Abstract The aim of this thesis is to devise new paradigms on radio resource sharing including cache-enabled virtualized large cellular networks for mobile network operators (MNOs). Also, self-organizing resource allocation for small cell networks is considered. In such networks, the MNOs rent radio resources from the infrastructure provider (InP) to support their subscribers. In order to reduce the operational costs, while at the same time to significantly increase the usage of the existing network resources, it leads to a paradigm where the MNOs share their infrastructure, i.e., base stations (BSs), antennas, spectrum and edge cache among themselves. In this regard, we integrate the theoretical insights provided by stochastic geometrical approaches to model the spectrum and infrastructure sharing for large cellular networks. In the first part of the thesis, we study the non-orthogonal multi-MNO spectrum allocation problem for small cell networks with the goal of maximizing the overall network throughput, defined as the expected weighted sum rate of the MNOs. Each MNO is assumed to serve multiple small cell BSs (SBSs). We adopt the many-to-one stable matching game framework to tackle this problem. We also investigate the role of power allocation schemes for SBSs using Q-learning. In the second part, we model and analyze the infrastructure sharing system considering a single buyer MNO and multiple seller MNOs. The MNOs are assumed to operate over their own licensed spectrum bands while sharing BSs. We assume that multiple seller MNOs compete with each other to sell their infrastructure to a potential buyer MNO. The optimal strategy for the seller MNOs in terms of the fraction of infrastructure to be shared and the price of the infrastructure, is obtained by computing the equilibrium of a Cournot-Nash oligopoly game. Finally, we develop a game-theoretic framework to model and analyze a cache-enabled virtualized cellular networks where the network infrastructure, e.g., BSs and cache storage, owned by an InP, is rented and shared among multiple MNOs. We formulate a Stackelberg game model with the InP as the leader and the MNOs as the followers. The InP tries to maximize its profit by optimizing its infrastructure rental fee. The MNO aims to minimize the cost of infrastructure by minimizing the cache intensity under probabilistic delay constraint of the user (UE). Since the MNOs share their rented infrastructure, we apply a cooperative game concept, namely, the Shapley value, to divide the cost among the MNOs. / Tiivistelmä Tämän väitöskirjan tavoitteena on tuottaa uusia paradigmoja radioresurssien jakoon, mukaan lukien virtualisoidut välimuisti-kykenevät suuret matkapuhelinverkot matkapuhelinoperaattoreille. Näiden kaltaisissa verkoissa operaattorit vuokraavat radioresursseja infrastruktuuritoimittajalta (InP, infrastructure provider) asiakkaiden tarpeisiin. Toimintakulujen karsiminen ja samanaikainen olemassa olevien verkkoresurssien hyötykäytön huomattava kasvattaminen johtaa paradigmaan, jossa operaattorit jakavat infrastruktuurinsa keskenään. Tämän vuoksi työssä tutkitaan teoreettisia stokastiseen geometriaan perustuvia malleja spektrin ja infrastruktuurin jakamiseksi suurissa soluverkoissa. Työn ensimmäisessä osassa tutkitaan ei-ortogonaalista monioperaattori-allokaatioongelmaa pienissä soluverkoissa tavoitteena maksimoida verkon yleistä läpisyöttöä, joka määritellään operaattoreiden painotettuna summaläpisyötön odotusarvona. Jokaisen operaattorin oletetaan palvelevan useampaa piensolutukiasemaa (SBS, small cell base station). Työssä käytetään monelta yhdelle -vakaata sovituspeli-viitekehystä SBS:lle käyttäen Q-oppimista. Työn toisessa osassa mallinnetaan ja analysoidaan infrastruktuurin jakamista yhden ostaja-operaattorin ja monen myyjä-operaattorin tapauksessa. Operaattorien oletetaan toimivan omilla lisensoiduilla taajuuksillaan jakaen tukiasemat keskenään. Myyjän optimaalinen strategia infrastruktuurin myytävän osan suuruuden ja hinnan suhteen saavutetaan laskemalla Cournot-Nash -olipologipelin tasapainotila. Lopuksi, työssä kehitetään peli-teoreettinen viitekehys virtualisoitujen välimuistikykenevien soluverkkojen mallintamiseen ja analysointiin, missä InP:n omistama verkkoinfrastruktuuri vuokrataan ja jaetaan monen operaattorin kesken. Työssä muodostetaan Stackelberg-pelimalli, jossa InP toimii johtajana ja operaattorit seuraajina. InP pyrkii maksimoimaan voittonsa optimoimalla infrastruktuurin vuokrahintaa. Operaattori pyrkii minimoimaan infrastruktuurin hinnan minimoimalla välimuistin tiheyttä satunnaisen käyttäjän viive-ehtojen mukaisesti. Koska operaattorit jakavat vuokratun infrastruktuurin, työssä käytetään yhteistyöpeli-ajatusta, nimellisesti, Shapleyn arvoa, jakamaan kustannuksia operaatoreiden kesken.

Made available in DSpace on 2015-05-15T11:46:19Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2353317 bytes, checksum: d71ead9d4e0f785df35982fc9318c7da (MD5) Previous issue date: 2014-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this thesis, we study controllability results of some phenomena modeled by Partial Differential Equations (PDEs): Multi objective control problem, for parabolic equations, following the Stackelber-Nash strategy is considered: for each leader control which impose the null controllability for the state variable, we find a Nash equilibrium associated to some costs. The leader control is chosen to be the one of minimal cost. Null controllability for the linear Schrödinger equation: with a convenient space-time discretization, we numerically construct boundary controls which lead the solution of the Schrödinger equation to zero; using some arguments of Fursikov-Imanuvilov (see [Lecture Notes Series, Vol 34, 1996]) we construct controls with exponential decay at final time. Null controllability for a Schrödinger-KdV system: in this work, we combine global Carleman estimates with energy estimates to obtain an observability inequality. The controllability result holds by the Hilbert Uniqueness Method (HUM). Controllability results for a Euler type system, incompressible, inviscid, under the influence of a temperature are obtained: we mainly use the extension and return methods / Nesta tese, estudaremos resultados de controle para alguns problemas da teoria das equações diferenciais parciais (EDPs): Problema de controle multi objetivo para um problema parabólico, seguindo estratégias do tipo Stackelberg-Nash: para cada controle líder, que impõe a controlabilidade nula para o estado, encontramos seguidores, em equilíbrio de Nash, associados a funcionais custo. Em seguida, determinamos o líder de menor custo. Controlabilidade nula para a equação de Schrödinger linear: com uma discretização espaço-tempo adequada, construímos numericamente controles-fronteira que conduzem a solução de Schrödinger a zero; utilizando técnicas de Fursikov-Imanuvilov (veja [Lecture Notes Series, Vol 34, 1996]) contruímos controles que decaem exponencialmente no tempo final. Controlabilidade nula para um sistema acoplado Schrödinger-KdV: neste trabalho, combinando estimativas globais de Carleman com estimativas de energia, obtemos uma desigualdade de observabilidade. O resultado de controlabilidade segue pelo método de unicicade Hilbert (HUM). Controlabilidade para um sistema do tipo Euler, incompressível, invíscido, sob influência de uma temperatura: Utilizamos os métodos de extensão seguido do método do retorno para provar resultados de controlabilidade para este sistema

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported.

Game theory and mechanism design have emerged as an important tool to model, analyze,and solve decentralized design problems involving multiple agents that interact strategically in a rational and intelligent way. Some examples of these design problems include: auctions and markets in electronic commerce; network economics; dynamic pricing; routing protocols in wireless networks; resource allocation in computational grids; algorithms for selfish agents;etc. The motivation for this doctoral work springs from the high level of current interest indesigning innovative mechanisms for solving emerging game theoretic problems in the area of electronic commerce. In this thesis, we focus on three such problems and advance the current art in mechanism design while developing new, innovative mechanisms to solve the problems. The first problem we explore is the highly strategic problem of forming a high value E-business supply chain by choosing the best mix of supply chain partners. In our research, we formulate the supply chain formation problem as a mechanism design problem in a generic wayand show that the well known VCG (Vickrey-Clarke-Groves) mechanisms provide an apt frame-work for solving this problem. We provide a compelling example of a three stage automotive distribution network to illustrate the power and e±cacy of the proposed methodology. The second problem we model and solve is that of designing a revenue maximizing sponsored search auction. This is a problem that is faced by every Internet search engine, such as Google,MSN, and Yahoo!, whenever it receives a search query. In our research, we take a comprehensivelook at existing auction mechanisms for this problem. Our work leads to an innovative new auction mechanism, which we call OPT (optimal mechanism), that exhibits a superior level ofperformance. The proposed mechanism extends, in a non-trivial way, the well known Myersonoptimal auction to the specific setting of sponsored search auctions. The proposed mechanism maximizes the revenue to the search engine and also satisfies two crucial properties, Bayesian incentive compatibility and interim individual rationality. The third contribution is in respect of Stackelberg problems, which are game theoretic problems that involve hierarchical and sequential decision making. By focusing attention on an important subclass of these problems, namely the Single-Leader-Rest-Followers (SLRF) problems, we extend all relevant aspects of classical mechanism design theory to the case of SLRF problems. We derive many important results in respect of procurement auctions with reserve prices using the developed theory. The research carried out as part of this doctoral work, we believe, advances the current art in mechanism design while developing innovative mechanisms to solve those problems.

The present paper aims to show that the oligopoly problem is much more determined than commonly believed. In oligopoly prerequisites are likely to prevail inducing a 'normal' behaviour in accordance with profit maximization. This leads to a price combination located at an exactly definable line section. Finally some consequences upon economic policy are outlined. / Dieser Beitrag versucht zu zeigen, daß das Oligopolproblem wesentlich determinierter ist als gemeinhin angenommen. Im Oligopol liegen die Voraussetzungen besonders günstig, daß durch ein aus dem Streben nach Gewinnmaximierung abgeleitetes, "normales" Verhalten eine Preiskombination auf einem exakt abgrenzbaren Kurvenabschnitt zustande kommt. Abschließend werden wirtschaftspolitische Konsequenzen angedeutet.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-06T15:24:59Z No. of bitstreams: 1 LUCIANO CIPRIANO DA SILVA - DISSERTAÇÃO PPGMAT 2013..pdf: 1125916 bytes, checksum: d2b1ef64aa3ef95093acedfd0f7a711c (MD5) / Made available in DSpace on 2018-08-06T15:24:59Z (GMT). No. of bitstreams: 1 LUCIANO CIPRIANO DA SILVA - DISSERTAÇÃO PPGMAT 2013..pdf: 1125916 bytes, checksum: d2b1ef64aa3ef95093acedfd0f7a711c (MD5) Previous issue date: 2013-02 / Capes / Neste trabalho estudamos o controle hierárquico, para um sistema parabólico, em um domínio não cilíndrico. O controle hierárquico é um problema que consiste em aproximar, em um tempo fixado, as soluções das equações de estado que temos, (essas soluções dependem de funções chamadas controles), de um estado considerado ideal, através de um sistema de líder, que é o controle independente, e seguidores, que são os controles que dependem da ação do líder. Começamos fazendo uma transformação do problema original para um equivalente em domínio cilíndrico, então estudamos o controle hierárquico deste sistema. Usaremos a estratégia de Stackelberg-Nash, processo no qual, para cada escolha do líder, procuramos por seguidores que satisfaçam um certo problema de minimização, as soluções deste problema formam o que chamamos de Equilíbrio de Nash, resolvido esse problema, trabalhamos para provar que o sistema é aproximadamente controlável usando o líder. Resolvemos ainda um sistema sistema de otimalidade para os seguidores. / We present hierarchic control to a parabolic system in a noncylindrical domain. The hierarchic control is a problem that is how to bring in a fixed time, the solutions of the equations of state we have, (these solutions depend on a functions called controls), a state considered ideal, througha system of leading, independent control, and followers, the leader controls dependents. We start by making a transformation of the original problem to an equivalent cylindrical domain, then do the hierarchic control of this problem. We use the strategy Stackelberg-Nash, a process in which each leader’s choice, look for followers to satisfy a minimization problem, the solution of this problem form what we call the Nash equilibrium, solved this problem, work to prove that the approximately system is controllable using the leader. We further resolve to a of optimality for followers.

No description available.

The present paper aims to show that the oligopoly problem is much more determined than commonly believed. In oligopoly prerequisites are likely to prevail inducing a 'normal' behaviour in accordance with profit maximization. This leads to a price combination located at an exactly definable line section. Finally some consequences upon economic policy are outlined. / Dieser Beitrag versucht zu zeigen, daß das Oligopolproblem wesentlich determinierter ist als gemeinhin angenommen. Im Oligopol liegen die Voraussetzungen besonders günstig, daß durch ein aus dem Streben nach Gewinnmaximierung abgeleitetes, "normales" Verhalten eine Preiskombination auf einem exakt abgrenzbaren Kurvenabschnitt zustande kommt. Abschließend werden wirtschaftspolitische Konsequenzen angedeutet.

Resource allocation in wireless networks is one of the most studied class of problems. Generally, these problems are formulated as utility maximization problems under relevant constraints. The challenges posed by these problems vary widely depending on the nature of the utility function under consideration. Recently, the widespread prevalence of wireless devices prompted researchers and engineers to delve into the security issues of wireless communication. As compared to the wired medium, ensuring security for the wireless medium is more challenging mainly due to the broadcast nature of the transmission. But the ongoing research on physical layer security promises robust and reliable security schemes for wireless communication. Contrary to conventional cryptographic schemes, physical layer security techniques are impregnable as the security is ensured by the inherent randomness present in the wireless medium. In this thesis, we consider several wireless scenarios and propose secrecy enhancing resource allocation schemes for them in the first few chapters. We initially address the problem of secure transmission by following the conventional approach in the secrecy literature|secrecy rate maximization. Needless to say, in these chapters, secrecy rate is the utility function and the constraints are posed by the available power budget. Then we consider a pragmatic approach where we target the signal-to-noise ratio (SNR) of participating nodes and ensure information secrecy by appropriately constraining the SNRs of those nodes. In those SNR based formulations, SNR at the destination is the utility function and we are interested in maximizing it. In the last two chapters, we study two scenarios in a non-secrecy setting. In one of them, end-to-end data rate is the utility, whereas, in the other one, two utility functions|based on revenue generated|are defined for two rational agents in a game-theoretic setting. In the second chapter, we study parallel independent Gaussian channels with imperfect channel state information (CSI) for the eavesdropper. Firstly, we evaluate the probability of zero secrecy rate in this system for (i) given instantaneous channel conditions and (ii) a Rayleigh fading scenario. Secondly, when non-zero secrecy is achievable in the low SNR regime, we aim to solve a robust power allocation problem which minimizes the outage probability at a target secrecy rate. In the third, fourth and fifth chapters, we consider scenarios where the source node transmits a message to the destination using M parallel amplify-and-forward (AF) relays in the presence of a single or multiple eavesdroppers. The third chapter addresses the problem of the maximum achievable secrecy rate for two specific network models: (a) degraded eavesdropper channel with complex channel gain and (b) scaled eavesdropper channel with real-valued channel gains. In the fourth chapter, we consider the SNR based approach and address two problems: (i) SNR maximization at the destination and (ii) Total relay power minimization. In the fifth chapter, we assume that the relay nodes are untrusted and to counter them, we deliberately introduce artificial noise in the source message. For this model, we propose and solve SNR maximization problems for the following two scenarios: (i) Total power constraint on all the relay nodes and (ii) Individual power constraints on each of the relay nodes. In the sixth chapter, we address the problem of passive eavesdroppers in multi-hop wire-less networks using the technique of friendly jamming. Assuming decode-and-forward (DF) relaying, we consider a scheduling and power allocation (PA) problem for a multiple-source multiple-sink scenario so that eavesdroppers are jammed, and source-destination throughput targets are met. When channel state information (CSI) of all the node are available, we intend to minimize the total power consumption of all the transmitting nodes. In the absence of eavesdroppers CSI, we minimize vulnerability region of the network. In chapter seven, the problem of cooperative beamforming for maximizing the achievable data rate of two-hop amplify-and-forward (AF) network (in the absence of eavesdropper(s)) is considered. Along with an individual power constraint on each of the relay nodes, we consider a weighted sum power constraint. To solve this problem, we propose a novel algorithm based on the Quadratic Eigenvalue Problem (QEP) and discuss its convergence. In chapter eight, we study a Stackelberg game between a base station and a multi-antenna power beacon for wireless energy harvesting in a multiple sensor node scenario. Assuming imperfect CSI between the sensor nodes and the power beacon, we propose a utility function that is based on throughput non-outage probability at the base station. We find the optimal strategies for the base station and the power beacon that maximize their respective utility functions.