# On the Evaluation of Complex Networks Designs for an Energy-Efficient IP/WDM Core Network
## 1 Introduction  
Over the past decade, the growth of internet traffic has significantly contributed to the increase in the amount of backbone network equipment required and the capacities of such equipment [1]. This growth has resulted in an increase in the running cost and energy consumption. Energy consumption rather than cost has been considered as a major concern as it has been found to be a contributor of greenhouse gases which have a great impact on the environment. Recently, many research efforts have been devoted to greening the internet to reduce its carbon footprint and impact on the environment [2, 3]. In [1], a MILP optimization model and energy efficient heuristics were developed to reduce power consumption for the IP over WDM networks. Results have shown that savings ranging from 25% to 45% can be achieved with the bypass Light path in comparison to the non-bypass. In [4], the authors developed a MILP model to optimize the physical topology of the National Science Foundation (NSF) network topology with the objective of reducing total network power consumption considering the different approaches, nodal degrees, and topologies. Authors in [4] also investigated the full mesh and star topologies and have shown significant savings in power that reach 95% and 92%, respectively. In [4], the authors have considered the use of renewable energy to reduce energy consumption and hence reduce the emissions ofgreenhouse gases. The authors in [4] have also studied the adaptive link rates for different loads and its impact on the total power consumption. Results have demonstrated that with the use of renewable energy and adaptive rates, energy savings can reach 65%. In [5], the authors studied and investigated means of reducing the power consumption of IP over WDM networks with data centers. Authors have developed an MILP model to optimize the location of data centers and found that the routing approach, topology design, and number of data centers are the main factors that control the percentage of power savings that can be achieved while optimizing the locations of data centers. The authors in [5] demonstrated that savings in energy consumption can be up to 73% if data centers are located near the renewable energy sources and a replication scheme is considered. In this study, for the achievement of more power savings on top of previously proposed approaches, we implement the MILP model developed in [1] to evaluate the NSF network with highly connected topology designs, such as the small-world, scale-free, and random complex networks to reduce energy consumption by efficiently utilizing communication links, router ports, and paths through means of grouping and consolidation. The main contributions of our research are summarized as follows:  
* We investigated network-related factors/properties including the clustering coefficient, network diameter, average path length, and their impact on overall network power consumption in IP over WDM networks. * We improved the clustering coefficient and diameter of the NSFNet. The clustering coefficient indicates how good a node is connected to its neighbors' neighbors. A high clustering coefficient indicates that the network is composed of many strong ties. Our results demonstrated a 246% increase in the clustering coefficient when compared with the current NSF design. * We improved the NSFNet path length. Our results, as shall be illustrated in a subsequent section, demonstrated that a reduction of 15% in the NSF network path length can be achieved with a small-world network design with \(p=1\). * The contribution of backbone networks to the total network power consumption is increasing significantly with the growing popularity of bandwidth-intensive applications. This growth has resulted in an increase in the running cost and energy consumption. Energy consumption, rather than cost, has been considered as a major concern as it has been found to be a contributor of greenhouse gases which have a great impact on the environment.