Liavas AthanasiosΛιαβας ΑθανασιοςKostoulas GeorgiosΚωστουλας Γεωργιος2024-10-312024-10-3120152015-03-23Georgios Kostoulas, "Decomposition methods for network utility maximization", Diploma Work, School of Electronic and Computer Engineering, Technical University of Crete, Chania, Greece, 2015Γεώργιος Κωστούλας, "Decomposition methods for network utility maximization", Διπλωματική Εργασία, Σχολή Ηλεκτρονικών Μηχανικών και Μηχανικών Υπολογιστών, Πολυτεχνείο Κρήτης, Χανιά, Ελλάς, 2015https://dspace.library.tuc.gr/handle/123456789/1081Network Utility Maximization (NUM) is the problem of allocating the right amount of resources to the nodes of a network, in order to maximize an overall utility function. There are many optimization tools to solve this problem in a centralized manner. In this thesis, we discuss distributed ways to solve various formulations of NUM problems. We decompose the problems into subproblems using Primal Decomposition, by applying direct resource allocation and then adjust the resources by small steps until equilibrium, and Dual Decomposition by pricing the resource in such manner that each node achieves the optimal utility. Many alternatives can be derived from these two methods, in different NUM formulations, with the use of multilevel decompositions. These decompositions may lead to better understanding of existing networks, reverse engineering of network protocols like TCP, better management of existing networks, and ways to design and operate new networks by layering as optimization. Finally, we experiment with the message passing of these algorithms and try to minimize the data transferred by quantizing the values.73 pagesenhttp://creativecommons.org/licenses/by/4.0/Project networksnetwork analysis planningproject networksOptimization (Mathematics)Optimization techniquesOptimization theorySystems optimizationmathematical optimizationoptimization mathematicsoptimization techniquesoptimization theorysystems optimizationΔιπλωματική Εργασία