*}{\(A_{u,r}\)} & \multirow{2}{*}{\(A_{u,r}\)} \\  & parameters for the upstream & & \\  & in a residential sub-area & & \\ \hline \multirow{2}{*}{\(w_{l}^{(i),k}\)} & Number of wavelengths needed in & \multirow{2}{*}{\(n_{w}^{(i)}\)} & Number of wavelengths needed for the \(i\)-th \\  & the link \(l\) of the \(i\)-th Optical Ring & & Optical Ring \\  & and in the \(k\)-th SI & & \\ \hline \multirow{2}{*}{\(x_{l}^{p,j}\)} & It assumes value 1 if the CPRI and & \multirow{2}{*}{\(n_{\lambda,EH}^{p,j,k}\)} & Number of wavelengths needed to \\  & CPRI flows from \(AS_{ij}\) to CO & \multirow{2}{*}{\(n_{\lambda,EH}^{p,j,k}\)} & carry Ethernet flows in the \(k\)-th SI \\  & \((p=u)\) or from CO to \(AS_{ij}\) (\(p=d\)) are & & from \(AS_{ij,l}\) to CO \(AS_{ij,l}\) or \\  & routed on link \(l\); otherwise its value is 0 & & from CO to \(AS_{ij,l}\) (\(p=d\)) \\ \hline \multirow{2}{*}{\(n_{\lambda,CPRI}^{p,j,k}\)} & Number of wavelengths needed to & \multirow{2}{*}{\(N_{AS,VE,EH}^{p,j,k}\)} & Number of Ethernet flows (random \\  & carry Ethernet flows in the \(k\)-th SI & & variable) to be carried from \(AS_{ij,l}\) to \\  & from \(AS_{ij,l}\) to CO \(AS_{ij,l}\) or & & CO in the \(k\)-the SI \\  & from CO to \(AS_{ij,l}\) (\(p=d\)) & & \\ \hline \multirow{2}{*}{\(N_{AS,VE,PRI}^{p}\)} & Number of CPRI flows (random & \multirow{2}{*}{\(n_{\lambda,EH}^{p,j,k}\)} & \multirow{2}{*}{\(A_{u,r}\)} \\  & variable) to be carried from \(AS_{ij,l}\) to & & \\ \hline \multirow{2}{*}{\(n_{\lambda,VE,PRI}^{p,j,k}\)} & Number of wavelengths needed to & \multirow{2}{*}{\(n_{\lambda,VE,EH}^{p,j,k}\)} & Number of Ethernet flows (random \\  & carry Ethernet flows in the \(k\)-th SI & & variable) to be carried from \(AS_{ij,l}\) to \\  & from \(AS_{ij,l}\) to CO \(AS_{ij,l}\) or & & CO in the \(k\)-the SI \\  & from CO to \(AS_{ij,l}\) (\(p=d\)) & &We assume that the traffic offered to each sub-area is cycle-stationary with \(N=24\) stationary intervals modeling the daily traffic trend.