## 5 Evaluation Scenario
### Traffic and Network  
We consider the traffic measured on the Abilene network composed of 12 nodes and 15 physical supply links [35; 36]. The traffic data \(\hat{d}_{a,b}(t)\) covers the set of periods \(\hat{T}\) from 1 March 2004 at 00:00 a.m. until 10 September 2004 at 11:55 p.m. with the granularity \(\hat{\Delta}t=5\,\mathrm{min}\), for a total of 48,096 saved traffic matrices (7776 traffic matrices are missing in [35; 36]). The minimum and maximum values \(A_{min}^{a,b}\) and \(A_{max}^{a,b}\) needed for each traffic demand \(\tilde{d}_{a,b}(t)\) in the model from Equation (1) are computed as follows:  
\[A_{min}^{a,b}=s\cdot\mathrm{avg}_{(i,j)\in V^{2}}\left\{\begin{matrix} \mathrm{percentile}_{\mathrm{20}}\left\{\hat{d}_{ij}(t)\right\}\right\}/ \mathrm{avg}_{(i,j)\in V^{2}}\left\{\mathrm{median}_{t\in\hat{T}}\left\{\hat {d}_{ij}(t)\right\}\right\}\cdot\mathrm{median}_{t\in\hat{T}}\left\{\hat{d}_ {ab}(t)\right\}\quad\text{(bps)}, \tag{9}\]  
\[A_{max}^{a,b}=s\cdot\mathrm{avg}_{(i,j)\in V^{2}}\left\{\begin{matrix} \mathrm{percentile}_{\mathrm{20}}\left\{\hat{d}_{ij}(t)\right\}\right\}/ \mathrm{avg}_{(i,j)\in V^{2}}\left\{\mathrm{median}_{t\in\hat{T}}\left\{\hat {d}_{ij}(t)\right\}\right\}\cdot\mathrm{median}_{t\in\hat{T}}\left\{\hat{d}_ {ab}(t)\right\}\quad\text{(bps)}, \tag{10}\]  
where \(s\) is a scaling factor to account for increased traffic demands with respect to the time when the original traffic matrices were captured. Usage of percentiles and medians is motivated by unusual values or measurement errors occasionally present in the traffic data \(\hat{d}_{a,b}(t)\) from [35; 36]. Three values of the scaling factor \(s\) (229.52, 688.57, and 1147.62 [32; 33] (chosen for consistency reasons, i.e., the same values were used in [32; 33], where total traffic demand during network design phase was set to 100, 300 and 500 Gbps per node) are applied to the original traffic data \(\hat{d}_{a,b}(t)\) from [35; 36]. This corresponds to 85, 254, and 423 Gbps, respectively, of traffic generated at each node (maximum total demand for the artificially generated sets of traffic matrices). Furthermore, we set the period length for the traffic matrices generated with our model as \(\Delta t=\hat{\Delta}t=5\,\mathrm{min}\), and cover daily traffic, what corresponds to 288 traffic matrices (each covering 5 minutes) in a single set \(T\). We vary the following parameters in our traffic model (summarized in Table 1). Focusing on temporal traffic distribution, we vary first the ratio \(A_{min}^{a,b}/A_{max}^{a,b}\) keeping it fixed over all node pairs \((a,b)\in V^{2}\). More precisely, we keep the values for \(A_{max}^{a,b}\) according to statistics taken from measurements as explained above, and vary \(A_{min}^{a,b}\) to be a fraction {0.25, 0.5, 0.75, 1.0} of it. Second, we vary the total length of the set of low-demand time periods \(T_{low}\) keeping the lengths of \(T_{inc}\) and \(T_{dec}\) fixed. In other words, when the length of \(T_{low}\) is increased (decreased), the length of \(T_{high}\) is decreased (increased). Third, we vary the pace of traffic increase and decrease by changing the lengths of periods when traffic increases and decreases (\(T_{inc}\) and \(T_{dec}\) respectively, see Figure 1). Fourth, we vary again the ratio \(A_{min}^{a,b}/A_{max}^{a,b}\), but this time we keep the total load \(\sum_{t\in T}\sum_{(a,b)\in V^{2}}a_{a,b}(t)\) in the network fixed. This requires modification (compared to the values taken from measurements) of two parameters of the traffic model (Equation (1)), i.e., \(A_{min}^{a,b}\) and \(A_{max}^{a,b}\). This is achieved by modifications of the ratios of averages in Equations (9) and (10). Focusing on spatial traffic variation, we fix \(|T_{low}|=72\), \(|T_{high}|=144\), and \(|T_{inc}|=|T_{dec}|=36\). This choice corresponds to 6 h, 12 h, and 3 h, respectively, as well as to the values shown in Figure 1 (except for the time granularity). In order to study the spatial traffic variation, we have to assume a