# On the Evaluation of Complex Networks Designs for an Energy-Efficient IP/WDM Core Network
## 7 Results and Discussion  
The base evaluated network model is the NSF network, as illustrated in Figure 2, and consists of 14 nodes located in different states of the United States (US) with 21 bi-directional links and with an average shortest path of 2.175. As depicted in Figure 2, the nodes of the NSF are in four time zones: Eastern Standard Time (EST), Central Standard Time (CST), Mountain Standard Time (MST), and Pacific Standard Time (PST). There is a one hour difference between every two adjacent time zones. During the day and night, different nodes experience different traffic loads. Figure 9 illustrates the traffic load in Gb/s between all node pairs for a period of 24 h. The traffic is generated using a gravity model based on the population of the city where the node is located [14]. The average traffic load between node pairs varies between 20 to 120 Gb/s, and the peak occurs at 22:00. In this work, we follow assumptions made in [4] and assume that the traffic load between node pairs in the same time zone is random with a uniform distribution and no lower than 10 Gb/s [4]. Table 4 shows the parameters used in the MILP model, in terms of number of wavelengths, capacity of a wavelength, distance between two adjacent EDFAs, and the energy consumption of different components in the network such as the router's port, optical switch, multiplexer/demultiplexer, EDFA, regenerators, and transponders. The MILP solver program used is AMPL/CPLEX on Lenovo with core i7 CPU, with a 2.8 GHz processor and 8 GB RAM [19]. CPLEX and AMPL make a powerful modelling tool for solving optimization problems, developed by IBM and Bell laboratories, respectively [19]. Figure 9: Average traffic load in the four time zones [4]. Given the traffic between nodes in the NSFNET network as depicted in Figure 9, along with IP router ports power consumption in Table 4, it is clear that the power consumption of the IP routers is the major contributor to the total power consumption of the network. The power optimized topologies will be supported by the minimum number of IP router ports. Hence, after traffic being groomed on a minimum number of ports, unused router ports will be eliminated from the total network power calculations and considered as being in sleep mode. Multiple random experiments (around 15 experiments) were conducted to get different sample graph networks for each of the scale-free, random, and small-world network designs. Sample networks provided in Figures 3-5 are our best obtained graphs in terms of power consumption conservation. However, the mathematical MILP model for each sample gave the same results (optimum) regardless of the number of times the model was run for each topology. In this work, we show that a re-design of the topology interconnection can be undertaken to improve energy efficiency in IP over WDM core networks. As previously discussed in Section 4, the impact of the topology can greatly impact the average path length and clustering coefficient. In Section 4, we have demonstrated that a small change of rewiring probability creates shortcuts that can connect widely separated nodes, and consequently result in a significant reduction on the network diameter. In addition to network diameter, we have also shown that the design of the topology interconnection impacts the node's clustering coefficient, which is seen as a network property that indicates how weak or strong the ties between a node and its neighbors are. Reducing the diameter of a network while improving the clustering coefficient of the network's nodes can effectively reduce the network average path length and the number of nodes traversed during traffic forwarding. Consequently, the overall number of used links and network active components such as IP routers, EDFAs, regenerators, OXC, and transponders needed to support traffic demands are reduced.