## Appendix A
\begin{table}
\begin{tabular}{c c l} \hline \hline
**Symbol** & **Description** \\ \hline \(G=(V,E)\) & undirected physical supply network with set of nodes \(V\) and set of physical supply links \(E\subseteq\{\{i,j\}\subseteq V^{2}:i\
eq j\}\) \\ \(H=(V,L)\) & undirected logical supply network with set of nodes \(V\) and set of logical supply links \(L\subseteq\{\{i,j\}\subseteq V^{2}:i\
eq j\}\) \\  & \(C\) & capacity of a lightpath \\  & \(B\) & number of wavelengths per fiber \\  & \(P\) & set of all (undirected) paths through \(G\) on which capacity modules can be installed \\  & \(P_{i}\) & set of all paths from \(P\) where one of the end nodes is \(i\in V\) \\  & \(P_{i,j}\) & set of all paths from \(P\) whose end nodes are the end nodes of \((i,j)\in L\) \\  & \(P_{e}\) & set of all paths from \(P\) that traverse physical supply link \(e\in E\) \\  & \(N\) & set of routers that can be installed in the network \\  & \(R_{n}\) & capacity of router \(n\in N\) \\  & \(\delta\) & maximum lightpath utilization, \(\delta\in(0,1]\) \\  & \(\kappa^{\text{oxc}}\) & CapEx cost of installing an Optical Cross-Connect (OXC) \\  & \(\kappa^{\text{ipr}}_{n}\) & CapEx cost of installing router \(n\in N\) \\  & \(\kappa^{\text{ip}}\) & CapEx cost of installing a lightpath with Line Cards (LCs) \\  & \(\kappa^{\text{f}}_{e}\) & CapEx cost of installing a fiber on physical supply link \(e\in E\) \\ \hline \multirow{4}{*}{**Symbol**} & \(W_{L}\) & threshold on the utilization of the last lightpath on a logical link to trigger attempts to \\  & \(W_{H}\) & threshold on the utilization of the last lightpath on a logical link to trigger attempts to \\  & \(\psi\) & maximum utilization of the last lightpath on a logical link, \(\psi\in(0,1]\) \\  & \(X^{LC}_{i}\) & number of LCs installed at node \(i\in V\) \\ \hline \multirow{4}{*}{**Symbol**} & \(T\) & set of considered time periods in the proposed traffic model \\  & \(\hat{T}\) & set of time periods covered by traffic measurements \\  & \(T_{low}\) & set of time periods with low traffic, \(T_{low}\subseteq T\) \\  & \(T_{high}\) & set of time periods with high traffic, \(T_{high}\subseteq T\) \\  & \(T_{inc}\) & set of time periods with increasing traffic, \(T_{inc}\subseteq T\) \\  & \(T_{dec}\) & set of time periods with decreasing traffic, \(T_{dec}\subseteq T\) \\  & \(\Delta t\) & length of each time period \(t\in T\) \\  & \(\hat{\Delta}t\) & length of each time period \(t\in\hat{T}\) \\  & \(A^{ab}_{max}\) & maximum traffic demand value for the node pair \((a,b)\in V^{2}\) in the proposed traffic model \\  & \(A^{ab}_{min}\) & minimum traffic demand value for the node pair \((a,b)\in V^{2}\) in the proposed traffic model \\  & \(\hat{d}_{a,b}(t),d_{a,b}(t)\) & traffic demand between the ordered node pair \(a,b\in V^{2}\) during time period \(t\in T\) \\  & \(d_{a,b}\) & maximum traffic demand between the ordered node pair \(a,b\in V^{2}\) (Equation (8)) \\  & \(d^{+}_{i},d^{-}_{i}\) & maximum emanating (ending) traffic demand at node \(i\in V\) (Equation (A11)) \\  & \(\hat{d}_{a,b}(t)\) & measured traffic demand between the ordered node pair \(a,b\in V^{2}\) during time period \(t\in\hat{T}\) \\  & \(s\) & scaling factor to account for increased traffic demands with respect to the time when \\  & & the original traffic data \(\hat{d}_{a,b}(t)\) was captured \\  & \(\Theta\) & Time Zone Matrix (TZM) with \(\theta_{a,b}\) denoting an element of the TZM \(\Theta,(a,b)\in V^{2}\) \\  & \(\Gamma\) & Spatial Variation Matrix (SVM) with \(\gamma_{a,b}\) denoting an element of the SVM \(\Gamma\), \((a,b)\in V^{2}\) \\  & \(k\) & time displacement parameter, \(k\in\{1,\ldots,|T|-1\}\) \\  & \(\zeta_{a,b}\) & number of time periods by which the demand between nodes \((a,b)\in V^{2}\) is shifted temporally due to spatial traffic variation \\ \hline \multirow{4}{*}{**Symbol**} & \(\pi^{\text{ip}}\) & power of a LC (W) \\  & \(AF^{sleep}\) & ratio between the failure rates of an LC dynamically switched between sleep and active \\  & \(\chi\) & weight for the frequency of the active-sleep-active mode cycles of a LC (h/cycle) \\  & \(r_{MTR}\) & Mean Time To Repair (MTTR) of a LC (h) \\  & \(r_{FR}\) & Failure Rate (FR) of a LC (failure/h) \\  & \(r_{Wh}\) & cost of energy (USD/Wh) \\  & \(r_{CM}\) & hourly rate of a reparation crew member (USD/h/period) \\ \hline \hline \end{tabular}
\end{table}