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Models and Methods for Traffic Engineering Problems with Single Models and methods for Traffic Engineering problems with single-path routing Martim Joyce-Moniz To cite this version: Martim Joyce-Moniz. Models and methods for Traffic Engineering problems with single-path routing. Operations Research [cs.RO]. Université Libre de Bruxelles (U.L.B.), Belgium, 2016. English. tel- 01421865 HAL Id: tel-01421865 https://hal.inria.fr/tel-01421865 Submitted on 4 Jan 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Universite´ Libre de Bruxelles Facult´edes Sciences D´epartement d'Informatique Models and methods for Traffic Engineering problems with single-path routing Martim Joyce-Moniz Th`esepr´esent´eeen vue de l'obtention du grade acad´emique de Docteur en Sciences October 2016 ii To my family. iv This thesis has been written under the supervision of Prof. Bernard Fortz and Prof. Lu´ısGouveia. The members of the jury are: • Prof. Bernard Fortz (Universit´eLibre de Bruxelles, Belgium) • Prof. Bernard Gendron (Universit´ede Montreal, Canada) • Prof. Lu´ısGouveia (Universidade de Lisboa, Portugal) • Prof. Martine Labb´e(Universit´eLibre de Bruxelles, Belgium) • Prof. Ivana Ljubic (ESSEC Business School Paris, France) • Prof. Thomas St¨utzle(Universit´eLibre de Bruxelles, Belgium) The research of Martim Joyce-Moniz was done with the support of the COMEX (Combinatorial Optimization: Metaheuristics & Exact Methods) project. v vi Acknowledgements Over the last 4 years, I've often expressed how lucky I am, and how luck was fundamental for me to arrive where I have. With this, I don't mean to indulge in false modesty - naturally, a mix of hard work and good decisions played a part. Nor do I intent to conjecture about the nature, meaning or reason for said luck. What I do wish, is to simply acknowledge the often unsung role of good fortune, every time one's fate does not merely depend on will and want. I am extremely lucky to have had a pair of supervisors, Bernard and Lu´ıs, who ideally epitomized the job, by providing all the necessary support and orientation to successfully write this thesis. Lu´ıs,who I was lucky to have studied under, and learn about network optimization with. Lu´ıs,who recog- nized and understood my yearn to do a Ph.D. abroad, and immediately put me in contact with the right people. Lu´ıs,whose great knowledge and good advise I could always count on, only an email or phone call away. Bernard, who I was lucky to have take a chance on me. Bernard, who always gave me the freedom to grow as a researcher, yet always had his door open, ready to offer me guidance and support, when needed. Bernard, whose hours spent with, staring at formulations in the blackboard, were among the most fasci- nating and enriching in my lifetime. Bernard, who always went a step further to ensure I evolved in the OR community, by allowing me to attend a great number of conferences and PhD schools. I am very lucky to belong to a thriving and exciting academic community, filled with brilliant and friendly people. Of this community, I must highlight of course, the members of my jury, Bernard G., Ivana, Martine and Thomas, to whom I extend my deepest appreciation. Their precious time spent reading my thesis, and their constructive and helpful comments were invaluable. I cannot emphasize enough how lucky I am to count on their love, support and upbringing of my parents. All that I am today, is thanks to how they raised me. I am remarkably lucky that they have always pushed me to follow my dreams, even if they take me to far away lands. I am also exceedingly lucky to have a sister and brother-in-law, who I can always count on for inspiration, guidance and friendship. I am exceptionally lucky to have many great friends, who are always ready to celebrate the good times, and help me go through the tough ones - in Lisbon, Brussels, and other places around the world. Finally, I am just-the-luckiest, to have an amazing girlfriend, Ashley, who manages to prove to me everyday that love, care and encouragement are not a function of physical distance. Abstract Traffic Engineering (TE) uses methods and models from a variety of math- ematical fields, such as statistics and optimization, to improve the perfor- mance of telecommunication networks. In this thesis, we study TE problems dealing with networks that impose single-path routing. As the name infers, in this type of routing, the traffic flow of each \commodity" cannot be split in its path between its origin and destination. Given its cheap cost, single-path routing is widely used in today's data centers, where thousands of stored servers perform computations or host Internet services. One common case of single-path routing is the one enforced by the Spanning Tree Protocol (STP) in switched Ethernet networks. The STP requires the network to keep its activated links loop-free, while maintaining the other redundant links ready for back-up, in case of link failure. The Multiple Spanning Tree Protocol (MSTP) extends the STP by installing multiple virtual networks compliant with the STP, over a single physical topology. Therefore, the MSTP is greatly beneficial for network service providers, as it allows for a more efficient use of the existing resources. Network design problems dealing with the MSTP are generally highly com- binatorial and very hard to solve. As such, TE literature mainly suggests heuristic methods, which can quickly produce reasonable designs. Notwith- standing, due to a scarce existence of lower bounds to the optimum values of such problems, there is little knowledge about the quality of the solutions provided by these heuristics. In this sense, we propose mathematical programming models and methods that can provide optimal designs for these networks, or at the very least, obtain valid lower bounds. Taking into mind the goal of avoiding congestion in the network, we focus on two problems that deal with the following load- balancing objectives: the minimization of the worst-case link utilization, and the minimization of flow costs given by piecewise linear functions that penal- ize heavily-loaded links. The study of both these problems yielded relevant by-products: the first is the study of a MSTP network design problem, where we minimize the total load, and the second is the study of a fundamental unsplittable multicommodity flow problem with piecewise linear costs. For all the considered problems, we provide studies of complexity, extensive polyhedral studies to compare the proposed formulations, and a wide array of computational experiments to evaluate the performance of the proposed models and methods. x R´esum´e L'Ing´enieriedu Trafic (IT) utilise des m´ethodes et des mod`elesde plusieurs domaines math´ematiques,comme la statistique et l'optimisation, pour am´eliorerles performances des r´eseauxde t´el´ecommunication. Dans cette th`ese,nous ´etudionsdes probl`emesde l'IT qui traitent de r´eseauxqui imposent l'utilisation du mono-routage. Comme le nom l'indique, dans ce type de routage, le flux de trafic de chaque demande ne peut pas tre divis´esur son trajet entre son origine et sa destination. Vu son co^utfaible, le mono-routage est largement utilis´edans les centres de donn´eesactuels, o`udes milliers de serveurs effectuent des calculs ou h´ebergent des services Internet. Une utilisation courante du mono-routage est l'usage du Spanning Tree Protocol (STP), bas´esur les arbres couvrants, dans les r´eseauxde type switched Ethernet. Le STP impose que le r´eseaumaintienne un ensemble de liens activ´essans circuits, tandis que les autres liaisons sont redondantes et prtes pour la sauvegarde, en cas de d´efaillanced'un lien. Le Multiple Spanning Tree Protocol (MSTP) ´etendSTP, en installant plusieurs r´eseaux virtuels se conformant `aSTP, sur une seule topologie physique. Par cons´equent, MSTP est tr`esb´en´efiquepour les fournisseurs de services r´eseau,car il permet une utilisation plus efficace des ressources existantes. Les probl`emesde conception de r´eseau avec MSTP sont g´en´eralement tr`escom- binatoires et tr`esdifficiles. De ce fait, la litt´eraturesur l'IT sugg`ereprincipalement des m´ethodes heuristiques, qui peuvent rapidement produire des solutions raisonnables. N´eanmoins,en raison de l'existence de rares bornes inf´erieuresaux valeurs optimales de ces probl`emes,il y a peu de connaissances sur la qualit´edes solutions fournies. En cons´equence,nous proposons des mod`elesde programmation math´ematiqueet des m´ethodes qui peuvent fournir des plans optimaux pour ces r´eseaux,ou `atout le moins, obtenir des bornes inf´erieuresvalides. Compte tenu de l'objectif d'´eviterla congestion dans le r´eseau, nous nous concentrons sur deux probl`emesqui traitent les objectifs d'´equilibragede charge suivants : la minimisation de l'utilisation maximale des liens et la minimisation des co^uts des flux donn´espar des fonctions lin´eairespar morceaux qui p´enalisent les liens tr`escharg´es. L'´etudede ces deux probl`emes a abouti `ades r´esultatsd´eriv´espertinents: le premier est l'´etuded'un probl`emede conception de r´eseau utilisant MSTP, o nous minimisons la charge totale, et le second est l'´etuded'un probl`eme fondamental de mono-routage avec des co^utslin´eairespar morceaux.
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