## Section: New Results

### Network Design and Management

Participants : Jean-Claude Bermond, Christelle Caillouet, David Coudert, Frédéric Giroire, Frédéric Havet, Nicolas Huin, Joanna Moulierac, Nicolas Nisse, Stéphane Pérennes, Andrea Tomassilli.

Network design is a very wide subject which concerns all kinds of networks. In telecommunications, networks can be either physical (backbone, access, wireless, ...) or virtual (logical). The objective is to design a network able to route a (given, estimated, dynamic, ...) traffic under some constraints (e.g. capacity) and with some quality-of-service (QoS) requirements. Usually the traffic is expressed as a family of requests with parameters attached to them. In order to satisfy these requests, we need to find one (or many) paths between their end nodes. The set of paths is chosen according to the technology, the protocol or the QoS constraints.

We mainly focus on the following topics: Firstly, we study the new network paradigms, Software-Defined Networks (SDN) and Network Function Virtualization (NFV). On the contrary to legacy networks, in SDN, a centralized controller is in charge of the control plane and takes the routing decisions for the switches and routers based on the network conditions. This new technology brings new constraints and therefore new algorithmic problems such as the problem of limited space in the switches to store the forwarding rules. We then tackle the problem of placement of virtualized resources. We validated our algorithms on a real SDN platform (Testbed with SDN hardware, in particular a switch HP 5412 with 96 ports, hosted at I3S laboratory. A complete fat-tree architecture with 16 servers can be built on the testbed.). Secondly, we consider different scenarios regarding wireless networks and connected Unmanned Aerial Vehicules (UAVs). Third, we tackle routing in the Internet. Last, we study live streaming in distributed systems.

#### Software Defined Networks (SDN)

Software-defined Networks (SDN) is a new networking paradigm enabling innovation through network programmability. SDN is gaining momentum with the support of major manufacturers. Over past few years, many applications have been built using SDN such as server load balancing, virtual-machine migration, traffic engineering and access control.

##### Bringing Energy Aware Routing Closer to Reality With SDN Hybrid Networks

Energy-aware routing aims at reducing the energy consumption of Internet service provider (ISP) networks. The idea is to adapt routing to the traffic load to turn off some hardware. However, it implies to make dynamic changes to routing configurations which is almost impossible with legacy protocols. The software defined network (SDN) paradigm bears the promise of allowing a dynamic optimization with its centralized controller. In [34], we propose smooth energy aware routing (SENAtoR), an algorithm to enable energy-aware routing in a scenario of progressive migration from legacy to SDN hardware. Since in real life, turning off network devices is a delicate task as it can lead to packet losses, SENAtoR also provides several features to safely enable energy saving services: tunneling for fast rerouting, smooth node disabling, and detection of both traffic spikes and link failures. We validate our solution by extensive simulations and by experimentation. We show that SENAtoR can be progressively deployed in a network using the SDN paradigm. It allows us to reduce the energy consumption of ISP networks by 5%–35% depending on the penetration of SDN hardware while diminishing the packet loss rate compared to legacy protocols.

##### Energy-Aware Routing in Software-Defined Network using Compression

Over past few years, many applications have been built using SDN such as server load balancing, virtual-machine migration, traffic engineering and access control. In [31], we focus on using SDN for energy-aware routing (EAR). Since traffic load has a small influence on the power consumption of routers, EAR allows putting unused links into sleep mode to save energy. SDN can collect traffic matrix and then computes routing solutions satisfying QoS while being minimal in energy consumption. However, prior works on EAR have assumed that the SDN forwarding table switch can hold an infinite number of rules. In practice, this assumption does not hold since such flow tables are implemented in Ternary Content Addressable Memory (TCAM) which is expensive and power-hungry. We consider the use of wildcard rules to compress the forwarding tables. In [31], we propose optimization methods to minimize energy consumption for a backbone network while respecting capacity constraints on links and rule space constraints on routers. In details, we present two exact formulations using Integer Linear Program (ILP) and introduce efficient heuristic algorithms. Based on simulations on realistic network topologies, we show that using this smart rule space allocation, it is possible to save almost as much power consumption as the classical EAR approach.

##### Complexity of Compressing Two Dimensional Routing Tables with Order

Motivated by routing in telecommunication network using Software Defined Network (SDN) technologies, we consider the following problem of finding short routing lists using aggregation rules. We are given a set of communications $\mathcal{X}$, which are distinct pairs $(s,t)\subseteq S\times T$, (typically $S$ is the set of sources and $T$ the set of destinations), and a port function $\pi :\mathcal{X}\to P$ where $P$ is the set of ports.
A *routing list* $\mathcal{R}$ is an ordered list of triples which are of the form $(s,t,p)$, $(*,t,p)$, $(s,*,p)$ or $(*,*,p)$ with $s\in S$, $t\in T$ and $p\in P$.
It *routes* the communication $(s,t)$ to the port $r(s,t)=p$ which appears on the first triple in the list $\mathcal{R}$ that is of the form $(s,t,p)$, $(*,t,p)$, $(s,*,p)$ or $(*,*,p)$. If $r(s,t)=\pi (s,t)$, then we say that $(s,t)$ is *properly routed* by $\mathcal{R}$ and
if all communications of $\mathcal{X}$ are properly routed, we say that $\mathcal{R}$ *emulates* $(\mathcal{X},\pi )$.
The aim is to find a shortest routing list emulating $(\mathcal{X},\pi )$.
In [30], we carry out a study of the complexity of the two dual decision problems associated to it.
Given a set of communication $\mathcal{X}$, a port function $\pi $ and an integer $k$, the first one called Routing List (resp. the second one, called List Reduction ) consists in deciding whether there is a routing list emulating $(\mathcal{X},\pi )$ of size at most $k$ (resp. $\left|\mathcal{X}\right|-k$).
We prove that both problems are NP-complete.
We then give a 3-approximation for List Reduction , which can be generalized to higher dimensions. We also give a 4-approximation for Routing List in the fundamental case when there are only two ports (i.e. $\left|P\right|=2$), $\mathcal{X}=S\times T$ and $\left|S\right|=\left|T\right|$.

#### Provisioning Service Function Chains

##### Optimal Network Service Chain Provisioning

Service chains consist of a set of network services, such as firewalls or application delivery controllers, which are interconnected through a network to support various applications. While it is not a new concept, there has been an extremely important new trend with the rise of Software-Defined Network (SDN) and Network Function Virtualization (NFV). The combination of SDN and NFV can make the service chain and application provisioning process much shorter and simpler. In [33], [48], we study the provisioning of service chains jointly with the number/location of Virtual Network Functions (VNFs). While chains are often built to support multiple applications, the question arises as how to plan the provisioning of service chains in order to avoid data passing through unnecessary network devices or servers and consuming extra bandwidth and CPU cycles. It requires choosing carefully the number and the location of the VNFs. We propose an exact mathematical model using decomposition methods whose solution is scalable in order to conduct such an investigation. We conduct extensive numerical experiments, and show we can solve exactly the routing of service chain requests in a few minutes for networks with up to 50 nodes, and traffic requests between all pairs of nodes. Detailed analysis is then made on the best compromise between minimizing the bandwidth requirement and minimizing the number of VNFs and optimizing their locations using different data sets.

##### Energy-Efficient Service Function Chain Provisioning

Network Function Virtualization (NFV) is a promising network architecture concept to reduce operational costs. In legacy networks, network functions, such as firewall or TCP optimization, are performed by specific hardware. In networks enabling NFV coupled with the Software Defined Network (SDN) paradigm, Virtual Network Functions (VNFs) can be implemented dynamically on generic hardware. This is of primary interest to implement energy efficient solutions, in order to adapt the resource usage dynamically to the demand. In [35], we study how to use NFV coupled with SDN to improve the energy efficiency of networks. We consider a setting in which a flow has to go through a Service Function Chain, that is several network functions in a specific order. We propose an ILP formulation, an ILP-based heuristic, as well as a decomposition model that relies on joint routing and placement configuration to solve the problem. We show that virtualization provides between 22% to 62% of energy savings for networks of different sizes.

##### Placement of Service Function Chains with Ordering Constraints

A Service Function Chain (SFC) is an ordered sequence of network functions, such as load balancing, content filtering, and firewall. With the Network Function Virtualization (NFV) paradigm, network functions can be deployed as pieces of software on generic hardware, leading to a flexibility of network service composition. Along with its benefits, NFV brings several challenges to network operators, such as the placement of virtual network functions. In [49], [50], [62], we study the problem of how to optimally place the network functions within the network in order to satisfy all the SFC requirements of the flows. Our optimization task is to minimize the total deployment cost. We show that the problem can be seen as an instance of the Set Cover Problem, even in the case of ordered sequences of network functions. It allows us to propose two logarithmic factor approximation algorithms which have the best possible asymptotic factor. Further, we devise an optimal algorithm for tree topologies. Finally, we evaluate the performances of our proposed algorithms through extensive simulations. We demonstrate that near-optimal solutions can be found with our approach.

##### Resource Requirements for Reliable Service Function Chaining

We study in [51], [49] the problem of deploying reliable Service Function Chains over a virtualized network function architecture. While there is a need for reliable service function chaining, there is a high cost to pay for it in terms of bandwidth and VNF processing requirements. We investigate two different protection mechanisms and discuss their resource requirements, as well as the latency of their paths. For each mechanism, we develop a scalable exact mathematical model using column generation.

##### Path protection in optical flexible networks with distance-adaptive modulation formats

Thanks to a flexible frequency grid, Elastic Optical Networks (EONs) will support a more efficient usage of the spectrum resources. On the other hand, this efficiency may lead to even more disruptive effects of a failure on the number of involved connections with respect to traditional networks. In [52], we study the problem of providing path protection to the lightpaths against a single fiber failure event in the optical layer. Our optimization task is to minimize the spectrum requirements for the protection in the network. We develop a scalable exact mathematical model using column generation for both shared and dedicated path protection schemes. The model takes into account practical constraints such as the modulation format, regenerators, and shared risk link groups. We demonstrate the effectiveness of our model through extensive simulation on two real-world topologies of different sizes. Finally, we compare the two protection schemes under different scenario assumptions, studying the impact of factors such as number of regenerators and demands on their performances.

##### Reconfiguring Service Functions chains with a make-before-break approach

The centralized routing model of SDN jointly with the possibility of instantiating VNFs on-demand open the way for a more efficient operation and management of networks. In [58], we consider the problem of reconfiguring network connections with the goal of bringing the network from a sub-optimal to an optimal operational state. We propose optimization models based on the *make-before-break* mechanism, in which a new path is set up before the old one is torn down. Our method takes into consideration the chaining requirements of the flows and scales well with the number of nodes in the network.
We show that, with our approach, the network operational cost defined in terms of both bandwidth and installed network function costs can be reduced and a higher acceptance rate can be achieved.

#### Capacity defragmentation

Optical multilayer optimization continuously reorganizes layer 0-1-2 network elements to handle both existing and dynamic traffic requirements in the most efficient manner. This delays the need to add new resources for new requests, saving CAPEX and leads to optical network defragmentation.

In [46], [47], we focus on Layer 2, i.e., on capacity defragmentation at the Optical Transport Network (OTN) layer when routes (e.g., LSPs in MPLS networks) are making unnecessarily long detours to evade congestion. Reconfiguration into optimized routes can be achieved by redefining the routes, one at a time, so that they use the vacant resources generated by the disappearance of services using part of a path that transits the congested section. For the Quality of Service, it is desirable to operate under Make-Before-Break (MBB), with the minimum number of rerouting. The challenge is to identify the rerouting order, one connection at a time, while minimizing the bandwidth requirement. We propose in [46], [47] an exact and scalable optimization model for computing a minimum bandwidth rerouting scheme subject to MBB in the OTN layer of an optical network. Numerical results show that we can successfully apply it on networks with up to 30 nodes, a very significant improvement with the state of the art. We also provide some defragmentation analysis in terms of the bandwidth requirement vs. the number of reroutings.

In [37], we focus on wavelength defragmentation in WDM networks. We propose a MBB wavelength defragmentation process which minimizes the bandwidth requirement of the resulting provisioning. Comparisons with minimum bandwidth provisioning that is not subject to MBB show that, on average, the best seamless lightpath rerouting is never more than 5% away (less than 1% on average) from an optimal lightpath provisioning.

#### Spectrum assignment in elastic optical tree-networks

To face the explosion of the Internet traffic, a new generation of optical networks is being developed; the Elastic Optical Networks (EONs). EONs use the optical spectrum efficiently and flexibly, but that gives rise to more difficulty in the resource allocation problems. In [16], we study the problem of Spectrum Assignment (SA) in Elastic Optical Tree-Networks. Given a set of traffic requests with their routing paths (unique in the case of trees) and their spectrum demand, a spectrum assignment consists in allocating to each request an interval of consecutive slots (spectrum units) such that a slot on a given link can be used by at most one request. The objective of the SA problem is to find an assignment minimizing the total number of spectrum slots to be used. We prove that SA is NP-hard in undirected stars of 3 links and in directed stars of 4 links, and show that it can be approximated within a factor of 4 in general stars. Afterwards, we use the equivalence of SA with a graph coloring problem (interval coloring) to find constant-factor approximation algorithms for SA on binary trees with special demand profiles.

#### Optimizing drone coverage

In the context of a collaboration with Tahiry Razafindralambo from the University of la Réunion we have studied several problems related to deployment of drones in order to collect data generated from sensors. Those problems may be seen as belonging to the category of "cover" problems and we have designed and proposed efficient formulations using linear programming models with columns generation.

Drones (Unmanned Aerial Vehicles, UAV) can be used to provide anytime and anywhere network access to targets located on the ground, using air-to-ground and air-to-air communications through directional antennas. In [43] we study how to deploy these drones to cover a set of fixed targets. It is a complex problem since each target should be covered, while minimizing (i) the deployment cost and (ii) the drones altitudes to ensure good communication quality. We also consider connectivity between the drone and a base station in order to collect and send information to the targets, which is not considered in many similar studies. We provide an efficient optimal program to solve the problem and show the trade-off analysis due to conflicting objectives. We propose a fair trade-off optimal solution and also evaluate the cost of adding connectivity to the drone deployment.

In [41], [42] we introduce a Linear Programming (LP) model for the problem of data gathering with mobile drones. The goal is to deploy a connected set of Unmanned Aerial Vehicles (UAVs) continuously monitoring mobile sensors and reporting information to a fixed base station for efficient data collection. We propose an effective optimization model reducing the number of variables of the problem and solved using column generation. Results show that our model is tractable for large topologies with several hundreds of possible 3D locations for the UAVs deployment and provides integer solutions with the generated columns very close to the optimum. Moreover, the deployment changes among time remains low in terms of number of UAVs and cost, to maintain connectivity and minimize the data collection delay to the base station.

We also have studied a problem arising when one will to recharge wireless sensor networks using drones and wireless power transfer; in [44] we consider the optimal energy replenishment problem (OERP). The goal is to operate a given number of flying drones in order to efficiently recharge wireless sensor nodes. We present a linear program that maximizes the amount of harvested energy to the sensors. We show that the model is solved to optimality in a few seconds for sensor networks with up to 50 nodes. The small number of available drones is shown to be optimally deployed at low altitude in order to efficiently recharge the batteries of at least half of the sensor nodes.

#### Other results in wireless networks

##### Backbone colouring and algorithms for TDMA scheduling

We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the $BPRN$-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the $BMRN$-colouring model, which can be used to model link scheduling problems where particular types of collisions must be avoided during the node transmissions.

In [64], we initiate the study of the $BMRN$-colouring model by providing several bounds on the minimum number of colours needed to $BMRN$-colour digraphs, as well as several complexity results establishing the hardness of finding optimal colourings. We also give a special focus on these considerations for planar digraph topologies, for which we provide refined results. Some of these results extend to the $BPRN$-colouring model as well.

##### Gossiping with interference in radio chain networks

In [53], we study the problem of gossiping with interference constraint in radio chain networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and wants to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and efficient algorithms that attain this makespan. The network is assumed to be synchronous, the time is slotted into steps, and each device is equipped with a half duplex interface; so, a node cannot both receive and transmit during a step. We use a binary asymmetric model of interference based on the distance in the communication digraph. We determine exactly the minimum number of rounds $R$ needed to achieve a gossiping when transmission network is a dipath ${P}_{n}$ on $n\ge 3$ nodes and the interference distance is ${d}_{I}=1$.