## Section: New Results

### Network Design and Management

Participants : 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 four 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, in particular, wireless backhaul networks, linear access networks for transportation systems, 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), in particular OpenFlow, 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.

##### Minnie : an SDN World with Few Compressed Forwarding Rules

While SDN brings flexibility to the management of flows within the data center fabric, this flexibility comes at the cost of smaller routing table capacities. Indeed, the Ternary Content-Addressable Memory (TCAM) needed by SDN devices has smaller capacities than CAMs used in legacy hardware. Also, we investigate in [37] compression techniques to maximize the utility of SDN switches forwarding tables. We validate our algorithm, called Minnie , with intensive simulations for well-known data center topologies, to study its efficiency and compression ratio for a large number of forwarding rules. Our results indicate that Minnie scales well, being able to deal with around a million of different flows with less than 1000 forwarding entries per SDN switch, requiring negligible computation time.

To assess the operational viability of Minnie in real networks, we deployed a testbed able to emulate a $k=4$ Fat-Tree data center topology. We demonstrate on the one hand, that even with a small number of clients, the limit in terms of number of rules is reached if no compression is performed, increasing the delay of new incoming flows. Minnie , on the other hand, reduces drastically the number of rules that need to be stored, with no packet losses, nor detectable extra delays if routing lookups are done in the Application-Specific Integrated Circuits (ASICs).

Hence, both simulations and experimental results suggest that Minnie can be safely deployed in real networks, providing compression ratios between 70% and 99%.

##### Bringing Energy Aware Routing closer to Reality with SDN Hybrid Networks

Energy aware routing aims at reducing the energy consumption of ISP networks. The idea is to adapt routing to the traffic load in order to turn off some hardware. However, it implies to make dynamic changes to routing configurations which is almost impossible with legacy protocols. The SDN paradigm bears the promise of allowing a dynamic optimization with its centralized controller.

In [49], [59], we propose 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 equipments is a delicate task as it can lead to packet losses, SENAtoR provides also 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 Minnie can be progressively deployed in a network using the SDN paradigm. It allows to reduce the energy consumption of ISP networks by 5 to 35% depending on the penetration of SDN hardware, while diminishing the packet loss rate compared to legacy protocols.

##### Network Function Virtualization (NFV) and Service Function Chains

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, network functions can be implemented dynamically on generic hardware. The challenge is then to efficiently provision the service chain requests, while finding the best compromise between the bandwidth requirements, the number of locations for hosting Virtual Network Functions (VNFs), and the number of chain occurrences.

In [48], we propose two ILP (Integer Linear Programming) models for routing service chain requests, one of them with a decomposition modeling. 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. We investigate the best compromise between the bandwidth requirements and the number of VNF nodes.

In [50], 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 a decomposition model that relies on lightpath configuration to solve the problem. We show that virtualization allows to obtain between 30% to 55% of energy savings for networks of different sizes.

#### Wireless networks

We study optimization problems on various kinds of wireless networks.

##### Computing and maximizing the exact reliability of wireless backhaul networks

The reliability of a fixed wireless backhaul network is the probability that the network can meet all the communication requirements considering the uncertainty (e.g., due to weather) in the maximum capacity of each link. We provide in [45] an algorithm to compute the exact reliability of a backhaul network, given a discrete probability distribution on the possible capacities available at each link. The algorithm computes a conditional probability tree, where at each leaf in the tree a valid routing for the network is evaluated. Any such tree provides bounds on the reliability, and the algorithm improves these bounds by branching in the tree. We also consider the problem of determining the topology and configuration of a backhaul network that maximizes reliability subject to a limited budget. We provide an algorithm that exploits properties of the conditional probability tree used to calculate reliability of a given network design, and we evaluate its computational efficiency.

##### Analysis of the Failure Tolerance of Linear Access Networks

In [28], we study the disconnection of a moving vehicle from a linear access network composed by cheap WiFi Access Points in the context of the telecommuting in massive transportation systems. In concrete terms, we analyze the probability for a user to experience a disconnection longer than a given time interval (${t}^{*}$) such that all on-going communications between the vehicle and the infrastructure network are disrupted. We provide an approximation formula considering two scenarios (intercity bus and train). We then carry out a sensitivity analysis and supply a guide for operators when choosing the parameters of the networks. Last, we show that such systems are viable, as they attain a very low probability of long disconnections with a very low maintenance cost.

##### Efficient Deployment of Connected Unmanned Aerial Vehicles for Optimal Target Coverage

Anytime and anywhere network access can be provided by Unmanned Aerial Vehicles (UAV) with air-to-ground and air-to-air communications using directional antennas for targets located on the ground. Deploying these Unmanned Aerial Vehicles to cover targets is a complex problem since each target should be covered, while minimizing (i) the deployment cost and (ii) the UAV altitudes to ensure good communication quality. We also consider connectivity between the UAVs and a base station in order to collect and send information to the targets, which is not considered in many similar studies. In [40], we provide an efficient optimal program to solve this 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 UAV deployment.

#### Routing in the Internet

##### Routing at Large Scale: Advances and Challenges for Complex Networks

A wide range of social, technological and communication systems can be described as complex networks. Scale-free networks are one of the well-known classes of complex networks in which nodes degree follow a power-law distribution. The design of scalable, adaptive and resilient routing schemes in such networks is very challenging. In [38], we present an overview of required routing functionality, categorize the potential design dimensions of routing protocols among existing routing schemes and analyze experimental results and analytical studies performed so far to identify the main trends/trade-offs and draw main conclusions. Besides traditional schemes such as hierarchical/shortest-path path-vector routing, the article pays attention to advances in compact routing and geometric routing since they are known to significantly improve the scalability in terms of memory space. The identified trade-offs and the outcomes of this overview enable more careful conclusions regarding the (in-)suitability of different routing schemes to large-scale complex networks and provide a guideline for future routing research. This article concludes the European Project FP7 STREP EULER (2010-2014).

##### Grid spanners with low forwarding index for energy efficient networks

A routing $R$ of a connected graph $G$ is a collection that contains simple paths connecting every ordered pair of vertices in $G$. The *edge-forwarding index with respect to $R$* (or simply the forwarding index with respect to $R$) $\pi (G,R)$ of $G$ is the maximum number of paths in $R$ passing through any edge of $G$. The *forwarding index* $\pi \left(G\right)$ of $G$ is the minimum $\pi (G,R)$ over all routings $R$'s of $G$. This parameter has been studied for different graph classes. Motivated by energy efficiency, we look in
[30] for different numbers of edges, at the best spanning graphs of a square grid, namely those with a low forwarding index.

#### Live streaming in distributed systems

Peer to peer networks are an efficient way to carry out video live streaming as the forwarding load is distributed among peers. These systems can be of two types: unstructured and structured. In unstructured overlays, the peers obtain the video in an opportunistic way. The advantage is that such systems handle churn well. However, they are less bandwidth efficient than structured overlays, and the control overhead has a non-negligible impact on the performance. In structured overlays, the diffusion of the video is made via an explicit diffusion tree. The advantage is that the peer bandwidth can be optimally exploited. The drawback is that the departure of peers may break the diffusion tree.

In [29], we propose and analyze a simple local algorithm to balance a tree. In this distributed repair algorithm, each node carries out local operations based on its degree and on the subtree sizes of its children. In a synchronous setting, we first prove that starting from any $n$-node tree our process converges to a balanced binary tree in $O\left({n}^{2}\right)$ rounds. We then describe a more restrictive model, adding a small extra information to each node, under which we adapt our algorithm to converge in $\Theta (nlogn)$ rounds.

In [58], we propose new simple distributed repair protocols for video live streaming structured systems. We show, through simulations with real traces, that structured systems can be very efficient and robust to failures, even for high churn and when peers have very heterogeneous upload bandwidth capabilities.