## 6 Results
### Influence of Spatial Traffic Variation  
We focus on the spatial traffic variation fixing \(|T_{low}|=72\), \(|T_{high}|=144\), and \(|T_{inc}|=|T_{dec}|=36\) as well as both \(A^{a,b}_{min}\) and \(A^{a,b}_{max}\) based on traffic measurements (as explained in Section 5.1). EWA is executed on the scenarios with real TZM \(\Theta\) for different values of \(k\), different values of traffic scaling factor \(s\), and 5 randomly generated SVMs. In particular, we choose different values of \(k\) between 0 (corresponding to the case in which no time shift is set) and 144 (in which a maximum time shift of 12 h is enforced). Moreover, we consider the case of zero TZM (i.e., the case when all network nodes are assumed to be located in the same time zone and \(k=0\)) denoted as \"NO TZM\". Figure 9 reports the obtained results in terms of energy consumed by all LCs in the network over a day \(E^{EWA}_{total}\). Figure 10 reports the obtained results in terms of \(AF_{arg}\) over all LCs in the network after 14 days of network operation. In both cases, averages over all considered SVMs are reported (bar plots) and complemented with the maximum and minimum values (error bars).  
Figure 8: \(AF_{arg}\)with \(AF^{leap}=0.5\) units and \(\chi=0.5\) h/cycle after 14 days vs. the ratio \(A^{a,b}_{min}/A^{a,b}_{max}\) with fixed total load.  
Figure 7: Energy consumption \(E^{EWA}_{total}\)over a day vs. the ratio \(A^{a,b}_{min}/A^{a,b}_{max}\) with fixed total load.  
Figure 9: Average energy consumed by all LCs over a day over all SVMs in the Abilene-based network using two EWA settings. The error bars indicate the minimum and maximum values over all SVMs.  
Interestingly, it is possible to save energy for most values of the time displacement parameter \(k\). This can be clearly observed in the case of a scaling factor 688.57 (Figure 8(b)). Average energy consumption increases when traffic is scaled with the factor 1147.62 and when \(k\) becomes high (Figure 8(c)). This is caused by the existence of multiple shortest paths between some node pairs. In particular, EWA sometimes finds other shortest paths than the ones used in the SBN and therefore occasionally has problems with satisfying all the traffic demands. We have verified that unsatisfied demands never exceed 6%. EWA does not put LCs into SM in such cases, and therefore energy consumption is identical with that in the SBN (compare SBN in Figure 8(c) with the maximum energy consumption values for \(k\geq 72\)). This effect of occasional routing incompatibilities is even stronger when the scaling factor is low (see high and intermediate values of \(k\) in Figure 8(a)). On the contrary, it is always possible to save energy when no TZM is used and when \(k\) is equal to 0, i.e., when all demands have an off-peak zone occurring during the same hours (cf. Figure 1(a)) or when the peak times only depend on the time zone where nodes are located.  
Considering \(AF_{avg}\) (Figure 10), it is interesting to note that these figures are complementary to the energy figures, i.e., the lower the energy consumption, the higher the AF. \(AF_{avg}\) usually takes values between 1.2 and 2.5 meaning that energy saving reduces devices lifetime. For the cases in which EWA encounters routing incompatibilities, \(AF_{avg}\) decreases. This happens more frequently with increasing \(k\). In the cases when most LCs are constantly powered on (i.e., the energy consumption of the network using EWA is close to the one of the SBN), few power state reconfigurations are introduced, resulting in an AF close to 1 (see, e.g., the case for \(k=144\) in Figure 9(a) for \(W_{L}=0.1\) and \(W_{H}=\psi=0.5\)).