## 5 Description of the Heuristics
### Second Phase: Maximum Edge Disjoint Path Problem (MEDPP)--Greedy Heuristics
Figures 8 and 9 present the results for the Multistart Ad-Hoc heuristic in phase 2. It is important to notice here that the amount of flows or activations that are scheduled is larger than that obtained with the Simple heuristic. Although the time required is larger, the possibility of scheduling more flows or activations is important as it is a figure of merit of the system. Clearly, the amount of energy saved in these cases is lower; however, this is related to the fact that the network is busy for a longer time. ## 7 Discussion

The experimental results presented in the previous section show the complexity of the problem we are attempting to solve. The first aspect to mention is that the ILP model and its exact solution through solvers, like CPLEX, is not possible in a reasonable time when the problem grows in some of its variables. The second aspect to mention is that the heuristics used, although they are really simple, provide good results. There is a trade off between the complexity of the heuristic and the time required to find a schedule. The results show

Figure 8: Multistart ad-hoc heuristic, flow scheduling. Figure 9: Multistart ad-hoc heuristic, activation scheduling. that, with more iterations in the second and third phases, more flows or activations can be feasible. Clearly, this implies more energy demand. However, the main objective of the optimization process is to send as many flows or activations as possible consuming as less energy as possible; however, the second objective is a subsidiary of the first. The best results are obtained with Multistart Ad-Hoc and 50 iterations in the last phase. However, with 20 iterations, the results are similar, less than 1% improvement, and they are obtained in about two thirds of the time. In general, in the figures it is not possible to discriminate between the results obtained with 20 or 50 iterations; thus, it is reasonable to think that it is enough to perform up to 20 iterations in the last phase. With high bandwidth demands to the servers, from 0.8 to 1, not all flows or activations can be scheduled on time. This is related to the interference that flows imposed within destination servers that produce priority inversions at the source servers. In relation to the energy saving, with high utilization factors and a large amount of flows to schedule, there is as much as 5% saving. This is a consequence of the need to use all possible paths to transmit the flows on time. With a few servers and flows, the energy saving is more significant; however, in this case, the flows have a large duty-cycle but likely require less paths. The computation time of the schedule is a key issue. The benefits of doing a proper schedule with energy saving have to be measured in relation to the delay in beginning the processing demand by servers. The use of this kind of policies can be applied when the dynamic of the system is such that setting the paths in the DCN represents a small amount of the time the system will operate in that configuration. Considering a 30 [s] computation time for 1000 flows between 12 eight servers, this implies for 10% overload in scheduling, dynamics of 300 [s] or five minutes, and with 1% overload, dynamics of 3000 [s] or fifty minutes. In the case that the system does not change its demand for five minutes, the cost of scheduling the flows is about 10%; however, if the time is extended to fifty minutes, the cost of scheduling the system is about 1%, which is quite reasonable. #### 3.2.2 Becoming Real

The use of DCNs is common today in management areas within governments, banks, universities, military, business and health systems, among others. They rely on the operation of networks of servers where all the information is stored. Different requirements are associated, such as security, availability, reliability, latency and, most importantly, the costs of implementation and maintenance.