+ D Toratani

D Delahaye
email: delahaye@recherche.enac.fr

S Ueno
email: s-ueno@ynu.ac.jp

T Higuchi
email: higuchi@ynu.ac.jp

[EN-A-010] Merging Optimization Method with Multiple Entry Points for Extended Terminal Maneuvering Area

Keywords: Merging Optimization, E-TMA, Optimal Control, Mixed-Integer Linear Programming

To implement the Continuous Descend Operation (CDO) to the high-density flow, Flight-deck Interval Management (FIM) is proposed by some researchers. To enhance the FIM, the merging optimization method with the multiple entry points for the Extended Terminal Maneuvering Area (E-TMA) is developed in this study. The simultaneous optimization method for trajectory and sequence is employed as the merging optimization method. The simultaneous optimization method is able to optimize the trajectory and the sequence simultaneously by introducing the criterion function which expresses the relation between the terminal time and the value of the criterion of the trajectory. However, the simultaneous optimization method for trajectory and sequence is not enough for the merging optimization method for the E-TMA, because aircraft enter the TMA from some entry points to merge the arrival flow, and the previous method is able to treat only one merging point. To enable the simultaneous optimization method to treat the multiple entry points, the criterion function is modified in this paper. The ability of the proposed method is demonstrated by the simulations. The simulation results show the merging optimization method is able to optimize the merging with the multiple entry points.

INTRODUCTION

Continuous Descent Operation (CDO) is the one of the hot topics in the field of the Air Traffic Management (ATM) [START_REF] Robinson | Benefits of Continuous Descent Operations in High-Density Terminal Airspace Under Scheduling Constraints[END_REF]. The CDO is expected to be able to reduce fuel consumption and noise pollution. However, the CDO is currently applied to only low-density air traffic flow to avoid conflicts between aircraft. To implement the CDO in high-density flow, the autonomous arrival flow control system as Flight-deck Interval Management (FIM) is developed. The FIM is the one of the airborne time separation system utilizing Aircraft Surveillance Applications System (ASAS). Itoh et al. developed the FIM for the arrival flow with the CDO and demonstrated the ability of the FIM in practical simulations [START_REF] Itoh | Applying Flight-deck Interval Management based Continuous Descent Operation for Arrival Air Traffic to Tokyo International Airport[END_REF].

To enhance the FIM, the merging optimization method is useful. Before the aircraft take the arrival flow, the aircraft fly from various directions to the merging point to make the sequence. Then, the aircraft must merge keeping the minimum time interval to avoid wake turbulence. If the sequence keep the minimum time interval at the merging point by the merging optimization method, it is easy for the FIM to keep the time interval in the arrival flow. Therefore, the merging optimization method is developed in this study. The merging optimization method optimizes the trajectories outside the Terminal Maneuvering Area (TMA). This area is called Extended TMA (E-TMA), and the image of the E-TMA is shown in Fig. 1. In this study, the merging optimization for the E-TMA is developed to enhance the FIM.

There are some previous studies with respect to the merging optimization method. However, these studies have problems to implement to the practical air traffic control. These problems are roughly classified as shown below.

 Some studies are not able to optimize trajectory and sequence simultaneously [START_REF] Zhou | Optimization of Arrival and Departure Routes in Terminal Maneuvering Area[END_REF]. Mathematically, trajectory is continuous system, and sequence is discrete system. Therefore, it is difficult to optimize them simultaneously.  Others are not able to treat the nonlinear model [START_REF] Chen | Sequential Dynamic Strategies for Real-Time Scheduling of Terminal Traffic[END_REF]. One of the solution to optimize the trajectory and the sequence simultaneously is to employ Mixed-Integer Linear Programming (MILP). The MILP is able to treat both real numbers and integers. Accordingly, the MILP is able to optimize both the continuous and discrete system simultaneously. Generally, the commercial aircraft model is formulated as the nonlinear function, for example, Base of Aircraft Data (BADA) developed by EUROCONTROL [START_REF] Eurocontrol | User Manual for the Base of Aircraft Data (BADA) revision 3.10[END_REF]. However, the MILP is able to treat only linear function. In the previous studies, the aircraft is modeled as the simple vehicle model.

To resolve these problems, the authors developed the simultaneous optimization method for trajectory and sequence [START_REF] Toratani | Simultaneous Optimization Method for Trajectory and Sequence for Receding Horizon Guidance in Terminal Area[END_REF]. This method combines the optimal control and the MILP to optimize the trajectory and the sequence simultaneously. Employing the optimal control to optimize the trajectory, the method is able to treat the nonlinear functions. By the simulation, it is confirmed that the simultaneous optimization method is able to optimize the trajectory and the sequence simultaneously.

However, the simultaneous optimization method for trajectory and sequence is not enough for the merging optimization method for the E-TMA. That is why the E-TMA has several entry points (These points is called merging points in the simultaneous optimization method.) to the TMA as shown in Fig. 1, but in Ref. [START_REF] Toratani | Simultaneous Optimization Method for Trajectory and Sequence for Receding Horizon Guidance in Terminal Area[END_REF], the merging point was only one. In the E-TMA, it is better for the red aircraft to enter the TMA form the left entry point, but it may be optimal for the red aircraft to enter from the right entry point depending on the conditions as rough weather and congestion. Accordingly, the simultaneous optimization method for trajectory and sequence is improved to the merging optimization method with the multiple entry points in this paper.

This paper is composed of 5 sections. Section 2 presents the trajectory optimization method for single aircraft. Section 3 presents the merging optimization method for the E-TMA. Section 4 shows the simulations. Section 5 presents the conclusion the future plans.

TRAJECTORY OPTIMIZATION MTHOD FOR SINGLE AIRCRAFT 2.1. Aircraft Model

In this study, the BADA is employed as the aircraft model. Generally, the model is represented as the differential equation whose independent variable is time. However, to treat the temporal constraint along with the spatial constraint, the space-time coordinate system (STCS) is employed in this study [START_REF] Toratani | A Study on Optimal Conflict-Free Trajectory for Climbing Aircraft in Terminal Area[END_REF]. In the STCS, the time is treated as the state variable, and the independent variable of the differential equation is the length of the trajectory. The aircraft model based on the BADA in the STCS is formulated as shown below.

where 𝑠 denotes the length of the trajectory in the STCS, 𝜓 𝑠 denotes the spatial angle which is same as the azimuth angle, 𝜓 𝑡 denotes the temporal angle which represents the velocity in the STCS, 𝑥 and 𝑦 are the position of the aircraft, 𝐻 𝑝 denotes the pressure altitude, 𝑔 0 denotes the gravitational acceleration, 𝛾 denotes the flight path angle, 𝜙 denotes the roll angle, , 𝑚 denotes the mass of the aircraft, 𝑇ℎ𝑟 denotes the thrust, and 𝐷 denotes the drag. 𝐷 is defined as shown below.

𝐷 = 𝐶 𝐷0 𝜌𝑉 𝑇𝐴𝑆 2 𝑆 2 + 𝐶 𝐷2 2𝑚 2 𝑔 0 2 𝜌𝑉 𝑇𝐴𝑆 2 𝑆cos 2 𝜙 , (2)
where 𝐶 𝐷0 and 𝐶 𝐷2 denote the drag coefficient provided by the BADA, 𝑉 𝑇𝐴𝑆 is the true air speed, and the 𝑆 denotes the wing reference area. 𝜌 denotes the air density and defined as shown below.

𝜌 = 𝑝 0 𝑅𝑇 0 (1 + 𝛽 𝑇 0 𝐻 𝑝 ) -1- 𝑔 0 𝛽𝑅 , (3)
where 𝑝 0 denotes the standard pressure, 𝑅 denotes the real gas coefficient, 𝑇 0 denotes the standard temperature, and 𝛽 denotes the temperature gradient with the altitude. 𝑇ℎ𝑟 is defined in the BADA as shown below.

𝑇ℎ𝑟 𝑐𝑙 = 𝐶 𝑇𝑐1 (1 - 𝐻 𝑝 𝐶 𝑇𝑐2 + 𝐶 𝑇𝑐3 𝐻 𝑝 2 ), (4)
𝑇ℎ𝑟 𝑑𝑒𝑠 = 𝐶 𝑇𝑑𝑒𝑠 𝑇ℎ𝑟 𝑐𝑙 , (5)
𝑇ℎ𝑟 𝑐𝑟 = 𝐷, (6)
where the subscripts cl, des, and cr denote climb, descent, and cruise phase respectively,𝐶 𝑇𝑐1 , 𝐶 𝑇𝑐2 , and 𝐶 𝑇𝑐3 denote the maximum climb thrust coefficient, and 𝐶 𝑇𝑑𝑒𝑠 denotes the descent thrust coefficient. The fuel flow is derived by the following equation.

𝐹𝐹 = 𝐶 𝑓1 (1 + 𝑉 𝑇𝐴𝑆 𝐶 𝑓2 ) 𝑇ℎ𝑟, (7)
where 𝐶 𝑓1 , 𝐶 𝑓2 denote the thrust specific fuel consumption coefficient. Here, the cruise fuel flow is corrected as shown below.

𝐹𝐹 𝑐𝑟 = 𝐶 𝑓𝑐𝑟 𝐹𝐹, (8)
where 𝐶 𝑓𝑐𝑟 denotes the cruise fuel flow correction coefficient.

Optimal Control for Trajectory Optimization

In this study, the model as shown in 2.1. is employed to optimize the trajectory. The objective function is set as the fuel flow to calculate the minimum fuel consumption trajectory. To optimize the trajectory, the optimal control is employed. The optimal control problem is transformed to the Two Point Boundary Value Problem (TPBVP), and the optimal trajectory is derived by solving the TPBVP [START_REF] Bryson | Applied Optimal Control: Optimization, Estimation, and Control[END_REF].

MERGING OPTIMIZATION METHOD FOR EXTENDED TERMINAL AREA 3.1. Simultaneous Optimization Method for Trajectory and Sequence

In this section, the summary of the simultaneous optimization method for trajectory and sequence is explained. To optimize the trajectory and the sequence, criterion function is introduced in this method. Fig. 2 shows the image of the criterion function. In the left figure of Fig. 2, the horizontal axis denotes time, and the vertical axis denotes the distance from the initial position to the merging point. When one trajectory is optimized without constraints with respect to the terminal time, the trajectory is optimal with respect to the terminal time 𝑡 𝑓 , where the optimal terminal time is denoted as 𝑡 𝑓𝑜𝑝𝑡 . Then, the value of the criterion of the trajectory 𝐽 is minimized with respect to 𝑡 𝑓 as the blue circle in the right figure of Fig. 2, where the optimal value of the criterion is denoted as 𝐽 𝑜𝑝𝑡 . When the trajectory is optimized with specified terminal time constraints as earlier or later than 𝑡 𝑓𝑜𝑝𝑡 . Then, the value of the criterion will increase. Here, the function 𝑓 𝐽 (𝑡 𝑓 ) which expresses the relation between 𝑡 𝑓 and 𝐽 is called criterion function in this method.

When three aircraft are in the airspace, the trajectories and the criterion functions are expressed as Fig. 3. Then, all aircraft must keep the minimum time interval ∆𝑡 𝑚𝑖𝑛 . Therefore, the merging optimization problem is transformed to the problem to minimize the sum of the value of the criterion keeping ∆𝑡 𝑚𝑖𝑛 in Fig. 3. This optimization problem is formulated as shown below.

where 𝑁 𝐴𝐶 denotes the number of the aircraft. Eq. ( 9) includes "or", and it is difficult to solve this kind of the problem. To solve the problem formulated as Eq. ( 9), the constraints with respect to the minimum time interval is transformed to Eq. ( 10).

-𝑡 𝑓𝑝 + 𝑡 𝑓𝑞 -𝑀𝑐 1 ≤ -∆𝑡 𝑚𝑖𝑛 and 𝑡 𝑓𝑝 -𝑡 𝑓𝑞 -𝑀𝑐 2 ≤ -∆𝑡 𝑚𝑖𝑛 and ∑ 𝑐 𝑘

2 𝑘=1 = 1 (𝑝, 𝑞 = 1, ⋯ , 𝑁 𝐴𝐶 | 𝑝 < 𝑞), (10)
where 𝑝 and 𝑞 denote the index of the aircraft, 𝑀 denotes the positive number that is much larger than any value in the problem, and 𝑐 denotes the binary variable. Eq. ( 10) is formulated as the linear inequalities. Therefore, the MILP is able to treat Eq. ( 10). Here, the criterion function is nonlinear function, and the MILP is able to treat the only linear function. To enable the MILP to treat the criterion function, the criterion function is piecewise-linearized as Eq. ( 11) and Fig. where 𝑎 and 𝑏 are the slope and the intercept of the piecewise-linear function, 𝑒 denotes the binary variable, and 𝑁 𝑠𝑒𝑐 denotes the number of the piecewise-linearizing section of the criterion function. Then, the optimization problem as Eq. ( 9) is transformed to the linear equations and inequalities. This formulation is able to be optimized by the MILP. The form of the MILP is shown below.

min 𝑥 𝑓 𝑇 𝑥 subject to: 𝐴𝑥 ≤ 𝑏 𝐴 𝑒𝑞 𝑥 = 𝑏 𝑒𝑞 𝑙 𝑏 ≤ 𝑥 ≤ 𝑢 𝑏 𝑥 𝑖𝑛𝑡 ∈ ℤ 𝑥 𝑖𝑏𝑖𝑛 ∈ {0,1} (12)
In the simultaneous optimization method for trajectory and sequence, the criterion function is derived by the trajectory optimization, and the optimal terminal times for all aircraft keeping ∆𝑡 𝑚𝑖𝑛 is derived by the MILP. Afterward, the all trajectories are reoptimized with the optimal terminal times to derive the optimal merging.

Multiple Entry Points

In this paper, the simultaneous optimization method for trajectory and sequence is improved to enable to treat the multiple entry points. In the previous study, the merging point was only one, and the merging point is set as the entry point in the merging optimization method for the E-TMA. Fig. 5 shows the image of the merging optimization problem with the multiple entry points. In Fig. 5, it is better for the red aircraft to enter the TMA from the left entry point, but it may be better to enter from the right entry point depending on the condition, for example rough weather and congestion. It is better that the selection of the entry points is also optimized with the trajectory and the sequence simultaneously, because it depends on the conditions that the entry points from which to enter is better. Therefore, the entry point optimization problem is also introduced to the merging optimization problem. To introduce the entry point optimization, the criterion function is modified as shown Fig. 6. In Fig. 6, the red aircraft has the two criterion functions for the left and right entry points. Selecting either entry point, the aircraft merge to one flow finally, and the aircraft must keep the minimum time constraints. The two criterion functions are not connected. Therefore, the aircraft selects the one criterion function by the MILP. Then, the selection of the entry points is also optimized.

By this modification, the simultaneous optimization method for trajectory and sequence is improved to the merging optimization method with the multiple entry points. Then, the merging optimization method is able to be applied to the E-TMA.

SIMULATIONS

The ability of the merging optimization method with the multiple entry points is demonstrated by the simple simulations. In this simulations, some aircraft enter the E-TMA and enter the TMA form entry points. The obstacle as storm is set to demonstrate the entry point optimization. Without the entry point optimization, namely all the entry points are specified, the red aircraft takes roundabout trajectory to avoid the obstacle and enter the TMA from the left entry point as Fig. 7. On the other hand, with the entry point optimization, the red aircraft enter the TMA from the right entry point as Fig. 8. Selecting the right entry point by the entry point optimization, the trajectory of the red aircraft is smoother than the trajectory optimized without the entry optimization. By the simulations, it is confirmed that the merging optimization method is able to treat the merging problem with the multiple entry points. Then, the trajectory, the sequence, and the entry point are optimized simultaneously.

CONCLUSION AND FUTURE PLANS

To enhance the ability of the FIM, the merging optimization method for the E-TMA is developed in this paper. The simultaneous optimization method for trajectory and sequence is applied to the merging optimization method. Employing the simultaneous optimization method, the merging optimization method is able to optimize the trajectory and the sequence simultaneously and treat the nonlinear function as the model of the aircraft. The aircraft is modeled based on the BADA, and the fuel consumption is minimized by the optimal control. To enable the merging optimization method to treat the entry point optimization, the criterion function is modified.

By the simple simulation, the ability of the merging optimization method for the E-TMA is demonstrated. In this paper, two simulations are held. One is the case without the entry point optimization, and another is the case with the entry point optimization. In the simulation, the obstacle is set as storm. Without the entry point optimization, the aircraft takes the roundabout trajectory to avoid the obstacle and enter the specified entry point. On the other hand, with the entry point optimization, the aircraft is able to enter the TMA from better entry point. The merging optimization method for the E-TMA is able to treat the multiple entry point in the simulations. By the merging optimization method, not only the trajectory and the sequence but also the entry point is optimized simultaneously.

In this paper, only the simple simulations are held. Therefore, the future plans on this study are more practical simulations and the quantitative evaluation of the optimization method. Especially, the effect of the entry point optimization with respect to the fuel consumption will be evaluated.

Figure 1

 1 Figure 1 Image of the E-TMA.

  𝐽 𝑖 = 𝑓 𝐽𝑖 (𝑡 𝑓 𝑖) (𝑖 = 1, ⋯ , 𝑁 𝐴𝐶 ) 𝑡 𝑓𝑖 -𝑡 𝑓𝑖+1 ≥ ∆𝑡 𝑚𝑖𝑛 or 𝑡 𝑓𝑖+1 -𝑡 𝑓𝑖 ≥ ∆𝑡 𝑚𝑖𝑛 (𝑖 = 1, ⋯ , 𝑁 𝐴𝐶 -1),

1 (Figure 2

 12 Figure 2 Trajectories and criterion function.Figure 3 Criterion functions of 3 aircraft.

Figure 3

 3 Figure 2 Trajectories and criterion function.Figure 3 Criterion functions of 3 aircraft.

Figure 4 ?Figure 5

 45 Figure 4 Piecewise-linearized criterion function.

Figure 6

 6 Figure 6 Criterion function for multiple entry points.

Figure 7

 7 Figure 7 Simulation without entry point optimization.

ACKNOWLEDGMENTS

A big part of this work was accomplished at the MAIAA, ENAC. We are grateful to the members of the MAIAA for helpful discussions.


A polarization-based fast numerical method for computing the effective conductivity of composites

Vincent Monchiet, Guy Bonnet

To cite this version:

Vincent Monchiet, Guy Bonnet. A polarization-based fast numerical method for computing the effective conductivity of composites. International Journal of Numerical Methods for Heat and Fluid Flow, 2013, 23 (7), pp.1256-1271. hal-01078486


Toward a More Equitable Use of Resources

Christmann, P. 1 1 BRGM Directorate for Strategy and Research, BP 36009, F-45060-ORLEANS Cedex 2 (France) ___________________________________________________________________________ "Equitable'' means "dealing fairly and equally with all concerned" [START_REF]Webster dictionary[END_REF]. The concerned parties are all current and future stakeholders related to natural resources use, which means not only those diretcly involved in breeding, harvesting or extractive activities, but every human on Earth, as the ways natural resources are used have far reaching implications on biodiversity, climate, environmental and human health, and from there on the world's future. It also implicitly means that there is a return, a benefit, to share. Further to the impetus of globalisation, resource use activities are no longer limited to the sole satisfaction of the needs of local communities. They are the initial stage of industrial activities that can be located thousands of kilometres away from the site where the resources were harvested or extracted. Using natural capital to turn it into other forms of capital, such as built, social or financial capital can provide benefits that last for generations, well beyond the end of the actual resource using activity. It can also generate negative legacies that can have negative impacts for centuries. How these benefits and negative impacts are distributed is central to equity.

Industrial-scale resource use activities in agriculture, cattle rearing, forestry, water supply or mining, involve a wide range of stakeholders. Each one has specific, more often than not conflicting interests in the way the resource is used and the returns or services expected from the resource use. These stakeholders can comprise companies, their suppliers and the downstream supply chains depending on their products and/or services, the consumers that will purchase the goods and services derived from the use of these resources, employees, unions, the local communities impacted by the activities, authorities, media, academia and research, international organisation, banks and insurance companies, NGOs. Nature, the silent stakeholder, is frequently forgotten here, while it provides the resources at the heart of most economic activities as well as essential life-supporting services. Without a healthy, well-functioning ecosystem at global and local scale lasting wealth generation is impossible. There is a nexus of natural resources, whereby tha vailability and quality o one resource, for instance water, has an impact of the availability of another one, for instance minerals and metals.

The world faces severe resources constraints due to demographic growth, urbanisation and the development of a large global middle-class (+3 bn people between 2009-2030 [START_REF] Brandi | [END_REF] with resourceintensive lifestyles. Unsustainable resources use practices are widespread. This makes absolute decoupling [START_REF]Decoupling natural resource use and environmental impacts from economic growth-International Resource Panel report[END_REF] between growth, which is needed to foster social well-being, and the diverse negative impacts of growth an absolute must. In such a context humanity needs to re-think the way it uses natural resources and how the benefits are shared form an intra-and intergenerational perspective. Based on the work of the UNEP International Resource Panel the issues and the way forward will be outlined, with a special focus on mineral resources, governance issues and developing countries.


Ahmed Amokrane
email: ahmed.amokrane@lip6.fr

Rami Langar
email: rami.langar@lip6.fr

Raouf Boutaba
email: rboutaba@uwaterloo.ca

Guy Pujolle
email: guy.pujolle@lip6.fr

† D R Cheriton

Flow-based Management For Energy Efficient Campus Networks

Keywords: Energy Efficiency, Campus Networks, Management, SDN, Optimization

Recent studies have shown that the energy consumption of wireless access networks is a threat to the sustainability of mobile cloud services. Consequently, energy efficient solutions are becoming crucial for both local and wireless access networks. In this paper, we propose a flow-based management framework to achieve energy efficiency in campus networks. We address the problem from the dynamic perspective, where users come and leave the system in unpredictable way. Specifically, we propose an online flow-based routing approach, that allows dynamic reconfiguration of existing flows as well as dynamic link rate adaptation, while taking into account users' demands and mobility. Our approach is compliant with the emerging Software Defined Networking (SDN) paradigm since it can be integrated as an application on top of an SDN controller. To achieve this, we first formulate the flow-based routing problem as an integer linear program (ILP). As this problem is known to be N P-hard, we then propose a simple yet efficient Ant Colony-based approach to solve the formulated ILP. Through extensive simulations, we show that our proposed approach is able to achieve significant gains in terms of energy consumption, compared to heuristic solutions and conventional routing solutions such as the Shortest Path (SP) routing, the Minimum link Residual Capacity routing metric (MRC) and the load balancing (LB) scheme. In particular, we show that the energy consumption can be reduced by up to 7%, 35%, 44% and 49% compared to Greedy-OFER, MRC, SP and LB, respectively, while ensuring the required Quality of Service (QoS).

I. INTRODUCTION

The unprecedented expansion of broadband communication networks has led to a significant increase in energy consumption of communication networks. Indeed, according to a recent report [START_REF] Mills | The cloud begins with coal -an overview of the electricity used by the global digital ecosystem[END_REF], the Information and Communication Technologies (ICT) ecosystem is approaching 10% of the world's electricity usage. This corresponds to the same amount of power used to light the planet in 1985 and over 50% of the aviation consumption nowadays. Moreover, based on current trends, wireless access technologies such as WiFi will soon be the dominant methods for accessing emerging cloud services [START_REF]The Power of Wireless Cloud[END_REF]. In fact, according to a study published in 2013 [START_REF]The Power of Wireless Cloud[END_REF], wireless cloud services energy consumption, in which wireless access networks represent 90%, will increase by 460% in 2015 to reach 43 TWh, up from 9.2 TWh only in 2012. To make things worse, this will result in an increase in carbon footprint from 6 megatonnes of CO 2 in 2012 to up to 30 megatonnes of CO 2 in 2015, which represents the equivalent of adding 4.9 million cars on the roads. Facing the fact that the cost of energy continues to rise and the increasing environmental awareness, operators and institutions are urged to reduce the energy consumption of their campus networks including enterprise campuses, school campuses, shopping malls, airports, etc [START_REF]One Net Green Campus Network Solution[END_REF], to reduce operational expenditures (OPEX) and achieve long term sustainability.

The application of green and energy efficient networking to campus networks has seldom been reported in the literature. A topology of a typical campus network is illustrated in Fig. 1. Typically, it comprises static Access Points (APs), a set of switches, and gateway routers. Each AP serves multiple mobile users and connects them directly or through a multi-hop wireless routing to the wired backbone. The wired backbone itself is composed of a set of switches that form more or less a hierarchy and converge towards gateway routers. The gateway routers ensure the forwarding of the traffic towards the Internet. It is worth noting that this topology can be used in enterprise or university campuses to enable cost-effective and scalable deployment of secure outdoor wireless LANs, as highlighted by Cisco [START_REF]Cisco wireless mesh networking[END_REF]. For example, Concordia University (Canada) used a wireless mesh network in its campus [START_REF]Pioneering university deploys canadas first 802.11n wireless network[END_REF].

According to recent studies [START_REF]The Power of Wireless Cloud[END_REF], [START_REF]Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update[END_REF], user traffic drained by campus networks is expected to soar in the next few years, which will result in high energy consumption [START_REF]The Power of Wireless Cloud[END_REF], [START_REF]Deploying Brocade PoE and PoE Solutions in the Campus Network[END_REF]. As such, it is important to design energy efficient planning and management strategies for campus networks that take into account the dynamic and unpredictable users' mobility.

On the other hand, Software Defined Networking (SDN) [START_REF] Yap | Towards software-friendly networks[END_REF] has emerged recently as a solution facilitating network management. The key idea behind SDN is to move the forwarding intelligence into a centralized network controller, while keeping the routers or switches simple. This allows to implement different forwarding approaches flexibly and achieve global optimizations easily. In SDN, the controller dictates the forwarding rules of flows to the forwarding elements using protocols such as OpenFlow [START_REF] Mckeown | OpenFlow: enabling innovation in campus networks[END_REF]. SDN presents an opportunity to improve the performance and reduce the energy consumption of campus networks [START_REF] Onf | SDN in the Campus Environment[END_REF].

Motivated by the potential of the new SDN paradigm, we propose in this paper a holistic energy conservation approach that uses online flow-based routing and link rate adaptation in campus networks. Our objective is to minimize the energy consumption of APs and switches, while routing incoming flows subject to QoS constraints (such as bandwidth and delay) and taking into account the dynamic and unpredictable arrival, departure and users' mobility. More specifically, our approach determines the AP to which each user will associate, along with a complete path in the wireless and wired parts of the network, towards the Internet, while minimizing the whole energy consumption and satisfying the QoS constraints. In this case, our proposed solution uses dynamic flow consolidation to reduce the energy consumption in the network. Moreover, it uses link rate adaptation to further reduce the energy consumption in the wired part of the network. Our proposed approach can be easily integrated in an SDN solution since it relies on a central controller that monitors and manages the network and decides on flow routes and link rates.

To achieve this, we first formulate the problem as an integer linear program (ILP), whose objective is to reduce the total energy consumption in the wireless and wired parts of the network. Moreover, The formulated objective function takes into account the costs for switching between sleeping and active modes of nodes (APs, switches and gateway routers), as well as re-routing or consolidating existing flows. As this problem is known to be N P-hard [START_REF] Ramanathan | Scheduling algorithms for multihop radio networks[END_REF], [START_REF] Kodialam | Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels[END_REF], we then propose a simple yet efficient algorithm based on Ant Colony, called Ant Colony Online Flow-based Energy efficient Routing (AC-OFER) to solve the formulated ILP problem. In this context, Greedy-OFER, Shortest Path (SP) routing strategy, the Minimum link Residual Capacity routing metric (MRC) and the Load Balancing (LB) schemes are used to develop baselines to which the AC-OFER improvements are compared. Through extensive simulations, we show that our proposed approach can achieve significant gains in terms of energy consumption. Specifically, the gains, can attain 6.5% 17%, 42% and 45% compared to Greedy-OFER, MRC, SP and LB, respectively, for medium-sized networks. These gains become 7%, 35%, 44% and 49%, respectively, in large-sized networks, while achieving the same users' requests acceptance ratio and QoS satisfaction.

In summary, our key contributions are the following:

• We formulate the problem of reducing energy consumption in campus networks as an Integer Linear Program (ILP), under dynamic arrival and departure of users. The objective includes the cost of re-routing or consolidating existing flows as well as the cost of switching nodes between active and sleep modes. • We propose a meta-heuristic low time complexity ap-proach based on Ant Colony to solve the ILP problem. We show that our approach achieves near optimal solution for network reconfiguration to reduce the overall energy consumption within few milliseconds, which makes it usable in practice.

• Our approach is online flow-based and defines users attachment as well as flows routing in both wireless and wired parts of the network under dynamic arrival and departure of users, and uses link rate adaptation in the wired backbone to achieve energy efficient campus networks.

• We compare our approach with several existing solutions and discuss the associated gains. The reminder of this paper is organized as follows. Section II presents an overview of the related work. In Section III, we describe the system model used in our analysis. Section IV formulates the problem as an ILP, followed by a presentation of our proposal in Section V. Simulation results are presented in Section VI. Finally, Section VII concludes this paper.

II. RELATED WORK

Energy management has been an active research area in the last few years. In the following, we survey relevant research in both wired and wireless networks.

A. Energy Reduction in Wired Networks

Numerous proposals have been presented to reduce energy consumption in wired networks [START_REF] Chowdhury | Building a green wireless-optical broadband access network (woban)[END_REF]- [START_REF] Francois | Optimizing link sleeping reconfigurations in isp networks with off-peak time failure protection[END_REF]. Authors in [START_REF] Chowdhury | Building a green wireless-optical broadband access network (woban)[END_REF] propose to reduce energy consumption in backbone networks by reducing the number of used nodes. They formulate the problem as an ILP for multi commodity flow and provide the optimal routing to reduce the number of used nodes. Authors in [START_REF] Chiaraviglio | Reducing power consumption in backbone networks[END_REF] propose to shut down nodes one by one and verify that the network still route the required traffic (i.e., the constraints are not violated). In [START_REF] Gelenbe | Power savings in packet networks via optimised routing[END_REF], authors investigated a model based on gradient optimization to reduce energy consumption in wired networks. They started from routing paths given by a shortest path routing. Then, they used a routing policy named Energy-Aware Routing Protocol (EARP) [START_REF] Mahmoodi | Energy-aware routing in the cognitive packet network[END_REF] to reduce energy consumption by up to 10% given that the required QoS is satisfied. Online flow-based routing has also been used in [START_REF] Avallone | Energy efficient online routing of flows with additive constraints[END_REF], where authors presented E 2 -MCRA, a flowbased routing approach that reduces the number of used nodes in a Internet Service Provider (ISP) network, while satisfying the QoS constraints. The idea is to route incoming flows by choosing among the possible paths, the one that achieves the best combination between the path length and the number of additional nodes to turn on. Authors in [START_REF] Addis | Energy management through optimized routing and device powering for greener communication networks[END_REF] proposed an ILP formulation to reduce the number of used nodes in the network while routing per-flow basis. They also derived heuristics for online routing of flows. They used results from real routers to assess their proposed approach. Authors in [START_REF] Francois | Optimizing link sleeping reconfigurations in isp networks with off-peak time failure protection[END_REF] addressed the problem of energy reduction in ISP networks. Their proposal is time-driven and relies on the observation that ISP networks exhibit regular/predictive traffic patterns during specified time windows. Hence, they first propose a heuristic that shuts down unnecessary links, and then an algorithm to compute the duration of the time window. Then, they show that their approach can achieve up to 18% energy saving (in terms of used links) without significantly impacting the network performance.

On the other hand, energy efficiency in data center networks has also been addressed by a few works. The objective is to reduce the number of used nodes (both servers and switches) through virtualization and flow consolidation. Specifically, authors in [START_REF] Heller | Elastictree: saving energy in data center networks[END_REF], presented ElasticTree, a network-wide power manager that relies on OpenFlow to dynamically adjust the set of active network elements (i.e., links and switches) to satisfy changing data center traffic loads. They show that ElasticTree can save up to 50% of network energy, while maintaining the ability to handle traffic surges. In [START_REF] Lin | Greendcn: A general framework for achieving energy efficiency in data center networks[END_REF], authors propose a two step solution to reduce energy consumption in datacenters. First, they propose to assign virtual machines (VMs) to servers to reduce the amount of traffic and to generate favorable conditions for traffic engineering. Then, to achieve energy conservation, they reduce the number of needed active switches that balance traffic flows, depending on the relationship between power consumption and routing. In [START_REF] Wang | Incorporating rate adaptation into green networking for future data centers[END_REF], authors showed the benefit of using link rate adaptation in a datacenter network. The objective is to find the rates of the different links that minimize the energy consumption of the whole network. They formulate the problem as an ILP and proposed an approximation method to solve the ILP. However, the proposed energy consumption model assumes proportional switch energy consumption (i.e., the energy consumption of the switch is proportional to the link rates), which is not true in practice.

In the specific case of campus networks, authors in [START_REF] Markiewicz | Energy consumption optimization for software defined networks considering dynamic traffic[END_REF] proposed an SDN-based approach (i.e., using a central controller) to reduce the energy consumption by switching off as many switches/routers as possible. They formulated the problem as a mixed integer linear programming (MILP) and then proposed a heuristic solution. However, authors did not address the case of wireless parts of the network. Moreover, no link rate adaptation is considered.

B. Energy Reduction in Wireless Networks

An important body of work on energy efficiency of devices and protocols in cellular, WLANs and Wireless Mesh Networks (WMNs) has been reported in the literature. A survey on energy efficient protocols for such networks can be found in [START_REF] Jones | A survey of energy efficient network protocols for wireless networks[END_REF]. In WLANs, authors in [START_REF] Jardosh | Green WLANs: On-Demand WLAN Infrastructures[END_REF], [START_REF] Debele | Experimenting resourceondemand strategies for green wlans[END_REF] presented strategies based on the resource on-demand concept. The proposed approaches derive strategies to reduce the number of used APs in a WLAN. In [START_REF] Marsan | A simple analytical model for the energy-efficient activation of access points in dense wlans[END_REF], authors proposed an analytical model to assess the effectiveness of this concept and authors in [START_REF] Todd | The need for access point power saving in solar powered wlan mesh networks[END_REF] showed management strategies for energy savings in solar powered 802.11 WMNs. In [START_REF] Ganji | Greening campus WLANs: Energy-relevant usage and mobility patterns[END_REF], authors derived mobility and traffic patterns in the specific case of WLAN university campus networks (day/night, week days and weekends) to decide on the APs to turn on/off in the campus to accommodate the traffic. In cellular access networks, authors in [START_REF] Chen | Network energy saving technologies for green wireless access networks[END_REF] summarized existing energy saving approaches, which use carrier aggregation, turn off transmission components during signal-free symbols, and turn off cells during low traffic periods.

In the context of WMNs, relevant works on energyefficiency are reported in [START_REF] Capone | Energy savings in wireless mesh networks in a time-variable context[END_REF]- [START_REF] Chen | E-Mesh: An energy-efficient cross-layer solution for video delivery in wireless mesh networks[END_REF]. These works consider offline routing in such networks. Specifically, authors in [START_REF] Capone | Energy savings in wireless mesh networks in a time-variable context[END_REF] consider the case of WMNs, where the users can choose the AP they connect to. To do so, they formulate and solve the problem as an ILP, where the objective is to minimize the number of used nodes (i.e., APs and gateways), and always satisfy users' bandwidth demands. However, they do not take into account the interference between APs since directional antennas are assumed. The authors extended this work in [START_REF] Silvia | Joint design and management of energy-aware Mesh Networks[END_REF] to consider the planning and deployment of APs (i.e., choosing the number of APs and their location). Another energy management study in WMNs is provided in [START_REF] Luo | Engineering Wireless Mesh Networks: Joint Scheduling, Routing, Power Control, and Rate Adaptation[END_REF], where a combination between different modulation techniques and power adaptation is presented. In [START_REF] Amokrane | A Green Framework for Energy Efficient Management in TDMA-based Wireless Mesh Networks[END_REF], we proposed a framework for energy efficient management in TDMA-based WMNs. However, all the afore-mentioned approaches are still limited since they are offline. Indeed, the traffic patterns are assumed to be known a priori and fixed at the planning stage, which is not usually the case in practice, as users can arrive and leave the network in an unpredictable way. This may limit the utilization of such approaches in real world deployments. Moreover, these approaches do not account for the wired part of a campus network.

To overcome these limitations, we first proposed in [START_REF]Online Flow-based Energy Efficient Management in Wireless Mesh Networks[END_REF] a flow-based management framework to achieve energy efficient WMNs, that takes into account the dynamic and unpredictable traffic patterns. In this paper, we rather focus on campus networks, which include both wireless and wired networks elements. It is worth noting that a more detailed survey of energy efficient approaches in wireless access networks, with a focus more on cellular and WLAN, is given in [START_REF] Budzisz | Dynamic Resource Provisioning for Energy Efficiency in Wireless Access Networks: A Survey and an Outlook[END_REF].

C. SDN-based Wireless Network Management

In the context of SDN, most of the proposed solutions to wireless network management focus on mobility management. For instance, authors in [START_REF] Dely | OpenFlow for Wireless Mesh Networks[END_REF] present an OpenFlowbased approach for efficient mobility management in WMNs. This approach implements the mobility management as an application on top of the SDN controller. In [START_REF] Suresh | Towards programmable enterprise WLANS with Odin[END_REF], authors present an SDN-based framework for network management in WLANs. The framework relies on a central controller that has a global view of the network. The mobility management is implemented as an application on top of the central controller that manages users' attachments through light virtual APs and OpenFlow-enabled switches.

Adopting the same SDN paradigm as in [START_REF] Suresh | Towards programmable enterprise WLANS with Odin[END_REF] and [START_REF] Dely | OpenFlow for Wireless Mesh Networks[END_REF], in this paper, we propose an online flow-based routing approach in campus networks. Specifically, we focus on energy efficient communications by routing the incoming traffic from the users to the campus gateway routers, while considering the required QoS, the energy consumption as well as the costs of flows reconfiguration and re-routing. To the best of our knowledge, we are the first to address green routing in SDN-based campus networks.

III. SYSTEM MODEL

A. Network Model

We represent a campus network by a directed graph G(V ∪ W, E s ∪ E d ), called a connectivity graph, where V is the set of APs, W is the set of switches, E s and E d are the set of wireless and wired links, respectively. We denote also by E = E s ∪ E d the set of all links. Each node v ∈ V represents an AP. Note that some of these APs can be interconnected to form a Wireless Mesh Network (WMN). A wireless link e ∈ E s between two APs has a number of channels denoted by nc e . The capacity along each channel is limited and denoted by C ek . Moreover, each AP i ∈ V has a limited capacity to serve its attached users denoted by C i .

Similarly, each wired link e ∈ E d between an AP and a switch or between two switches has a limited capacity denoted by C ek . In this case, nc e = 1, ∀e ∈ E d . Moreover, some switches have ports connected to gateway routers, which guarantee the connection to the Internet. Let S d denote this set of switches. One can think of these switches as the gateways towards the Internet for the wired backbone part of the network. Note that each gateway j ∈ S d router has a limited capacity for traffic forwarding towards the Internet denoted by G j .

B. AP Energy Consumption Model

First of all, recall that an AP v ∈ V has two physical interfaces: one for serving its mesh users (called AP interface) and one for relaying traffic in the wireless backbone towards the wireless backbone (called mesh interface). An additional third wired interface exists for APs that are directly connected to the switches to forward traffic to/from the wired network.

Given an AP v ∈ V , we distinguish between two operating modes: low power consumption and high power consumption. In the first mode, an AP has no users attached to it and no traffic to forward. In this case, it only uses its AP Interface to detect user's presence. In this mode, the energy consumption of the AP can be reduced by setting up a high sleeping period and reducing the transmission power as presented in [START_REF] Al-Hazmi | Energy-efficient wireless mesh infrastructures[END_REF], or shut down the AP by cutting down the power supply such as the Power over Ethernet (PoE). In the second mode, the AP has either active users attached to it or traffic to forward. Therefore, its power consumption is higher. It is worth noting that the contrast between low power and high power consumption stems from the study carried out by Gomez et al. [START_REF] Gomez | Analysing the energy consumption behaviour of wifi networks[END_REF]. Through real power measurements, authors showed that the power consumption of an AP when it does not carry traffic (i.e., active AP with traffic load equals to 0), represents 75% of its peak power. An active AP carrying traffic consumes an extra power proportional to the AP traffic load, and is calibrated as 25% of the power consumption multiplied by the traffic load over total AP capacity, as shown in the revised paper.

Hence, six power consumption profiles for an AP v ∈ V can be defined, and listed in Table I. Note that we denote by mesh router an AP that has traffic to forward in the wireless If v is used as an access point and a mesh router at the same time. This means that v has active users attached to it and uses its mesh interface to forward traffic in the wireless backbone. P AG If v is used as an access point and has traffic to forward to the wired network at the same time (i.e., the AP is acting as a mesh gateway and has active users attached to it). P RG If v is used as a mesh router and mesh gateway at the same time but no users are attached to it. P ARG If v is used as an access point, a mesh router and a mesh gateway at the same time. In this case, v uses simultaneously its three interfaces. This is the most power hungry profile. P S If v has no active users attached to it, no traffic to forward and is not used as a mesh gateway. This is the power saving mode of an AP. Note that P S could be negligible compared to the other profiles.

backbone and a mesh gateway if it has traffic to forward from the wireless backbone towards the wired network. Consequently, the power consumption of AP can be expressed as follows:

P = P S If load AP = 0 P prof ile * (0.75 + 0.25 × load AP
total AP capacity ), Otherwise where load AP is the current load of the AP, total AP capacity is the maximum capacity supported by the AP and P prof ile is the peak power consumption of the corresponding profile.

It is worth noting that in the case of one-hop wireless networks (i.e., all APs are directly connected to switches such as the topology discussed in [START_REF] Onf | SDN in the Campus Environment[END_REF]), the energy consumption modes are reduced to P AG and P S .

To reduce the energy consumption of the whole network, one should put as many nodes as possible into power saving mode and by switching them off in case where they have no traffic to carry. In practice, this can be achieved using technologies such as Wake-on-LAN or Power over Ethernet (PoE) powered APs as in [START_REF]One Net Green Campus Network Solution[END_REF], [START_REF]Deploying Brocade PoE and PoE Solutions in the Campus Network[END_REF], which are switched off by cutting the power Ethernet supply.

C. Switch Energy Consumption Model

A switch contains a number of interfaces. Each interface has its own Network Interface Card (NIC) card (a.k.a. line card). Each interface can have one or multiple ports. In this work, we use the energy consumption model proposed by Mahadevan et al in [START_REF] Mahadevan | A power benchmarking framework for network devices[END_REF] and reused in other works such as [START_REF] Kliazovich | Greencloud: A packet-level simulator of energy-aware cloud computing data centers[END_REF]. In this model, the energy consumption of a switch corresponds to a fixed amount of power consumed by the chassis, plus a variable amount of power that depends on the number of active interfaces along with the rate of each interface. It is given by:

P switch = P chassis +n linecards ×P linecards + R k=1 n ports.r ×P r (1)
where P chassis is related to the power consumed by the switch hardware, P linecards is the power consumed by an active network line card, and P r corresponds to the power consumed by a port (transceiver) running at rate r ∈ {r 1 , ..., r m }.

Note that in equation ( 1), only the last component appears to be dependent on the link rate, while other components, such as P chassis and P linecards , remain fixed for the whole switch operation duration.

D. Traffic Model

In this work, we model the traffic as a set of L flows. Each flow originates from a user, who is located in the coverage area of one or multiple APs. Users' location is captured by the coverage matrix A. Each flow l ∈ L has a bandwidth demand b l and a delay constraint d l . Note that these flows are unidirectional. As such, the downlink and uplink are considered to be two different flows and are treated differently in terms of allocated path. Moreover, we assume that the traffic demand of each flow can be determined by the controller. For instance, this could be achieved by using the counters per flow in the network forwarding elements, and use estimation techniques to determine the traffic rate.

IV. PROBLEM FORMULATION

As already mentioned, our objective is to minimize the energy consumption of the network nodes (i.e., APs and switches) over time, while routing dynamically the arriving and departing flows subject to QoS constraints (i.e., bandwidth and delay). In other words, our objective is to reduce the energy consumption, while guaranteeing traffic routing and QoS for the different traffic flows in campus networks. More specifically, the problem can be formulated as follows:

GIVEN:

• A physical topology represented by the graph G(V ∪ W, E s ∪ E d ), which is described by the connectivity and interference matrices M and I, respectively. • A set of gateway routers in the wired backbone network.

• A set L of flows originating from users, each one with its bandwidth demand b l and delay constraint d l . • The coverage matrix A of APs.

• The current attachment of users and their flows' routes. FIND:

• The optimal attachment of each user to one of the APs and, optimal routing of its flows that minimizes the network operation and reconfiguration costs, subject to QoS constraints (i.e., bandwidth and delay), and the link rates of the wired link in the network. In the following, we formulate the flow-based routing problem as an integer linear program (ILP). For ease of understanding, table II summarizes the symbols used in our analysis.

Let t be the epoch starting when one of the following events occurs: user arrival/departure or user movement between two APs. We denote by t -1 the epoch before t. For the sake of presentation, let us use the notation y and y to designate the state of any variable y at epoch t and t -1, respectively. The set of wired links f e,k,l 0 or 1, whether the channel k of a link e is used to route flow l w li 0 or 1, whether the user originating the flow l is attached to the AP i y i 0 or 1, whether an AP is in the active or sleep mode y + i 0 or 1, whether an AP is turned into the active mode y - i 0 or 1, whether an AP is turned into the sleep mode r + il 0 or 1, whether an AP i is added to the path of flow l r - il 0 or 1, whether an AP i is removed from the path of flow We introduce the binary variable w li to indicate whether a user originating flow l is attached to the AP i ∈ V as follows:

w li = 1 If user originating flow l is attached to AP i 0 Otherwise
To represent the link and channel allocation, we define another binary variable f e,k,l , which takes the value of 1 whenever the flow l uses the channel k on link e on its route.

f e,k,l = 1 If flow l is routed though link e using channel k 0 Otherwise. Recall that k = 1, ∀e ∈ E d .
To define the link rate (i.e., the rate at which the link is set to operate) of a link e ∈ E d , we use r e . Recall that r e ∈ {r 1 , ..., r m }. To indicate whether an AP i ∈ V is used or not, we introduce another binary variable y i defined by: Let us consider the variable y + i and y - i that represent, respectively, the decision of switching an AP i to active mode or sleep mode, at network reconfiguration. They are defined as follows:

y i =      0 If
y + i =
1 if y i = 0 and y i = 1 0 Otherwise.

y - i = 1 if y i = 1 and y i = 0 0 Otherwise.
Note that switching a node from a sleep mode to active mode and vice versa generates a cost. This cost is denoted by cs + i and cs - i , respectively, and could be the time needed to turn on the node or the energy that is consumed to set up the routing tables (e.g., flow table). In addition, we need to account for a cost when re-routing a flow over a more favorable route. Hence, let us consider the variables r + il and r - il representing, respectively, whether a flow l is re-routed through node i, after network reconfiguration, or removed from being routed through node i. They are defined as follows: The re-routing costs will be thus represented by cr + il and cr - il , respectively.

r + il =                  1
r - il =                  1
The power consumption of an AP i ∈ V is given by P i as follows: Otherwise.

P i =                                                                                                              P R If
Recall that the power consumption of a switch i ∈ W is given by the consumption model given in equation [START_REF] Mills | The cloud begins with coal -an overview of the electricity used by the global digital ecosystem[END_REF].

We now formulate the problem of routing the new incoming flow and dynamically re-optimizing the existing flows as an ILP with the following objective function:

M inimize α E i∈V ∪W P i + α S i∈V ∪W (y + i cs + i + y - i cs - i ) + α R i∈V ∪W l∈L (r + il cr + il + r - il cr - il ) (2)
Where, α E , α S and α R respectively represent weight factors to achieve a tradeoff between power consumption, re-routing flows and switching nodes to different states. For instance, they might represent the cost in USD (e.g., cost of electricity for α E ) or the cost translated into USD for any service disruption that might happen in the network if a flow is rerouted through a different path. Note that the first term in the objective function is related to the energy consumption when using a node i. The second term corresponds to the cost of switching nodes from sleeping/active states after reconfiguration, and the third term captures the cost of re-routing flows. Consequently, if a network administrator is interested only in the energy consumption and he is willing to give away possible service disruptions, he could set α S and α R to 0 and α E to 1 and have an objective function based only on energy consumption. The optimization is subject to the following constraints (3)-( 13):

• Not exceeding the capacities of links and channels:

l∈L f e,k,l × b l ≤ C ek , ∀e ∈ E s ∪ E d , ∀k ∈ {1, .., nc e } (3)
• Not exceeding gateway routers capacities:

l∈L e∈E nce k=1 f e,k,l × b l + l∈L w li × b l ≤ G i ∀e ∈ E d , d(e) = i and i ∈ S d (4)
• Not exceeding the APs capacities:

l∈L w li × b l ≤ C i ∀i ∈ V (5)
• A user can attach to, at most, one AP that covers its location:

i∈V w li ≤ A li , ∀l ∈ L (6)
• The delay constraint of a flow l should be satisfied:

e∈E nce k=1 f e,k,l ≤ d l , ∀l ∈ L (7)
• A flow is not routed when it reaches a gateway unless the gateway capacity is exceeded, in which case the traffic is forwarded to another gateway:

l∈L e∈E d d(e)=i nce k=1 f e,k,l × b l + l∈L w li × b l ≤ G i + l∈L e∈E d s(e)=i nce k=1 f e,k,l × b l , ∀i ∈ S d (8)
• No loops when routing. This means that a flow comes in or goes out from a node at most once. Hence, we have:

e∈E s(e)=i nce k=1 f e,k,l ≤ 1, e∈E d(e)=i nce k=1 f e,k,l ≤ 1, ∀i ∈ V ∪ W, ∀l ∈ L (9)
• Flow conservation constraint, which ensures that the network flow that enters a node plus the traffic originating from this node is equal to the outgoing traffic from this node. It can be written as follows:

l∈L e∈E s(e)=i nce k=1 f e,k,l × b l = l∈L e∈E d(e)=i nce k=1 f e,k,l × b l + l∈L w li × b l , ∀i ∈ (V ∪ W )\S d (10)
• In the wireless part, two links that interfere with each other cannot transmit at the same time. This means that the sum of their proportion of link usage should not exceed 1. • In the wired part, the link rates should be adjusted to the upper rate r i that satisfies the used bandwidth in the corresponding links.

r e = min j∈{1..m} r j ≥ l∈L f e,k,l × b l , ∀e ∈ E d (12)
• The decision variables are binary

f e,k,l , w li ∈ {0, 1} , ∀i ∈ V, ∀e ∈ E, ∀l ∈ L (13)
In a nutshell, constraints (3)-( 5) guarantee not violating the capacity constraints of the network nodes. This means not routing traffic beyond the capacity of the network nodes and links. Constraint [START_REF]Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update[END_REF] guarantees that a user can attach to only one AP at a time if his traffic flow is routed. Constraint [START_REF]Deploying Brocade PoE and PoE Solutions in the Campus Network[END_REF] guarantees that the delay requirement specified by a flow in terms of number of hops is satisfied. Constraints ( 8)- [START_REF] Onf | SDN in the Campus Environment[END_REF] guarantee that traffic flows are always routed to terminate at a gateway subject to the gateways capacities and that each flow is routed in a contiguous way through the network. Constraint [START_REF] Ramanathan | Scheduling algorithms for multihop radio networks[END_REF] guarantees that the interfering links in the wireless part are not used at their full capacity since they share the wireless transmission medium. Constraint [START_REF] Kodialam | Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels[END_REF] defines how the link rates are set in the wired part of the network. Finally, constraint [START_REF] Chowdhury | Building a green wireless-optical broadband access network (woban)[END_REF] guarantees that the decision variable are binary ones.

In the following, we present our meta-heuristic approach, called AC-OFER, that solves the above ILP problem.

V. AC-OFER PROPOSAL

The formulated ILP problem presented in Section IV is assumed to be solved by the network controller each epoch t (i.e., each incoming flow). Indeed, the time scale of t should be short enough to capture the dynamic of arrival and departure of clients, as the new flows should be routed at their arrival. Clearly, such approach is not feasible in practice, since it generates high overhead due to the frequent updates of the flow tables. In addition, the above ILP problem is N P-hard [START_REF] Ramanathan | Scheduling algorithms for multihop radio networks[END_REF], [START_REF] Kodialam | Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels[END_REF].

To overcome these issues, we propose a two step approach. First, each incoming flow is injected in the network without incurring any changes on the already established routes of existing flows by computing an energy efficient path. This step is referred to as "Network Event Handling". Then, a simple yet efficient meta-heuristic algorithm, called AC-OFER, is executed at each pre-defined time period T (and not at each flow arrival or departure). This step is called "Dynamic Network Reconfiguration". The benefit of doing so is twofold: (i) to reduce the overhead due to rerouting existing flows and (ii) to decide on flow rerouting that optimizes the overall energy consumption of the network by taking into account any rerouting costs. In the following, we detail these two steps.

A. Network Event Handling

Upon detecting the "user arrival" event, one or multiple served APs start by sending the corresponding flow QoS requirements (i.e., bandwidth and delay constraints) to the network controller. Depending on the AP location, we can use either a virtual interface if it is a mesh node as proposed and validated in [START_REF] Dely | OpenFlow for Wireless Mesh Networks[END_REF], where each physical wireless interface can be split into two virtual interfaces, or the usual secure channel as in OpenFlow-enabled switches if it is a switch [START_REF] Mckeown | OpenFlow: enabling innovation in campus networks[END_REF]. Since no dynamic reconfiguration is performed at this level, the network controller chooses, among the possible paths, the one with the minimum score given by the objective function in (2), without incurring any changes to existing flow routes. To do so, we use a modified version of the Dijkstra's algorithm presented in Algorithm 1. The algorithm takes as input the graph of the network (APs and switches) along with the residual capacities of the APs and links. Going through Algorithm 1, we first modify the graph G(V ∪ W, E s ∪ E d ) by adding a new node v l with an edge between v l and all the APs that can cover the originating user's location, and which has enough residual capacity. Then, we use the same process as in Dijkstra's algorithm. Note that the objective function given in ( 2) is used as a distance function. Indeed, dif f power(u, v) in Algorithm 1 refers to the additional score of the objective function if the node v is added to the path that goes through u for flow l. At the end, the algorithm returns the path that -Add a virtual edge between v l and the APs that can cover the location of the user l 5: Initialization: 6: for all v in V ∪ W do //dif f power(u, v) gives the additional power if we add the node v to the path that goes through u for flow l 23: Once the path is chosen, the rates at the different links are adapted. In our study, and as proposed in previous works such as [START_REF] Nedevschi | Reducing network energy consumption via sleeping and rateadaptation[END_REF] and [START_REF] Thanh | Modeling and experimenting combined smart sleep and power scaling algorithms in energy-aware data center networks[END_REF], we assume that the link rate (i.e., switch port) can be adjusted to one of the following predefined rates: 10 Mbps, 100 Mbps, 1 Gbps and 10 Gbps, denoted by r 10 , r 100 , r 1000 , r 10000 , respectively. Each one of these rates r i represents one power consumption profile of the link (and thus of the corresponding switch ports) as used in equation (1). To do so, we propose an intuitive algorithm, presented in Algorithm 2, to set up link rates according to their utilization. Note that in case of user's departure, its corresponding flow will be removed from the network and the used resources will be released.

if temp < power[v] then 24: power[v] ← temp 25: previous[v] ← u 26: if visited[v] = f alse then 27: Q.Enqueue(v)

B. Dynamic network reconfiguration using Ant Colony Online Flow-based Energy efficient Routing (AC-OFER)

As stated before, in order to optimize the overall energy consumption and resource utilization, the network controller needs to reconfigure the flow routes in the network taking into account the cost of re-routing or consolidating existing flows. This is performed at each predefined time period T . Note that T is a parameter that is specified by the network administrator, and can be in the order of minutes or hours. To this end, we propose to approximate the optimal solution of the above-mentioned ILP problem presented in Section IV using an Ant Colony-based approach [START_REF] Dorigo | Ant colony system: a cooperative learning approach to the traveling salesman problem[END_REF], called AC-OFER.

AC-OFER operates as illustrated in the flowchart given in Fig. 2. First, a set of solution components (i.e., paths) needs to be determined for each flow coming from a user. Next, A max artificial ants are launched and iteratively explore the search space until a predetermined number of iterations N max is reached. During each iteration, each ant among A max incrementally constructs the solution by adding in every step one solution component (i.e., a path for one user's flow) to the partial solution constructed so far. Note that the solution component to add among the candidates is chosen using a stochastic local decision policy. More specifically, the decision is based on heuristic information, denoted by η, and artificial pheromone trails, denoted by τ , which respectively quantify the desirability of a priori and a posteriori transition. Indeed, the heuristic represents the attractiveness of the move, indicating the a priori desirability of that move. On the other hand, the pheromone trails indicate how proficient it has been in the past (i.e., according to other ants experience) to add that solution component. Once an ant has built a solution, or while the solution is being built, the ant evaluates the partial solution and deposits pheromone trails on the components it used. This pheromone information will direct the search of the future ants.

More formally, our AC-OFER algorithm is described by the pseudo-code in Algorithm 3. The fundamental steps of AC-OFER are: 1) Formation of solution components, 2) Probabilistic selection of the candidate, 3) Selection of the best solution and 4) Updating the pheromone trails. In the following, we detail these stages. For each user, we consider K alternative paths towards a gateway (any of the m available gateways). Each path starts from the user, passes through an AP that the user attaches to, and then other intermediate APs then switches until reaching a gateway router. A solution component will be one of the predetermined K paths. As such, the number of possible solutions for the path formulation is K |L| , where |L| is the total number of lows, which is equal to the total number of users since each user is assumed to generate one flow. Hence the proposed meta-heuristic guides the algorithm to efficiently explore the graph of solutions.

2) Selection among the candidates for a component:

During each iteration, each ant among A max builds the solution step by step, by adding in each step another component (i.e., a path for a flow l). The component to add is chosen according to the attractiveness of the new constructed solution (i.e., the current solution augmented by the selected component) which is called the heuristic, and the amount of pheromone deposits, which represents how this component is evaluated during the previous iterations by all ants. The heuristic is given by : Choose path j according to P lj given in [START_REF] Gelenbe | Power savings in packet networks via optimised routing[END_REF] 16:

end if

17:
Add the j th path for flow l to current solution if current solution is the best solution for the current iteration And j th path is selected for flow l then Once the objective function score computed, the choice of the next component to add to the partial solution constructed so far (i.e., a path j for flow l) is selected according to a given probability. Note that in Ant Colony System meta-heuristic [START_REF] Dorigo | Ant colony system: a cooperative learning approach to the traveling salesman problem[END_REF], two strategies can be used: exploitation and exploration. More specifically, exploitation is used with a probability q 0 , whereas exploration is adopted with a probability (1 -q 0 ).

Regarding exploration, the knowledge and experience of other ants is stochastically taken into account. Indeed, the next component is selected according to a probability P lj given by:

P lj = τ α AN T lj η β AN T lj k∈N l τ α AN T lk η β AN T lk (15)
Where N l is the set of all possible paths for the solution component l (i.e., |N l | = K), η lj and τ lj denote, respectively, the heuristic value given in equation ( 14), and the pheromone trail of the j th path for the flow originating from user l, and α AN T and β AN T determine, respectively, the relative importance of τ lj and η lj . Recall that η lj represents the desirability of adding the solution component j (i.e., path j) to route the flow of user l, whereas τ lj represents how proficient it has been so far to route the flow of user l through path j. As such, α AN T and β AN T parameters have the following influence on the algorithm behavior. If β AN T = 0, the selection probabilities are proportional to the heuristic value η lj , which means that the components with high heuristic value are more likely to be selected. In this case, AC-OFER corresponds to a classical stochastic greedy algorithm. However, if α AN T = 0, only pheromone amplification is at work: the components with high pheromone trail are more likely to be selected, in which case a rapid convergence to a suboptimal solution may result as all ants are more likely to build the same solution.

On the other hand, in exploitation, the experience of the other ants is directly used. Indeed, among the possible components to add, the one with the highest value of τ α AN T lj ×η β AN T lj is selected.

3) Selection of the best solution:

The criterion to choose the best solution is the objective function given in equation ( 2), which takes into account the energy consumption, the on/off switching and re-routing costs.

4) Pheromone trail update:

At the end of each iteration, the pheromones (trail values) for each flow l are updated as follows:

τ lj = (1 -ρ)τ lj + ∆ best lj where ρ ∈ [0, 1] is the decay coefficient of the pheromone, ∆ best lj = Q/η best if
flow l is routed through the j th path in the best solution of the current iteration, 0 otherwise, and Q is a constant called the pheromone update constant. Recall that η best = 1/Objective f unction value of the best solution, as reported in equation [START_REF] Chiaraviglio | Reducing power consumption in backbone networks[END_REF].

It is worth noting that when the score of the objective function is computed, we use the link rate adaptation provided in Algorithm 2.

VI. PERFORMANCE EVALUATION

In this section, we evaluate the efficiency of our proposed approach. We first present the baselines we used for performance comparison as well as and the simulation parameters and environment. Then, we present detailed analysis of the simulation results.

A. Baselines

We compare the benefits of our AC-OFER approach with respect to four baselines: the Shortest Path (SP) routing, the Minimum link Residual Capacity (MRC) routing metric proposed in [START_REF] Chowdhury | Building a green wireless-optical broadband access network (woban)[END_REF], the Load Balancing (LB) scheme, and Greedy-OFER. Note that the latter is similar to AC-OFER in the fact that it uses the same algorithm for routing new incoming flows. However, for network reconfiguration, it uses a greedy algorithm to find the solution instead of the Ant Colony algorithm. In other words, it seeks a feasible and acceptable solution by exploring the solution space and choosing the next step without iteration to improve the solution. This results in short computation times. Regarding the MRC baseline approach, the aim is to consolidate the traffic through the same paths in order to reduce the number of used nodes. Finally, LB is used to illustrate the worst case power consumption scenario.

B. Simulation environment

To evaluate our proposal, we developed our own discrete event simulator in Java. The simulator generates traffic and performs the routing according to the paths defined by the corresponding routing algorithms.

C. Simulation parameters

Our analysis is based on random and tree-like topologies. However, due to space limitation, we present results only for tree-like campus network topologies. We considered different campus network sizes: small (≤100 APs), medium (100-200 APs), large (≥ 200 APs) and extra-large (≥ 2000 APs), with 1-8 gateway routers. As depicted in Fig. 1 and proposed in [START_REF] Onf | SDN in the Campus Environment[END_REF], the switches are divided into two groups: (i) Edge switches that connect the APs to the second layer composed of (ii) Aggregation/Core switches, which themselves are connected to the gateways.

In the wireless part, the interference range R I of each AP is set to 1.5 × R t , where R t is the transmission range. The wireless links capacities are set to 54 Mbps. Note that in practice, and SDN controller can send frequent monitoring probes to estimate wireless link capacities using either active or passive measurement, such as the one proposed in [START_REF] Chen | Monitoring access link capacity using TFRC probe[END_REF]. For the users' arrival, we have used two scenarios. The first one is exploiting real traces provided by CRAWDAD [START_REF] Kotz | CRAWDAD dataset dartmouth/campus (v. 2009-09-09)[END_REF]. Specifically, we have used a dataset that includes syslog records of user association/disassociation for several thousand users at Dartmouth College. The syslog record that indicates a user association is used as a new user arrival and its flow's lifetime is taken based on the corresponding syslog disassociation record. The second scenario models the users' arrival as a Poisson process with rate λ and an exponential lifetime of mean 1/µ = 90 minutes. Each user generates a flow with a uniform throughput demand between 1 and 10 Mbps in both uplink and downlink directions and a delay bound of 4 hops. Other simulation parameters are summarized in Table III and are based on works in [START_REF] Silvia | Joint design and management of energy-aware Mesh Networks[END_REF], [START_REF] Chen | E-Mesh: An energy-efficient cross-layer solution for video delivery in wireless mesh networks[END_REF], [START_REF] Mahadevan | A power benchmarking framework for network devices[END_REF] and [START_REF] Kliazovich | Greencloud: A packet-level simulator of energy-aware cloud computing data centers[END_REF]. It is worth noting that there is no optimal rule for setting the values of parameters β AN T , α AN T , ρ, q 0 , the number of ants and the number of iterations, as pointed out in [START_REF] Sieminski | Ant colony optimization parameter evaluation[END_REF], [START_REF] Dorigo | Ant colony optimization: a new metaheuristic[END_REF]. Hence, we experimentally tuned these parameters by running preliminary tests using different values for each of them. More specifically, we vary β AN T , α AN T , ρ, q 0 between 0 and 1, by step of 0.05, and compare the objective function given in equation [START_REF]The Power of Wireless Cloud[END_REF]. We then pick the values that result in the smallest objective function presented in (2) (see Table III). In addition, since we focus on energy consumption, we set the parameters α E to 0.9 and α S , α R to 0.05 each. Note that, for each network setup, Q is set to 1 |L|×Oinit , where |L| is the number of flows to route and O init is the objective function score produced by any solution given by any other heuristic approach, as suggested by Dorigo et al. in [START_REF] Dorigo | Ant colony optimization: a new metaheuristic[END_REF].

The results are obtained over many simulation runs for each scenario, with a margin error less than 5%, then we calculate the average value of each performance metric. For sake of presentation, we do not plot confidence intervals. In what follows, we first present the convergence of AC-OFER compared to the optimal solution and its computational complexity of AC-OFER. Then, we present the impact of the arrival rate λ and the reconfiguration interval T for the case of small, medium and large-sized campus networks. Finally, we present results on the scalability of our approach in large-sized networks.

D. Convergence to the optimal solution and computation time

First, we show the convergence of our proposed approach towards the optimal solution given by the ILP presented in section IV. To do so, we develop a brute force algorithm that uses exhaustive search to find the optimal solution. As this problem is N P-Hard, we run these tests only for small campus network topologies of 16 APs, and using real traces provided by CRAWDAD [START_REF] Kotz | CRAWDAD dataset dartmouth/campus (v. 2009-09-09)[END_REF], for 48 hours. We measured the energy consumption of the different approaches compared to the optimal solution. The results are reported in Table IV. We can notice that AC-OFER achieves near-optimal solution, with only 3.5% decrease in energy saving on average compared to the optimal solution, but with much shorter runtime. On the other hand, compared to the greedy algorithm, AC-OFER achieves nearly 7% increase in the energy saving on average, but with higher computation time.

Table V further investigates the computation time required to find a new route for a new incoming flow as well as the reconfiguration time for all approaches in small, medium, large and extra-large-sized networks. We can notice that the time required to route a new incoming flow is almost the same for all approaches (around 24-25 ms in the small-size case) since all approaches make use of the Dijkstra algorithm. However, the reconfiguration time of both Greedy-and AC-OFER are very short compared to the optimal solution. Indeed, more than 8 minutes are required for the optimal algorithm, while only 381 ms and 178 ms are required for AC-OFER and Greedy-OFER, respectively. Note also that the computation time is always stable and AC-OFER stays tractable as the reconfiguration time is slightly over one second in the worst case (i.e. extra-large-sized networks). It is worth noting that, for these two latter schemes (i.e., Greedy-and AC-OFER), the computation time for each reconfiguration remains low compared to the reconfiguration period T , which is in the order of minutes (8 minutes and higher in our simulations). However, the optimal algorithm is clearly not suitable as the reconfiguration time is almost equal to the reconfiguration interval T .

E. Impact of arrival rate λ

Second, we study the impact of traffic load on our proposed approach. To do so, we vary the users arrival rate and measure the power consumption in the network for a simulation duration of 48 hours. Fig. 3(a), 3(b), 3(c) and 3(d) show, respectively, the total energy consumption for different arrival rates, the energy consumed by the APs and switches and the flow acceptance ratio in the case of medium-sized networks. From these figures, we can notice that:

• AC-OFER reduces the power consumption compared to the other schemes. Indeed, from Fig. 3(a), when λ ∈ [10, 120], the power saving culminates at 10.5, 37, 100 and 120 kWh compared to Greedy-OFER, MRC, SP and LB, respectively. This corresponds to a power consumption decrease of approximately 6.5%, 17%, 42% and 45%, compared to Greedy-OFER, MRC, SP and LB, respectively. These gains are achieved in both the wireless part (i.e., APs) and the wired campus backbone, as shown in Figs. 3(b) and 3(c). Note that the energy consumption is reduced while the same acceptance ratio is realized for all schemes [see Fig. 3(d)].

• For low arrival rates (i.e., λ < 10), the power saving is negligible because of the light traffic load in the campus backbone. In fact, as there is few traffic in the network and spread around the whole network, flow consolidation is not always possible as the users are located in different areas and require turning on different APs and switches. • For high arrival rates (i.e., λ ≥ 125), the energy saving is stable. The reason behind this is that for high arrival rates, more capacity is needed mainly in the wireless part and flows can not be consolidated through the same paths due to APs capacity constraints.

F. Impact of the reconfiguration time T

Second, we study the impact of the reconfiguration interval T on the performance of AC-OFER. To do so, we fixed λ to 50 requests/hour and varied the reconfiguration interval T between 8 minutes and 1 hour. The total energy consumption and the acceptance ratio for the small-sized network case scenario are shown in Fig. 4.

We can observe from this figure that our approach outperforms the remaining solutions (i.e., Greedy algorithm, SP, MRC, and LB), especially in low values of T since frequent reconfiguration improves the flow re-routing and consolidation to achieve optimal energy consumption [see Fig. 4(a)]. Note that in these simulations, the same acceptance ratio is achieved in all approaches, as shown in Fig. 4(b).

G. Power consumption over time

To further show the behavior of our approach over time, we plot in Fig. 5 the power consumption over time as well as the network utilization of all schemes for medium network loads (i.e., λ = 80 requests/hour). It is clear from this figure that the trend for AC-OFER is maintained over time. In fact, the total energy consumption as well as the energy consumption in the wireless and wired parts are maintained over time, as illustrated in Fig. 5(a), 5(b) and 5(c), respectively. Note that at the same time, the acceptance ratio is similar to all approaches, as shown in Fig. 5(d). More specifically, AC-OFER maintains the energy saving stable around 7%, 17%, 42% and 48% compared to Greedy-OFER, MRC, SP and LB, respectively.

To have a complete picture of the network performance, we plotted in Fig. 6 the normalized values of several performance metrics including acceptance ratio, total consumed energy, consumed energy by APs, consumed energy by switches, proportion of used APs, proportion of used switches, proportion of used links and average link utilization for used links. From this figure, we can observe that, AC-OFER accepts as many flows as SP, MRC and LB. However, it reduces at the same time the energy consumption in both APs and switches. This energy saving is achieved by reducing the number of used APs and switches. For instance, compared to LB, the gains are 48% for the total energy consumption, using 52% less APs and 31% less switches, respectively.

In addition, we can observe that our approach uses a reduced number of links compared to other schemes. In fact, AC-OFER reduces the proportion of used links by 4%, 15%, 43% and 52% compared to Greedy-OFER, MRC, SP and LB, respectively. However, it results in high average link utilization of the used links due to flow consolidation. Indeed AC-OFER uses existing paths to route incoming flows, and performs the dynamic reconfiguration only at each time period T .

It is worth noting that MRC performs better than the LB and SP since, in this case, flows are consolidated according to the residual capacity. However, this scheme is clearly outperformed by AC-OFER thanks to the dynamic reconfiguration.

H. Scalability of AC-OFER

To study the scalability of our approach, we run additional simulations in the case of large-sized networks (i.e., 250 APs, 40 switches, 4 gateway routers) and extra large scale networks (i.e. 2000 APs, 280 switches and 8 gateways). Fig. 7 presents the final values (over 48 hours) of different metrics for the case of large networks. Similar performance results compared to small and medium networks are observed here. Indeed, the energy consumption is reduced by 7%, 35%, 44% and 49% compared to Greedy-OFER, MRC, SP and LB, respectively, while using a reduced number of APs and switches. In addition, the number of used links is reduced for AC-OFER compared to the other approaches. However, these links present higher link utilization.

Fig. 8 shows the final results in the case of extra large campus networks. The same observation is made here too with AC-OFER achieving energy savings of 6.5%, 28%, 38% and 41% compared to Greedy-OFER, MRC, SP and LB, respectively. Similar remarks are also made as AC-OFER uses less APs, switches and links while presenting higher link utilization for the used links.

VII. CONCLUSION

In this paper, we investigated the energy efficiency problem in campus networks. We proposed an online flow-based approach that takes into account the dynamic arrival and departure of users by formulating the problem as an ILP and presenting an ant colony-based approach, called AC-OFER, to approximate the ILP optimal solution. Our objective is to minimize the energy consumption of the network, while routing dynamically the arriving and departing flows subject to QoS constraints (i.e., bandwidth and delay). Moreover, our approach uses link rate adaptation to further reduce energy consumption. Through extensive simulations, we showed that AC-OFER achieves significant reductions in terms of energy consumption, compared to the Greedy algorithm, the Shortest Path (SP) routing, the Minimum link Residual Capacity (MRC) routing metric and the Load Balancing (LB) scheme, while ensuring the required QoS. More specifically, we showed that AC-OFER can reduce the energy consumption by up to 7%, 35%, 44% and 49% compared to Greedy-OFER, MRC, SP and LB, respectively, for different network sizes and traffic loads. At the same time, AC-OFER guarantees a low time complexity for both route discovery and network reconfiguration. This approach represents therefore a promising solution for energy management in campus networks.

Fig. 1 .

 1 Fig. 1. Typical campus network topology

  l∈L e∈E i∈{s(e),d(e)} nce k=1 f e,k,l + l∈L w li = 0 1 Otherwise.where E = E s ∪ E d , s(e) and d(e), respectively, denote the source and destination of link e ∈ E, and i ∈ {s(e), d(e)} denotes that AP i ∈ V is the source or destination of the link e ∈ E.

  If e∈E i∈{s(e),d(e)} nce k=1 f e,k,l = 0 and e∈E i∈{s(e),d(e)} nce k=1 f e,k,l ≥ 1 0 Otherwise.

  i∈{s(e),d(e)} nce k=1 f e,k,l ≥ 1 0

  l∈L f e,k,l × b l C ek + l ∈L e ∈Es f e ,l ,k × b l × I (e,k),(e ,k) C e k ≤ 1 ∀e ∈ E s , ∀k ∈ {1, .., nc e } (11)

Algorithm 1

 1 New arriving flow route computation 1: IN: Campus Network (G(V ∪ W, Es ∪ E d )) with residual capacities in the links and APs, a new l flow to route 2: OUT: A route for the new flow without changing existing flows 3: -Extend G(V ∪ W, Es ∪ E d ) by adding a new node v l 4:

19 :

 19 ] ← undef ined 10: end for 11: dist[l] = 0 12: Q.Enqueue(l) 13: Compute the paths: 14: while not Q.Empty() do 15: u ← Q.getSmallestDist() 16: // get the node with the smallest distance in Q for all v in neighbors u do 20: if (u, v) satisfies the bandwidth demand of d then 21: temp ← power[u] + dif f power(u, v) 22:

Fig. 2 .

 2 Fig. 2. AC-OFER flowchart diagram 1) Formation of solution components:

1 : 12 :

 112 IN: Campus Network with routed flows (i.e., previous routes) 2: OUT: New routes solution (One path for each flow) 3: Set Parameters: q0, αA, βA, Q 4: Initialize pheromone trails and best solution to the previous solution 5: for nb = 1 → Number of Iterations do Choose path j among the K paths where 13: j = Argmax k∈N l τ α A lk × η β A

29 :

 29 Return best solution

Fig. 3 .Fig. 4 .

 34 Fig. 3. Comparison of energy consumption for variable arrival rates (100 APs, 27 switches with 2 gateway routers)

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Comparison of power consumption and acceptance ratio over time for λ = 80 requests/hour (100 APs, 27 switches with 2 gateway routers)

Fig. 8 .

 8 Fig. 8. Comparison of the average values of the different metrics (2000 APs, 280 switches with 8 Gateways, λ = 350 requests/hour)

  If v is used as a mesh router only. This means that v has traffic to forward in the wireless backbone but does not have users attached to it. P AR

		TABLE I
		AP POWER CONSUMPTION PROFILES
	Profile	Explanation
	P R

TABLE II TABLE OF NOTATIONS

 IIOF

	Notation	Meaning
	Es	The set of wireless links
	E d

  Algorithm 2 Discrete Link Rate Adaptation 1: IN: Campus Network (G(V ∪ W, Es ∪ E d )) 2: OUT: link rates for the different links 3: for all e in E d do

	4:	if utilization(e) ≤ r10 then
	5:	rate[e] ← r10
	6:	end if
	7:	if r10 < utilization(e) ≤ r100 then
	8:	rate[e] ← r100
	9:	end if
	10:	if r100 < utilization(e) ≤ r1000 then
	11:	rate[e] ← r1000
	12:	else
	13:	rate[e] ← r10000
	14:	end if
	15: end for

ACKNOWLEDGMENT

This work was supported in part by the CNRS (France) WINDS project under grant agreement no. 25995, and in part by the Natural Science and Engineering Council of Canada (NSERC) under its Discovery Program.