## 6 Results
### Influence of Temporal Traffic Variation  
We first look at the influence of the ratio \(A_{min}^{a,b}/A_{max}^{a,b}\) on energy consumption of LCs (Figure 3) and \(AF_{avg}\) (Figure 4). As expected, energy consumption \(E_{total}^{EWA}\) increases when the traffic scaling factor is increased. For all the three scaling factors, energy consumption \(E_{total}^{EWA}\) increases also when the ratio \(A_{min}^{a,b}/A_{max}^{a,b}\) increases (see Figure 3a-c). When \(A_{min}^{a,b}/A_{max}^{a,b}=1.0\) the energy consumption tends to be equal to the one experienced by the SBN, since in this case no temporal traffic variation is imposed. As a result, the EWA is less effective in saving energy. This is particularly true for the most conservative configuration of EWA (i.e., a maximum utilization of the last lightpath \(\psi\) set to 0.5). In this case, the energy consumption of the network using EWA is identical to the energy consumption of the SBN already when the ratio \(A_{min}^{a,b}/A_{max}^{a,b}\) is set to 0.75 for all the three scaling factors. Moreover, \(AF_{avg}\) decreases when the ratio \(A_{min}^{a,b}/A_{max}^{a,b}\) is increased (Figure 4). For example, \(AF_{avg}=1\) when the ratio is set to 0.75 or higher in Figure 4c. This means that, in such cases, all the LCs are always powered on. As expected, \(AF_{avg}=1\) can be also observed for the SBN, since all LCs are in AM. Moreover, when the scaling factor is equal to 688.57 and the EWA parameter \(\psi\) is set to 0.9, \(AF_{avg}\) drops below 1 when \(A_{min}^{a,b}/A_{max}^{a,b}=1.0\). This effectively means that the lifetime of LCs is increased due to adoption of SM, thanks to the fact that different LCs are always kept in SM. In this case, in fact, a high lightpath utilization (even higher than the one used to design the SBN) is allowed. On the contrary, when the traffic variation is high (\(A_{min}^{a,b}/A_{max}^{a,b}=0.25\)), the energy consumption is reduced w.r.t. the one of SBN (Figure 3). However, this comes at the cost of increasing the AF (Figure 4) and therefore a lifetime decrease. Finally, we also confirm based on Figure 3 that more energy is consumed with the first EWA setting (\(W_{L}=0.1\), \(W_{H}=\psi=0.5\)) than with the second EWA setting (\(W_{L}=0.1\), \(W_{H}=\psi=0.9\)). This is due to the fact that with the second setting, the lightpaths can sustain higher utilization. In the next part, we vary the length of the set of low-demand time periods \(T_{low}\) in the range 0-7.5 h. Energy consumption \(E_{total}^{EWA}\) and \(AF_{avg}\) are shown in Figures 5 and 6, respectively. As expected, the longer the period when traffic is low, the lower the energy consumption. This can be observed for all the three scaling factors and the two EWA settings (with lower energy consumption achieved with the more liberal EWA setting). The length of the low-demand periods does not affect \(AF_{avg}\) as shown in Figure 6. This is due to the fact that traffic increases and decreases only once during the set of all considered time periods \(T\) (see Figure 1) even for \(|T_{low}|\) equal to 0. However, \(AF_{avg}\) values are consistently higher than 1. It is interesting to note that the \(AF_{avg}\) values are higher for the more conservative EWA setting. This is due to the fact that the targeted overprovisioning (\(\psi=0.5\)) leaves lower lightpath capacity for transporting traffic (with no unexpected variations). Given the same traffic and lightpath capacity \(C\) as input, the lightpath (and corresponding LCs) have to be more frequently activated/deactivated when \(\psi=W_{H}=50\%\) (corresponding to usable lightpath capacity 0.5-40 Gbps) than when \(\psi=W_{H}=90\%\) (corresponding to usable lightpath capacity 0.9-40 Gbps). We varied also the lengths of periods when traffic increases and decreases (\(T_{inc}\) and \(T_{dec}\)) in the range 0-3.75 h. Results in terms of energy consumption and \(AF_{avg}\) are shown in Table 2 for the scaling factor 1147.62.