Solving a resource allocation problem in RFB-based 5G wireless networks

International audienceIn this work, we consider the 5G network architecture outcome of the Horizon 2020 project Superfluidity, where the main building blocks are virtual entities, namely Reusable Functional Blocks (RFBs). This 5G Superfluid network composed of RFBs and physical 5G nodes allows a high level of flexibility, agility, portability and high performance. The emergency problem we face is how to optimally minimize the total installation costs of such a Superfluid network while guaranteeing a minimum required user coverage and minimum downlink traffic demand. We propose an approach to break down the main resource allocation problem in a set of simplified problems that allow the computation of the solution in a more efficient way. Numerical results illustrate our findings

Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity

International audienceFlow thinning (FT) is a concept of a traffic routing and protection strategy applicable to communication networks withvariable capacity of links. In such networks, the links do not attain their nominal (maximum) capacity simultaneously, so in atypical network state only some links are fully available whereas on each of the remaining links only a fraction of itsmaximum capacity is usable. Every end-to-end traffic demand is assigned a set of logical tunnels whose total capacity isdedicated to carry the demand’s traffic. The nominal (i.e., maximum) capacity of the tunnels, supported by the nominal(maximum) link capacity, is subject to state-dependent thinning to account for variable capacity of the links fluctuating belowthe maximum. Accordingly, the capacity available on the tunnels is also fluctuating below their nominal levels and hence theinstantaneous traffic sent between the demand’s end nodes must accommodate to the current total capacity available onits dedicated tunnels. The related multi-commodity flow optimization problem is NP-hard and its noncompact linearprogramming formulation requires path generation. For that, we formulate an integer programming pricing problem, atthe same time showing the cases when the pricing is polynomial. We also consider an important variant of FT, affinethinning, that may lead to practical FT implementations. We present a numerical study illustrating traffic efficiency of FT andcomputational efficiency of its optimization models. Our considerations are relevant, among others, for wireless meshnetworks utilizing multiprotocol label switching tunnels

Proportional and maxmin fairness for the sensor location problem with chance constraints

International audienceIn this paper we present a study on the Equitable Sensor Location Problem and we focus on the stochastic version of the problem where the surveying capacity of some sensors is measured as probability of intrusions detection. The Equitable Sensor Location Problem, which is an extension of the Equitable Facility Location Problem, considers installing surveying facilities as cameras/sensors in order to monitor and protect some important locations. Each location can be simultaneously protected by multiple facilities. Clearly this problem falls into the category of Maximal Coverage Location Problem and we focus on the equitable variant. The objective of the Equitable Sensor Location Problem is to provide equitable protection to all locations when the number of sensors that can be placed is limited. We study the resilient and ambiguous versions of this problem. The resilient sensor location problem considers the case when some sensors are assumed to fail partially or completely. The ambiguous version studies the case when the surveying probabilities are uncertain and represented by independent Bernouilli random variables with the corresponding ambiguity set containing the Bernouilli probability distributions. For each problem we consider two popular fairness measures which are the lexicographic optimal and proportionally fair solutions and provide an integer linear formulation together with the solution methodology. Numerical results for each studied problem are provided at the end of the paper

Review of Optimization Problems in Wireless Sensor Networks

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An automatic restoration scheme for switch-based networks

International audienceThis paper presents a fully automated distributed resilient routing scheme for switch-based or new generation router based networks. The failure treatment is done locally and other nodes in the network do not need to undertake special actions. In contrast to conventional IP routing schemes, each node routes the traffic on the basis of the entering arc and of the destination. The resulting constraint is that two flows to the same destination entering in a node by a common arc have to merge after this arc. It is shown that this is sufficient for dealing with all single link failure situations, assuming that the network is symmetric and two-link connected. Two heuristic approaches are proposed to handle the corresponding dimensioning problem for large network instances. The proposed method generalizes some methods of literature [6], [8] and provides more cost-efficient solutions

A dynamic programming approach for a class of robust optimization problems

Common approaches to solving a robust optimization problem decompose the problem into a master problem (MP) and adversarial problems (APs). The MP contains the original robust constraints, written, however, only for nite numbers of scenarios. Additional scenarios are generated on the y by solving the APs. We consider in this work the budgeted uncertainty polytope from Bertsimas and Sim, widely used in the literature, and propose new dynamic programming algorithms to solve the APs that are based on the maximum number of deviations allowed and on the size of the deviations. Our algorithms can be applied to robust constraints that occur in various applications such as lot-sizing, the traveling salesman problem with time windows, scheduling problems, and inventory routing problems, among many others. We show how the simple version of the algorithms leads to a fully polynomial time approximation scheme when the deterministic problem is convex. We assess numerically our approach on a lot-sizing problem, showing a comparison with the classical mixed integer linear programming reformulation of the AP

Resilient Network Design

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Optimisation lexicographique et ses applications aux réseaux de télécommunication

Cette thèse porte sur l'optimisation lexicographique et ses applications aux réseaux de télécommunication. Elle est organisée en trois parties. Dans la première partie nous présentons un bref rappel des notions de base de l'équité max-min et passons en revue les travaux les plus significatifs dans le domaine. Nous continuons avec la description d'une approche polynomiale pour le problème d'équilibrage de charge dans les réseaux de télécommunication. La deuxième partie est consacrée à l'application de la théorie d'équité max-min aux problèmes de sécurisation de réseaux. Nous nous intéressons aux pannes simples (i.e. non simultanée) de lien. Nous étudions le problème du calcul d'un routage réalisable dont le vecteur de satisfaction minimale des demandes associé à l'ensemble des pannes de lien est leximin maximal. Nous nous intéressons au cas de calcul des chemins pour le routage/reroutage de bout en bout partiel avec récupération des capacités libérées. Nous passons en revue également les autres stratégies de reroutage. La méthode de calcul est basée sur la formulation arc-chemin utilisant à la fois décomposition de Benders et génération de chemins. La troisième partie de cette thèse est consacrée aux stratégies de protection robuste destinées à faire face aux pannes de lien. Notre démarche consiste à obtenir un schéma de routage qui combine à la fois la robustesse face aux perturbations ponctuelles de trafic ainsi qu'aux incidents bien plus graves que sont les pannes ou les opérations de maintenance. Ce travail a été partiellement financé dans le cadre d'un contrat de recherche avec France Telecom Division R&D.This thesis summarizes the work done on lexicographic optimization and its applications to telecommunication networks. This document is composed of three main parts. In the first part, we present the theoretical background for the problem of Max-Min Fairness (MMF) and recall its relations with lexicographic optimization as well as a brief state of art on this area. We present in greater details a polynomial approach for achieving leximin maximization and its application to the lexicographically minimum loaded network problem. We continue with the second part, which focuses on the problem of computing the leximin maximal traffic satisfaction vector associated with the set of single link failures in a telecommunication network. We have first considered the case of partial end-to-end rerouting with stub-release where network resources could be used as well for traffic routing, as for traffic rerouting. The proposed solution approach is based on the arc-path flow formulation using Benders' decomposition and column generation. Discussions for the other end-to-end rerouting strategies followed by theoretical results are presented. Finally, we present in the third part, three specific applications in designing robust networks intended to face failure situations. The first application generalize the diverse routing in order to achieve acceptable levels of demand traffic satisfaction in case of link failures while avoiding rerouting procedures. The second application is a Shared Protected Robust Routing (SPRR) and the third application an Intelligent Robust Routing (IRR). This work is in great part supported by France Telecom Division R&D.COMPIEGNE-BU (601592101) / SudocSudocFranceF