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We compare these results in two instances that 1/3 node pairs have flows to transmit in Fig. 6, and 2/3 node pairs have flows to transmit in Fig. 7. For the two cases, we randomly generate node pairs 100 times and ran our algorithms 100 times to get the average value on a high-performance computer. In networks, the flows are dynamically generated, so the average value of 100 ex- periments is realistic and persuasive.

From Fig. 6, we can see the minimum percentage of SDN switch cost when fixed the proportion of the control flows. The Fig. 6 shows that, when we want to control 95% of the num- ber of flows, we need to upgrade only about 6% of the nodes to SDN switches. Similar to the results of Fig. 5, the Heuristic algo- rithm in Fig. 6 also outperform Degree-first algorithm and Random algorithm. Compared Fig. 6 to Fig. 7, the Heuristic algorithm can achieve good results whether 1/3 node pairs have flows or 2/3 node pairs have flows. In addition, the Fig. 6 and Fig. 7 show that the results of the algorithms are similar even in different topolo- gies. Moreover, the Heuristic is always better than Degree-first and Random in any case. Therefore, our algorithms are universal and extensive.

Since following the heavy-tailed distribution, the percentage of upgrading cost is relatively large when σ is equal to 100%.

6.3 Energy saving ratio using the scheme EPC.

We evaluate our solution EPC against the baseline schemes PLSP and EA-FA in network topologies. PLSP assumes that PLSPs are pre- defined, and ingress (IRs) and egress routers (ERs) are connected with each other by PLSPs. Active paths carry network traffic from IRs to ERs and passive paths stay in sleep mode. If controller wants to use them, it actives them by turning on network elements along the path. The main idea of Pre-established Label Switching Paths PLSP is move the traffic to a fewer number of paths. After adjust- ing the users’ traffic to reasonable paths, it put idle links and line- cards to sleep.

The scheme EA-FA [4] achieves energy efficiency only by per- forms optimizing traffic splitting ratio in SDN-enabled switches. In [4], they also put forward the scheme HEATE, but HEATE cannot be implemented in the networks. Because after deciding on the values of the weights, the scheme HEATE needs an automated system or a human operator to change the IGP configuration on one or more routers [14]. Fig. 8show energy saving ratio increasing with the de- ployment of SDNs for ISP 1755 and ISP 3967 network, respectively. The definition of energy saving ratio in our study is the ratio of formula (6a) computed by proposed scheme to which computed by traditional OSPF protocol. From Fig. 8, we can see that energy saving ratio of all schemes increase rapidly with the increase of deployed SDN-enabled switches in the network. The reason is that with the increase of SDNs, the central SDN controller can control more traffic flows and globally choose the optimal path for them to maximize energy saving. When the number of deployment SDNs is greater than a threshold, the variation of energy saving ratio be- comes relatively flat. This is because when the deployment of SDNs reaches a threshold, an approximately optimal energy saving flow allocation can be achieved. More SDN-enabled switches deployed into the network will make no obvious enhancement in energy saving. As we can see from the Fig. 8, the energy saving perfor- mance of the EPC always outperforms PLSP and EA-FA. Since EA-FA achieves energy efficiency only by performs traffic splitting ratio in SDN-enabled switches, the energy saving ratio is less than the scheme of PLSP when the number of SDN switches deployment is small. PLSP routing the flows by predefined fixed path that only connect ingress (IRs) with egress routers (ERs). Therefore, with the increasing of SDNs deployment, the energy saving ratio of EA-FA is large than PLSP. Seen from the whole view, EPC can save about 10% of the total power consumption on average when compared to the other solutions.

In this group of simulations, we adjust traffic load by chang- ing the number of flows in the network. As result shown in Fig. 9, with the increase of the traffic load in the network, energy saving ratio of all the algorithms are decrease. This is because larger traf- fic loads means that the forwarding needs more network elements. Thus, elements that can be closed become less. For all the volume of the traffic load, our scheme EPC is better than the other two scheme. When the flow is small, the difference between the differ- ent schemes is relatively large. Large traffic requires more network devices, so the number of links and switches that can be turned off is relatively small. Therefore, the gap of energy saving ratio is relatively small when the traffic load is large.

7 Conclusions and Further Work