## Section: New Results

### Network Design and Management

Participants : Julien Bensmail, Jean-Claude Bermond, Christelle Caillouet, David Coudert, Frédéric Giroire, Frédéric Havet, Nicolas Nisse, Stéphane Pérennes, Joanna Moulierac, Foivos Fioravantes, Adrien Gausseran, 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 Software Defined Networking (SDN) and Network Function Virtualization (NFV) and how to exploit their potential benefits. We propose algorithms for the Provisioning Service Function Chains (SFC) and algorithms to reconfigure the SFC in order to improve the network operational costs without any interruption (with a *make-before-break approach*) and Virtual Network Functions (VNF) placement algorithms to address the mono- and multi-tenant issues in edge and core networks.
We also propose algorithms for distributed Mininet (Mininet provides a virtual test bed and development environment for software-defined networks (SDN). See http://mininet.org.) in order to improve the performance, and also bandwidth-optimal failure recovery scheme for robust programmable networks.
Secondly, we study optimization problems within optical networks: wavelength reconfiguration for seamless migration and spectrum assignment in elastic optical tree-networks.
Thirdly, we study the scheduling of network tasks within a data center while taking into account the communication between the network resources. We also study distributed link scheduling in wireless networks.
Finally, we investigate on the placement of drones for maximizing the coverage of a landscape by drones in order to localize targets or collect data from sensors.

#### Software Defined Networks and Network Function Virtualization

Recent advances in networks such as Software Defined Networking (SDN) and Network Function Virtualization (NFV) are changing the way network operators deploy and manage Internet services. On the one hand, SDN introduces a logically centralized controller with a global view of the network state. On the other hand, NFV enables the complete decoupling of network functions from proprietary appliances and runs them as software applications on general purpose servers. In such a way, network operators can dynamically deploy Virtual Network Functions (VNFs). SDN and NFV, both separately, bring to network operators new opportunities for reducing costs, enhancing network flexibility and scalability, and shortening the time-to-market of new applications and services. Moreover, the centralized routing model of SDN jointly with the possibility of instantiating VNFs on demand may open the way for an even more efficient operation and resource management of networks. For instance, an SDN/NFV-enabled network may simplify the Service Function Chain (SFC) deployment and provisioning by making the process easier and cheaper. We addressed several questions in this context.

In [15], we aim at investigating how to leverage both SDN and NFV in order to exploit their potential benefits. We took steps to address the new opportunities offered in terms of network design, network resilience, and energy savings, and the new problems that arise in this new context, such as the optimal network function placement in the network. We show that a symbiosis between SDN and NFV can improve network performance and significantly reduce the network's Capital Expenditure (CapEx) and Operational Expenditure (OpEx).

In [50], [57], [58], we consider the problem of reconfiguring SFC 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, while not interrupting the flows.

In [59], we consider the placement of functions in 5G networks in which functions must not only be deployed in large central data centers, but also in the edge. We propose an algorithm that solves the Virtual Network Function Chain Placement Problem allowing a fine management of these rare resources in order to respond to the greatest number of requests possible. Because networks can be divided into several entities belonging to different tenants who are reluctant to reveal their internal topologies, we propose a heuristic that allows the NFV orchestrator to place the function chains based only on an abstract view of the infrastructure network. We leverage this approach to address the complexity of the problem in large mono- or multi-tenant networks. We analyze the efficiency of our algorithm and heuristic with respect to a wide range of parameters and topologies.

In [53], [80], [69], we rethink the network dimensioning problem with protection against Shared Risk Link Group (SLRG) failures in the SDN context. We propose a path-based protection scheme with a global rerouting strategy, in which, for each failure situation, there may be a new routing of all the demands. Our optimization task is to minimize the needed amount of bandwidth. After discussing the hardness of the problem, we develop a scalable mathematical model that we handle using the Column Generation technique. Through extensive simulations on real-world IP network topologies and on random generated instances, we show the effectiveness of our method. Finally, our implementation in OpenDaylight demonstrates the feasibility of the approach and its evaluation with Mininet shows that technical implementation choices may have a dramatic impact on the time needed to reestablish the flows after a failure takes place.

Finally, in [49], [78], [79], we consider the problem of performing large scale SDN networks simulations in a distributed environment. Indeed, networks have become complex systems that combine various concepts, techniques, and technologies. Hence, modelling or simulating them is now extremely complicated and researchers massively resort to prototyping techniques. Among other tools, Mininet is the most popular when it comes to evaluate SDN propositions. It allows to emulate SDN networks on a single computer. However, under certain circumstances experiments (e.g., resource intensive ones) may overload the host running Mininet. To tackle this issue, we propose Distrinet [49], [78], [79], a way to distribute Mininet over multiple hosts. Distrinet uses the same API than Mininet, meaning that it is compatible with Mininet programs. Distrinet is generic and can deploy experiments in Linux clusters or in the Amazon EC2 cloud. Thanks to optimization techniques, Distrinet minimizes the number of hosts required to perform an experiment given the capabilities of the hosting infrastructure, meaning that the experiment is run in a single host (as Mininet) if possible. Otherwise, it is automatically deployed on a platform using a minimum amount of resources in a Linux cluster or with a minimum cost in Amazon EC2.

#### Optimization of optical networks operation

##### Wavelength Defragmentation for Seamless Migration

Dynamic traffic in optical networks leads to spectrum fragmentation, which significantly reduces network performance, i.e., increases blocking rate and reduces spectrum usage. Telecom operators face the operational challenge of operating non-disruptive defragmentation, i.e., within the make-before-break paradigm when dealing with lightpath rerouting in wavelength division multiplexed (WDM) fixed-grid optical networks. In [39], we propose a make-before-break (MBB) Routing and Wavelength Assignment (RWA) defragmentation process, which provides the best possible lightpath network provisioning, i.e., with minimum bandwidth requirement. We tested extensively the models and algorithms we propose on four network topologies with different GoS (Grade of Service) defragmentation triggering events. We observe that, for a given throughput, the spectrum usage of the best make-before-break lightpath rerouting is always less than 2.5% away from that of an optimal lightpath provisioning.

##### On 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 [31], 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.

#### Scheduling

##### When Network Matters: Data Center Scheduling with Network Tasks

We consider in [51] the placement of jobs inside a data center. Traditionally, this is done by a task orchestrator without taking into account network constraints. According to recent studies, network transfers represent up to 50% of the completion time of classical jobs. Thus, network resources must be considered when placing jobs in a data center. In this paper, we propose a new scheduling framework, introducing network tasks that need to be executed on network machines alongside traditional (CPU) tasks. The model takes into account the competition between communications for the network resources, which is not considered in the formerly proposed scheduling models with communication. Network transfers inside a data center can be easily modeled in our framework. As we show, classical algorithms do not efficiently handle a limited amount of network bandwidth. We thus propose new provably efficient algorithms with the goal of minimizing the makespan in this framework. We show their efficiency and the importance of taking into consideration network capacity through extensive simulations on workflows built from Google data center traces.

##### Distributed Link Scheduling in Wireless Networks

In [55], we investigate distributed transmission scheduling in wireless networks. Due to interference constraints, “neighboring links” cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We use the model described by Bui, Sanghavi, and Srikant in [85], [93]. We assume that time is slotted and during each slot there are two phases: one control phase which determines what links will be activated and a data phase in which data are sent. We assume random arrivals on each link during each slot, so that a queue is associated to each link. Since nodes do not have a global knowledge of the network, our aim (like in [85], [93]) is to design for the control phase a distributed algorithm which determines a set of non-interfering links. To be efficient the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead). In this paper, we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues), and it does not require any knowledge of the queue-lengths. We prove that this algorithm gives a maximal set of active links, where in each interference set there is at least one active link. We also establish sufficient conditions for stability under general Markovian assumptions. Finally, the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.

##### 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 $\text{BPRN}$-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the $\text{BMRN}$-colouring model, which can be used to model link scheduling problems where particular types of collisions must be avoided during the node transmissions.

In [25], we initiate the study of the $\text{BMRN}$-colouring model by providing several bounds on the minimum number of colours needed to $\text{BMRN}$-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 $\text{BPRN}$-colouring model as well. We notably prove that every planar digraph can be 8-${\text{BMRN}}^{*}$-coloured, while there exist planar digraphs for which 8 colours are needed in a ${\text{BMRN}}^{*}$-colouring [72]. We also proved that the problem of deciding whether a planar digraph can be $k$-${\text{BMRN}}^{*}$-coloured is NP-hard for every $k\in \{3,...,6\}$.

#### Optimizing drone coverage

##### Self-organized UAV-based Supervision and Connectivity

The use of drones has become more widespread in recent years. Many use cases have been developed involving these autonomous vehicles, ranging from simple delivery of packages to complex emergency situations following catastrophic events. The miniaturization and very low cost of these machines make it possible today to create large meshes to ensure network coverage in disaster areas, for instance. However, the problems of scaling up and self-organization are necessary to solve problems in these use cases.

In the position paper [45], we first present different new requirements for the deployment of unmanned aerial vehicles (UAV) networks, involving the use of many drones. Then, we introduce solutions from distributed algorithms and real-time data processing to ensure quasi-optimal solutions to the raised problems.

In [44], [65], we propose VESPA, a distributed algorithm using only one-hop information of the drones, to discover targets with unknown location and auto-organize themselves to ensure connectivity between them and the sink in a multi-hop aerial wireless network. We prove that connectivity, termination and coverage are preserved during all stages of our algorithm, and we evaluate the algorithm performances through simulations. Comparison with a prior work shows the efficiency of VESPA both in terms of discovered targets and number of used drones.

##### Optimal placement of drones for fast sensor energy replenishment using wireless power transfer

Lifetime is the main issue of wireless sensors networks. Since the nodes are often placed in inaccessible places, the replacement of their battery is not an easy task. Moreover, the node maintenance is a costly and time consuming operation when the nodes are high in numbers. Energy harvesting technologies have recently been developed to replenish part or all of the required energy that allows a node to function. In [47], [48], we use dedicated chargers carried by drones that can fly over the network and transmit energy to the nodes using radio-frequency (RF) signals. We formulate and optimally solve the Optimal Drone Placement and Planning Problem (OD3P) by using a given number of flying drones, in order to efficiently recharge wireless sensor nodes. Unlike other works in the literature, we assume that the drones can trade altitude with coverage and recharge power, while each drone can move across different positions in the network to extend coverage. We present a linear program as well as a fast heuristic algorithm to meet the minimum energy demands of the nodes in the shortest possible amount of time. Our simulation results show the effectiveness of our approaches for network scenarios with up to 50 sensors and a $50\times 50$m terrain size.

##### Efficient Data Collection and Tracking with Flying Drones

Data collection is an important mechanism for wireless sensor networks to be viable. In [34], we address the Aerial Data Collection Problem (ADCP) from a set of mobile wireless sensors located on the ground, using a fleet of flying devices. The objective is i) to deploy a set of UAVs in a 3D space to cover and collect data from all the mobile wireless sensors at each time step through a ground-to-air communication, ii) to send these data to a central base station using multi-hop wireless air-to-air communications through the network of UAVs, iii) while minimizing the total deployment cost (communication and deployment) over time. The Aerial Data Collection Problem (ADCP) is a complex time and space coverage, and connectivity problem. We first present a mixed-integer linear program solving ADCP optimally for small instances. Then, we develop a second model solved by column generation for larger instances, with optimal or heuristic pricing programs. Results show that our approach provides very accurate solutions minimizing the data collection cost. Moreover, only a very small number of columns are generated throughout the resolution process, showing the efficiency of our approach.

#### Other results

##### The Structured Way of Dealing with Heterogeneous Live Streaming Systems

In peer-to-peer networks for video live streaming, peers can share the forwarding load in two types of systems: unstructured and structured. In unstructured overlays, the graph structure is not well-defined, and a peer can obtain the stream from many sources. In structured overlays, the graph is organized as a tree rooted at the server and parent-child relationships are established between peers. Unstructured overlays ensure robustness and a higher degree of resilience compared to the structured ones. Indeed, they better manage the dynamics of peer participation or churn. Nodes can join and leave the system at any moment. However, they are less bandwidth efficient than structured overlays. In [54], we propose new simple distributed repair protocols for video live streaming structured systems. We show, through simulations and with real traces from Twitch, that structured systems can be very efficient and robust to failures, even for high churn and when peers have very heterogeneous upload bandwidth capabilities.

##### Optimal SF Allocation in LoRaWAN Considering Physical Capture and Imperfect Orthogonality

In [46], we propose a theoretical framework for maximizing the long range wide-area networks (LoRaWAN) capacity in terms of the number of end nodes, when they all have the same traffic generation process. The model optimally allocates the spreading factor to the nodes so that attenuation and collisions are optimized. We use an accurate propagation model considering Rayleigh channel, and we take into account physical capture and imperfect spreading factors (SF) orthogonality while guaranteeing a given transmission success probability to each served node in the network. Numerical results show the effectiveness of our SF allocation policy. Our framework also quantifies the maximum capacity of single cell networks and the gain induced by multiplying the gateways on the covered area. We finally evaluate the impact of physical capture and imperfect SF orthogonality on the SF allocation and network performances.