Sécurisation de réseaux multicouches : modèles et polyèdres

This thesis deals with a problem related to survivability issues in multilayer IP-over-WDM networks. Given a set of traffic demands for which we know a survivable logical routing in the IP layer, the aim is determine the corresponding survivable topology in the WDM layer. We show that the problem is NP-hard even for a single demand. Moreover, we propose four integer linear programming formulations for the problem. The first one is based on the so-called cut inequalities. We consider the polyhedron associated with the formulation. We identify several families of valid inequalities and discuss their facial aspect. We also develop separation routines. Using this, we devise a Branch-and-Cut algorithm and present experimental results. The second formulation uses paths between terminals of the underlying graph as variables. We devise a Branch-and-Price algorithm based on that formulation. In addition, we investigate a natural formulation for the problem which uses only the design variables.  Finally, we propose an extended compact formulation which, in addition to the design variables, uses routing variables. We show that this formulation provides a tighter bound for the problem.Dans cette thèse, nous nous intéressons à un problème de fiabilité dans les réseaux multicouches IP-sur-WDM. Etant donné un ensemble de demandes pour lesquelles on connaît une topologie fiable dans la couche IP, le problème consiste à sécuriser la couche optique WDM en y cherchant une topologie fiable. Nous montrons que le problème est NP-complet même dans le cas d'une seule demande. Ensuite, nous proposons quatre formulations en termes de programmes linéaires en nombres entiers pour le problème. La première est basée sur les contraintes de coupes. Nous considérons le polyèdre associé. Nous identifions de nouvelles familles de contraintes valides et étudions leur aspect facial. Nous proposons également des algorithmes de séparation pour ces contraintes. En utilisant ces résultats, nous développons un algorithme de coupes et branchements pour le problème et présentons une étude expérimentale. La deuxième formulation utilise comme variables des chemins entre des terminaux dans le graphe sous-jacent. Un algorithme de branchements et génération de colonnes est proposé pour cette formulation. Par la suite, nous discutons d'une formulation dite naturelle utilisant uniquement les variables de design. Enfin, nous présentons une formulation étendue compacte qui, en plus des variables naturelles, utilise des variables de routage. Nous montrons que cette formulation fournit une meilleure borne inférieure

The edge-labeled survivable network design problem: Formulations and branch-and-cut

In this paper, we study a variant of the survivable network design problem, that is the survivable network design problem with labels (colors) on the edges. In particular, we address the Generalized Labeled Two Edge Connected Subgraph Problem (GLTECSP) that has many applications in telecommunication and transportation. Given a connected undirected graph G such that with each edge is associated a set of labels (colors), the GLTECSP consists in finding a two-edge connected spanning subgraph of G with a minimum number of distinct labels. We propose two Integer Programming (IP) formulations for the problem, a natural formulation using cuts on the edges, and a compact formulation using color-cuts. We devise Branch-and-Cut algorithms to solve both formulations and compare them on sets of randomly generated instances. Computational results show that the compact formulation outperforms the natural one regarding the linear relaxation and the computational time. Moreover, the compact formulation is able to solve to optimality several instances left unsolved within the time limit by the natural formulation

Equal Cost Multiple Path Energy-Aware Routing in Carrier-Ethernet Networks with Bundled Links

International audienceThe reduction of operational expenditure has become a major concern for telecommunication operators and Internet service providers. In this paper, we propose an energy aware routing (EAR) in Carrier Ethernet networks operating with Shortest Path Bridging (SPB) protocol with equal cost multi-path (ECMP). Since traffic load has no influence on power consumption of Carrier Ethernet network elements, the conventional solution to reduce power consumption is to find the maximal set of network elements that can be turned off/on so that the network performance is not deteriorated. To tackle this optimization problem, we propose an exact method based on Mixed Integer Linear Programming (MILP) formulation, called SPB energy-aware routing (SPB-EAR). Since SPB-EAR is proved to be NP-hard, we present two heuristics algorithm suitable for large-sized networks, called Green SPB (G-SPB) and Fast Greedy SPB (FG-SPB). In this work, we consider that a connection between two nodes is represented by bundled link consisting of multiple cables. Experimentations on four realistic network topologies show that G-SPB and FG-SPB can save almost as much power consumption as SPB-EAR

Le problème de sécurisation multicouche du réseau optique

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Design of Multilayer Survivable Optical Networks

We consider the following survivable IP-over-optical network design problem. Given a set of demands and two node-disjoint paths routing each demand in the IP layer, the problem is to find for each demand two node-disjoint paths in the optical layer going through the optical switches corresponding to the routers visited in the IP layer paths and respecting the same order. We give two integer programming formulations: a cut formulation and a path formulation. We discuss the polyhedron associated with the first one and the pricing problem of the latter and present some computational results.ou

Energy-Aware Routing in Carrier-Grade Ethernet using SDN Approach

International audienceSoft-Defined Networking (SDN) is a new approach that enables operators to easily manage all the network elements. In this paper, we address the problem of energy-aware routing in SDN-based carrier-grade Ethernet networks. Our approach is based on turning off network nodes and links to reduce energy consumption, while respecting the rule space capacity for each Openflow switch, and maintaining an allowable maximum link utilization. The problem of identifying the optimal set of network elements to be turned off is NP-hard. We first present an exact model based on an Integer Linear Programming formulation for the problem. Then, we describe a set of first-fit heuristic algorithms suitable for large-sized networks. The exact and heuristic approaches are tested on SNDlib-based instances. Experimentations show the efficiency of both exact and heuristic methods for different network topologies. In particular, our heuristic algorithms are able to achieve a good balance between energy consumption, resource utilization, and network performance

Two Node-Disjoint Paths Routing for Energy-Efficiency and Network Reliability

International audienceCarrier grade networks are in general over-dimensioned in order to protect against network resource failures and to handle probable traffic peaks. Such network design exhibits non-negligible energy waste. As well known, during network operation, the traffic load varies remarkably over day hours. Typically, a significant amount of energy saving can be achieved by turning off redundant and underutilized resources. Ensuring a sufficient level of reliability while taking into account energy saving objective is a very challenging task. In this paper, we study the multi-commodity reliable network design for carrier Ethernet networks. Each traffic demand is routed along one working path, and a corresponding backup path computed considering dedicated protection scheme. The primary and backup path must be node-disjoint. We also assume that the links of the carrier grade networks are made of multiple physical cables called bundles. We propose an exact method based on an Integer Linear Programming (ILP) formulation for the two node-disjoint paths with energy-aware routing (TNDP-EAR) problem. The studied problem is known to be NP-hard. In order to solve it efficiently, we propose a heuristic-based algorithm called GreenTNDP. Preliminary experimental results show the effectiveness of our algorithms to solve the problem

Multilayer Survivable Optical Network Design

With the explosive growth of traffic data, telecommunication networks have evolved toward a model of high-speed IP routers interconnected by intelligent optical core networks. This IP-over-optical architecture is particularly considered as an important opportunity for telecommunication carriers who want to vary services and add more multimedia applications. In our work, we are interested in the problem of survivability in multilayer IP-over-optical networks. Given a set of traffic demands for which we know a survivable logical routing in the IP layer, our purpose is to determine the corresponding survivable topology in the optical layer. We show that the problem is NP-hard even for one demand. We formulate the problem in terms of 0 − 1 linear program based on path variables. We discuss the pricing problem and prove that it reduces to a shortest path problem. Using this, we propose a Branch-and-Price algorithm. Some preliminary computational results are also discussed.ou

Probabilistic Tabu search with multiple neighborhoods for the Disjunctively Constrained Knapsack Problem

Given a set of items, each with a profit and a weight and a conflict graph describing incompatibilities between items, the Disjunctively Constrained Knapsack Problem is to select the maximum profit set of compatible items while satisfying the knapsack capacity constraint. We develop a probabilistic tabu search heuristic with multiple neighborhood structures. The proposed algorithm is evaluated on a total of 50 benchmark instances from the literature up to 1000 items. Computational results disclose that the proposed tabu search method outperforms recent state-of-the-art approaches. In particular, our approach is able to reach 46 best known solutions and discover 8 new best known solutions out of 50 benchmark instances