authors of [76] introduce the ADequacy Index (ADI), a traffic-agnostic metric, which depends on the algebraic connectivity, for quantifying the quality of a frugal topology. Two heuristic algorithms are proposed to create pruned topologies by removing links in some order until a given ADI threshold is reached. They differ on the order followed to remove the links. The first one relies on the algebraic connectivity, while the second on the betweenness centrality.
All the previously described works mainly tend to minimize the number of active network elements in the current topology restricting the path selection to meet some specific metric bound or connectivity rate according to the energy-aware routing, without properly address- ing the performance or traffic quality indicators. Moreover, their lack of awareness about the requirements of incoming connection requests can lead to performance degradations, which is highly undesired.
2.2
Energy Efficiency and Performance Concerns
While energy-aware routing solutions optimize the power efficiency finding the minimum number of active elements needed to support the concentrated traffic for all source-to-terminal requests, the performance of this remaining subnetwork in crucial parameters such as traffic delay and link utilization is more likely to be affected.
Precisely, the existing trade-off between energy saving and network performance is illustrated in the approach presented in [77]. This work presents Routing On Demand (ROD), an OSPF- based routing mechanism that considers energy saving and performance in terms of MLU. Using non-linear optimization approaches, authors formulate a problem that aims to minimize both the MLU and energy consumption of a network subject to capacity and flow conservation con- straints. After considering different scenarios, two stages are identified, namely power-sensitive and performance-sensitive each of them with a particular compromise between both metrics. They prove mathematically that, for each scenario, a set of link weights exist, under which routes derived from ROD can be converted into shortest paths and realized through OSPF. These link weights are the solution of their approach.
In this regard, there are several works that, in order to address performance concerns in the energy-aware routing problem, restrict the path selection to the ones that meet specific network metrics [53, 65, 78, 79].
For instance, authors in [78] propose a heuristic-based algorithm, Multiple Paths by Shortest Path First (MSPF), which aims to maximise the number of switched-off routers and cables subject to satisfying MLU and path length constraints. They consider links with bundled cables that can be switched off independently and demands are routed through one or more paths. Two versions of the algorithm are proposed, which differ in the type of network elements (links or nodes) that are first considered to be switched-off.
Similarly, the power-aware routing reported in [79] also takes into account the MLU con- straint. In this work the behavior of the overall power consumption achieved under different QoS requirements is studied. Specifically, the traffic transmission on the link was modeled as a M/M/1 queue (considering a service rate equal to the link capacity) and the analysis concerning the QoS requirements was carried out by varying the MLU factor between appropriate values that guarantee a low end-to-end delay.
Negative effects on signaling overhead and service quality experienced by traffic flows may be incurred in case of recurrent configuration changes. Following this idea, in [80] authors present an energy-aware management strategy that selectively turns off network devices considering a set of multiple traffic scenarios. Two single-path routing strategies are developed (i.e. a fixed and a variable routing), which include a penalty parameter for switch state transitions and an upper bound limiting the number of state changes of each network interface. Comparisons between both models suggest that the flexibility of the variable routing is beneficial for both congestion and consumption metrics. Moreover, the effects of restricting the number of times a network interface can be switched on are discussed. In this regard, it is shown that, compared with the conventional scheme, adding the card reliability constraint does not affect significantly the energy savings and prolongs the lifetime of equipments.
A different approach is introduced in [81], where authors analyze the increase in the number of control messages as a result of implementing energy-aware algorithms in an SDN controller. In particular, they model the problem as an ILP aiming to minimize the control overhead subject to an energy constraint that limits the total energy consumption of the network. Additionally, two polynomial-time heuristic algorithms are proposed to find near-optimal solutions for the problem. Finally, the existing trade-off between energy efficiency of green routing and the generated control overhead was validated in an SDN domain with a single controller.
2.2. Energy Efficiency and Performance Concerns
by network operators is naturally conditioned by the impact on other performance parameters. The work in [82] investigates the scope of the impact on route lengths and on fault tolerance. To do so, they propose a heuristic approach which iteratively tries to remove the edges that are less loaded. Simulation results show that the route lengths increase only 27% in average for almost all studied topologies. Meanwhile, to achieve fault tolerance fast switching-on technologies can be used or disjoint path constraints may be added to the problem.
Undoubtedly, network fault tolerance is one of the most concerning performance parameters that limits the deployment of energy-aware solutions. The disposition to put a network element into sleep mode is determined by the capability of the network to quickly react in case of failures. Authors of [83] discuss the trade-off between energy optimization and network reliability. They studied five existing green routing algorithms to analyze the impact of these proposed approaches on two reliability measures (terminal and route reliability). This work is extended in [84], where the authors formulate the Reliable Energy-Aware Routing (R-EAR) problem, which aims to switch off as many links as possible to optimize energy consumption, while guaranteeing the MLU and the required level of terminal reliability or route reliability. To solve this problem a heuristic algorithm is also provided.
The implications of achieving different levels of resiliency to failures and robustness to traffic variations for the network energy-aware efficiency are analyzed in [85]. To do so, two schemes are proposed: (i) optimization models minimizing the energy consumption of IP networks while guaranteing survivability and robustness; and (ii) suboptimal MILP-based heuristics exploiting variants of the original exact formulations. In particular, eight different protection/robustness strategies are considered combining the different features to quantitatively analyze the trade-off between energy cost and level of protection and robustness. It is shown that significant savings are achieved even when both survivability and robustness are fully guaranteed.
On the other hand, in some networking scenarios achieving energy saving does not neces- sarily affect negatively the network performance or its impact is tolerable. This is validated by the work presented in [54] where the average link utilization does not increase considerably as a consequence of the proposed green routing approach. By contrast, it is noted that the establishment of a maximum load bound on links may significantly limit the applicability of energy-aware techniques. This is due to the existence of low capacity access links which remain heavily loaded even under an energy-agnostic routing approach. Thus, reducing the maximum
link load may easily conduct to unfeasible solutions.
A similar analysis is conducted in [86], where authors investigate the impact of practical constraints on the performance of energy-aware routing schemes in SDN. For such purpose, the energy-aware routing problem is modeled as an ILP considering discreteness of link rates and limitation of flow rule space. Results confirm that the inclusion of these practical constraints has a major impact not only on the energy efficiency of SDN but also on routes length and links utilization.