[pt] Estendemos o formalismo de Fokker-Planck que foi usado previamente para descrever, a partir de primeiros princípios, o comportamento de um gás granular em esfriamento, com potencial de contato Hertziano e força de atrito viscoelástica o qual resulta em um sistema com coeficiente de restituição que depende da velocidade. Nesta tese é estudado, também a partir de primeiros princípios, o caso mais geral, o de um estado estacionário com energia cinética finita e fora do equilíbrio, devido ao acoplamento a um mecanismo externo de alimentação de energia. Estende- se assim a validade do resultado prévio. / [en] We extend the Fokker-Planck formalism used previously to describe the behavior of a cooling granular gas, with a Hertzian contact potential and viscoelastic radial friction, giving a velocity dependent coeficient of restitution. In this thesis, we study the more general case of a steady-state with finite kinetic, energy and far from equilibrium, due to the coupling to an external energy- feeding mechanism, also from first-principles, and extend the validity of the former results.

Ce manuscrit décrit comment les champs de vitesses solutions de l'équation de Navier-Stokes se comportent à grande échelle pour un forçage à petite échelle. Il analyse aussi le comportement à grande échelle des champs magnétiques solutions de l'équation d'induction cinématique lorsque le champs de vitesse est de petite échelle. Les résultats présentés ont été obtenus à l'aide de simulations numériques directes utilisant des algorithmes pseudo-spectraux des équations non modifiées ou avec un développement utilisant la méthode Floquet. Dans le cadre hydrodynamique, les simulations utilisant la méthode de Floquet permettent de retrouver les résultats de l'effet AKA à bas Reynolds et de les étendre pour des Reynolds d'ordre un. Elles permettent aussi d'étudier des écoulements AKA-stable et de mettre en évidence une autre instabilité pouvant être interprétée comme un effet de viscosité négative. Dans le cadre magnétique, l'effet alpha est observé sur une gamme de séparation d'échelle dépassant par plusieurs ordres de grandeur les autres résultats connus. Il est aussi montré que le taux de croissance de l'instabilité devient indépendant de la séparation d'échelle une fois que le champs magnétique est destabilisé dans ses petites échelles. Le spectre d'énergie et le temps du corrélation d'équilibre absolu solution de l'équation d'Euler tronquée sont présentés. Un nouveau régime où le temps de corrélation est régit par l’hélicité est mis en évidence. Ces résultats sont aussi comparés à ceux des modes de grande échelle de solutions de l'équation de Navier-Stokes forcée dans les petites échelles. Ils montrent que le temps de corrélation croit avec l'hélicité. / This manuscript describes how solutions of the Navier-Stokes equations behave in the large scales when forced in the small scales. It analyzes also the large scale behavior of magnetic fields solution of the kinetic induction equation when the velocity is in the small scales. The results were acquired with direct numeric simulation (DNS) using pseudo-spectral algorithms of the equations as well as their Floquet development. In the hydrodynamical case, the Floquet DNS were able to confirm the results of the AKA effect at low Reynolds number and extend them for Reynolds number of order one. The DNS were also used to study AKA-stable flows and identified a new instability that can be interpreted as a negative viscosity effect. In the magnetic case, the alpha effect is observe for a range of scale separation exceed know results by several orders of magnitude. It is also shown that the growth rate of the instability becomes independent of the scale separation once the magnetic field is destabilized in its small scales. The energy spectrum and the correlation time of absolute equilibrium solution of the truncated Euler equation are presented. A new regime where the correlation time is governed by helicity is exhibited. These results are also compared with those coming from large scale modes of solutions of the Navier-Stokes equation forced in the small scales. They show that the correlation time increases with the helicity of the flow.

The context of this thesis is the numerical simulation of turbulent flows at moderate Reynolds numbers and the improvement of the capabilities of an in-house 3D unsteady and incompressible flow solver called SFELES to simulate such flows. In addition to this abstract, this thesis includes five other chapters. The second chapter of this thesis presents the numerical methods implemented in the two CFD solvers used as part of this work, namely SFELES and PHASTA. The third chapter concentrates on the implementation of a new library called FlexMG. This library allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods, which require much less memory to solve linear systems than a direct sparse LU solver available in SFELES. Multigrid is an iterative procedure that relies on a series of increasingly coarser approximations of the original 'fine' problem. The underlying concept is the following: low wavenumber errors on fine grids become high wavenumber errors on coarser levels, which can be effectively removed by applying fixed-point methods on coarser levels. Two families of algebraic multigrid preconditioners have been implemented in FlexMG, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES (Generalized Minimal RESidual) method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics (unsteady flow past a circular cylinder at low Reynolds number), their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in this work. The fourth chapter is devoted to the study of subgrid scale models for the large eddy simulation (LES) of turbulent flows. It is well known that turbulence features a cascade process by which kinetic energy is transferred from the large turbulent scales to the smaller ones. Below a certain size, the smallest structures are dissipated into heat because of the effect of the viscous term in the Navier-Stokes equations. In the classical formulation of LES models, all the resolved scales are used to model the contribution of the unresolved scales. However, most of the energy exchanges between scales are local, which means that the energy of the unresolved scales derives mainly from the energy of the small resolved scales. In this fourth chapter, constant-coefficient-based Smagorinsky and WALE models are considered under different formulations. This includes a classical version of both the Smagorinsky and WALE models and several scale-separation formulations, where the resolved velocity field is filtered in order to separate the small turbulent scales from the large ones. From this separation of turbulent scales, the strain rate tensor and/or the eddy viscosity of the subgrid scale model is computed from the small resolved scales only. One important advantage of these scale-separation models is that the dissipation they introduce through their subgrid scale stress tensor is better controlled compared to their classical version, where all the scales are taken into account without any filtering. More precisely, the filtering operator (based on a top hat filter in this work) allows the decomposition u' = u - ubar, where u is the resolved velocity field (large and small resolved scales), ubar is the filtered velocity field (large resolved scales) and u' is the small resolved scales field. At last, two variational multiscale (VMS) methods are also considered. The philosophy of the variational multiscale methods differs significantly from the philosophy of the scale-separation models. Concretely, the discrete Navier-Stokes equations have to be projected into two disjoint spaces so that a set of equations characterizes the evolution of the large resolved scales of the flow, whereas another set governs the small resolved scales. Once the Navier-Stokes equations have been projected into these two spaces associated with the large and small scales respectively, the variational multiscale method consists in adding an eddy viscosity model to the small scales equations only, leaving the large scales equations unchanged. This projection is obvious in the case of a full spectral discretization of the Navier-Stokes equations, where the evolution of the large and small scales is governed by the equations associated with the low and high wavenumber modes respectively. This projection is more complex to achieve in the context of a finite element discretization. For that purpose, two variational multiscale concepts are examined in this work. The first projector is based on the construction of aggregates, whereas the second projector relies on the implementation of hierarchical linear basis functions. In order to gain some experience in the field of LES modeling, some of the above-mentioned models were implemented first in another code called PHASTA and presented along with SFELES in the second chapter. Finally, the relevance of our models is assessed with the large eddy simulation of a fully developed turbulent channel flow at a low Reynolds number under statistical equilibrium. In addition to the analysis of the mean eddy viscosity computed for all our LES models, comparisons in terms of shear stress, root mean square velocity fluctuation and mean velocity are performed with a fully resolved direct numerical simulation as a reference. The fifth chapter of the thesis focuses on the numerical simulation of the 3D turbulent flow over a re-entry Apollo-type capsule at low speed with SFELES. The Reynolds number based on the heat shield is set to Re=10^4 and the angle of attack is set to 180º, that is the heat shield facing the free stream. Only the final stage of the flight is considered in this work, before the splashdown or the landing, so that the incompressibility hypothesis in SFELES is still valid. Two LES models are considered in this chapter, namely a classical and a scale-separation version of the WALE model. Although the capsule geometry is axisymmetric, the flow field in its wake is not and induces unsteady forces and moments acting on the capsule. The characterization of the phenomena occurring in the wake of the capsule and the determination of their main frequencies are essential to ensure the static and dynamic stability during the final stage of the flight. Visualizations by means of 3D isosurfaces and 2D slices of the Q-criterion and the vorticity field confirm the presence of a large meandering recirculation zone characterized by a low Strouhal number, that is St≈0.15. Due to the detachment of the flow at the shoulder of the capsule, a resulting annular shear layer appears. This shear layer is then affected by some Kelvin-Helmholtz instabilities and ends up rolling up, leading to the formation of vortex rings characterized by a high frequency. This vortex shedding depends on the Reynolds number so that a Strouhal number St≈3 is detected at Re=10^4. Finally, the analysis of the force and moment coefficients reveals the existence of a lateral force perpendicular to the streamwise direction in the case of the scale-separation WALE model, which suggests that the wake of the capsule may have some preferential orientations during the vortex shedding. In the case of the classical version of the WALE model, no lateral force has been observed so far so that the mean flow is thought to be still axisymmetric after 100 units of non-dimensional physical time. Finally, the last chapter of this work recalls the main conclusions drawn from the previous chapters.

The context of this thesis is the numerical simulation of turbulent flows at moderate Reynolds numbers and the improvement of the capabilities of an in-house 3D unsteady and incompressible flow solver called SFELES to simulate such flows.<p>In addition to this abstract, this thesis includes five other chapters.<p><p>The second chapter of this thesis presents the numerical methods implemented in the two CFD solvers used as part of this work, namely SFELES and PHASTA.<p><p>The third chapter concentrates on the implementation of a new library called FlexMG. This library allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods, which require much less memory to solve linear systems than a direct sparse LU solver available in SFELES. Multigrid is an iterative procedure that relies on a series of increasingly coarser approximations of the original 'fine' problem. The underlying concept is the following: low wavenumber errors on fine grids become high wavenumber errors on coarser levels, which can be effectively removed by applying fixed-point methods on coarser levels.<p>Two families of algebraic multigrid preconditioners have been implemented in FlexMG, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES (Generalized Minimal RESidual) method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics (unsteady flow past a circular cylinder at low Reynolds number), their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in this work.<p><p>The fourth chapter is devoted to the study of subgrid scale models for the large eddy simulation (LES) of turbulent flows.<p>It is well known that turbulence features a cascade process by which kinetic energy is transferred from the large turbulent scales to the smaller ones. Below a certain size, the smallest structures are dissipated into heat because of the effect of the viscous term in the Navier-Stokes equations.<p>In the classical formulation of LES models, all the resolved scales are used to model the contribution of the unresolved scales. However, most of the energy exchanges between scales are local, which means that the energy of the unresolved scales derives mainly from the energy of the small resolved scales.<p>In this fourth chapter, constant-coefficient-based Smagorinsky and WALE models are considered under different formulations. This includes a classical version of both the Smagorinsky and WALE models and several scale-separation formulations, where the resolved velocity field is filtered in order to separate the small turbulent scales from the large ones. From this separation of turbulent scales, the strain rate tensor and/or the eddy viscosity of the subgrid scale model is computed from the small resolved scales only. One important advantage of these scale-separation models is that the dissipation they introduce through their subgrid scale stress tensor is better controlled compared to their classical version, where all the scales are taken into account without any filtering. More precisely, the filtering operator (based on a top hat filter in this work) allows the decomposition u' = u - ubar, where u is the resolved velocity field (large and small resolved scales), ubar is the filtered velocity field (large resolved scales) and u' is the small resolved scales field. <p>At last, two variational multiscale (VMS) methods are also considered.<p>The philosophy of the variational multiscale methods differs significantly from the philosophy of the scale-separation models. Concretely, the discrete Navier-Stokes equations have to be projected into two disjoint spaces so that a set of equations characterizes the evolution of the large resolved scales of the flow, whereas another set governs the small resolved scales. <p>Once the Navier-Stokes equations have been projected into these two spaces associated with the large and small scales respectively, the variational multiscale method consists in adding an eddy viscosity model to the small scales equations only, leaving the large scales equations unchanged. This projection is obvious in the case of a full spectral discretization of the Navier-Stokes equations, where the evolution of the large and small scales is governed by the equations associated with the low and high wavenumber modes respectively. This projection is more complex to achieve in the context of a finite element discretization. <p>For that purpose, two variational multiscale concepts are examined in this work.<p>The first projector is based on the construction of aggregates, whereas the second projector relies on the implementation of hierarchical linear basis functions.<p>In order to gain some experience in the field of LES modeling, some of the above-mentioned models were implemented first in another code called PHASTA and presented along with SFELES in the second chapter.<p>Finally, the relevance of our models is assessed with the large eddy simulation of a fully developed turbulent channel flow at a low Reynolds number under statistical equilibrium. In addition to the analysis of the mean eddy viscosity computed for all our LES models, comparisons in terms of shear stress, root mean square velocity fluctuation and mean velocity are performed with a fully resolved direct numerical simulation as a reference.<p><p>The fifth chapter of the thesis focuses on the numerical simulation of the 3D turbulent flow over a re-entry Apollo-type capsule at low speed with SFELES. The Reynolds number based on the heat shield is set to Re=10^4 and the angle of attack is set to 180º, that is the heat shield facing the free stream. Only the final stage of the flight is considered in this work, before the splashdown or the landing, so that the incompressibility hypothesis in SFELES is still valid.<p>Two LES models are considered in this chapter, namely a classical and a scale-separation version of the WALE model. Although the capsule geometry is axisymmetric, the flow field in its wake is not and induces unsteady forces and moments acting on the capsule. The characterization of the phenomena occurring in the wake of the capsule and the determination of their main frequencies are essential to ensure the static and dynamic stability during the final stage of the flight. <p>Visualizations by means of 3D isosurfaces and 2D slices of the Q-criterion and the vorticity field confirm the presence of a large meandering recirculation zone characterized by a low Strouhal number, that is St≈0.15.<p>Due to the detachment of the flow at the shoulder of the capsule, a resulting annular shear layer appears. This shear layer is then affected by some Kelvin-Helmholtz instabilities and ends up rolling up, leading to the formation of vortex rings characterized by a high frequency. This vortex shedding depends on the Reynolds number so that a Strouhal number St≈3 is detected at Re=10^4.<p>Finally, the analysis of the force and moment coefficients reveals the existence of a lateral force perpendicular to the streamwise direction in the case of the scale-separation WALE model, which suggests that the wake of the capsule may have some <p>preferential orientations during the vortex shedding. In the case of the classical version of the WALE model, no lateral force has been observed so far so that the mean flow is thought to be still axisymmetric after 100 units of non-dimensional physical time.<p><p>Finally, the last chapter of this work recalls the main conclusions drawn from the previous chapters. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

En la actualidad, la Internet de las Cosas (Internet of Things, IoT) es una tecnología esencial para la próxima generación de sistemas inalámbricos. La conectividad es la base de IoT, y el tipo de acceso requerido dependerá de la naturaleza de la aplicación. Uno de los principales facilitadores del entorno IoT es la comunicación machine-to-machine (M2M) y, en particular, su enorme potencial para ofrecer conectividad ubicua entre dispositivos inteligentes. Las redes celulares son la elección natural para las aplicaciones emergentes de IoT y M2M. Un desafío importante en las redes celulares es conseguir que la red sea capaz de manejar escenarios de acceso masivo en los que numerosos dispositivos utilizan comunicaciones M2M. Por otro lado, los sistemas celulares han experimentado un tremendo desarrollo en las últimas décadas: incorporan tecnología sofisticada y nuevos algoritmos para ofrecer una amplia gama de servicios. El modelado y análisis del rendimiento de estas redes multiservicio es también una tarea desafiante que podría requerir un gran esfuerzo computacional. Para abordar los desafíos anteriores, nos centramos en primer lugar en el diseño y la evaluación de las prestaciones de nuevos mecanismos de control de acceso para hacer frente a las comunicaciones masivas M2M en redes celulares. Posteriormente nos ocupamos de la evaluación de prestaciones de redes multiservicio y proponemos una nueva técnica analítica que ofrece precisión y eficiencia computacional. Nuestro principal objetivo es proporcionar soluciones para aliviar la congestión en la red de acceso radio cuando un gran número de dispositivos M2M intentan conectarse a la red. Consideramos los siguientes tipos de escenarios: (i) los dispositivos M2M se conectan directamente a las estaciones base celulares, y (ii) forman grupos y los datos se envían a concentradores de tráfico (gateways) que les proporcionan acceso a la infraestructura. En el primer escenario, dado que el número de dispositivos añadidos a la red aumenta continuamente, esta debería ser capaz de manejar el considerable incremento en las solicitudes de acceso. El 3rd Generation Partnership Project (3GPP) ha propuesto el access class barring (ACB) como una solución práctica para el control de congestión en la red de acceso radio y la red troncal. El ajuste correcto de los parámetros de ACB de acuerdo con la intensidad del tráfico es crítico, pero cómo hacerlo de forma dinámica y autónoma es un problema complejo cuya solución no está recogida en las especificaciones del 3GPP. Esta tesis doctoral contribuye al análisis del rendimiento y al diseño de nuevos algoritmos que implementen efectivamente este mecanismo, y así superar los desafíos introducidos por las comunicaciones masivas M2M. En el segundo escenario, dado que la heterogeneidad de los dispositivos IoT y las arquitecturas celulares basadas en hardware imponen desafíos aún mayores para permitir una comunicación flexible y eficiente en los sistemas inalámbricos 5G, esta tesis doctoral también contribuye al diseño de software-defined gateways (SD-GWs) en una nueva arquitectura propuesta para redes inalámbricas definidas por software que se denomina SoftAir. Esto permite manejar tanto un gran número de dispositivos como el volumen de datos que estarán vertiendo en la red. Otra contribución de esta tesis doctoral es la propuesta de una técnica novedosa para el análisis de prestaciones de redes multiservicio de alta capacidad que se basa en un nuevo enfoque del modelizado analítico de sistemas que operan a diferentes escalas temporales. Este enfoque utiliza el análisis del transitorio de una serie de subcadenas absorbentes y lo denominamos absorbing Markov chain approximation (AMCA). Nuestros resultados muestran que para un coste computacional dado, AMCA calcula los parámetros de prestaciones habituales de un sistema con mayor precisión, en comparación con los resultados obtenidos por otr / Nowadays, Internet of Things (IoT) is an essential technology for the upcoming generation of wireless systems. Connectivity is the foundation for IoT, and the type of access required will depend on the nature of the application. One of the leading facilitators of the IoT environment is machine-to-machine (M2M) communication, and particularly, its tremendous potential to offer ubiquitous connectivity among intelligent devices. Cellular networks are the natural choice for emerging IoT and M2M applications. A major challenge in cellular networks is to make the network capable of handling massive access scenarios in which myriad devices deploy M2M communications. On the other hand, cellular systems have seen a tremendous development in recent decades; they incorporate sophisticated technology and algorithms to offer a broad range of services. The modeling and performance analysis of these large multi-service networks is also a challenging task that might require high computational effort. To address the above challenges, we first concentrate on the design and performance evaluation of novel access control schemes to deal with massive M2M communications. Then, we focus on the performance evaluation of large multi-service networks and propose a novel analytical technique that features accuracy and computational efficiency. Our main objective is to provide solutions to ease the congestion in the radio access or core network when massive M2M devices try to connect to the network. We consider the following two types of scenarios: (i) massive M2M devices connect directly to cellular base stations, and (ii) they form clusters and the data is forwarded to gateways that provide them with access to the infrastructure. In the first scenario, as the number of devices added to the network is constantly increasing, the network should handle the considerable increment in access requests. Access class barring (ACB) is proposed by the 3rd Generation Partnership Project (3GPP) as a practical congestion control solution in the radio access and core network. The proper tuning of the ACB parameters according to the traffic intensity is critical, but how to do so dynamically and autonomously is a challenging task that has not been specified. Thus, this dissertation contributes to the performance analysis and optimal design of novel algorithms to implement effectively this barring scheme and overcome the challenges introduced by massive M2M communications. In the second scenario, since the heterogeneity of IoT devices and the hardware-based cellular architectures impose even greater challenges to enable flexible and efficient communication in 5G wireless systems, this dissertation also contributes to the design of software-defined gateways (SD-GWs) in a new architecture proposed for wireless software-defined networks called SoftAir. The deployment of these SD-GWs represents an alternative solution aiming at handling both a vast number of devices and the volume of data they will be pouring into the network. Another contribution of this dissertation is to propose a novel technique for the performance analysis of large multi-service networks. The underlying complexity of the network, particularly concerning its size and the ample range of configuration options, makes the solution of the analytical models computationally costly. However, a typical characteristic of these networks is that they support multiple types of traffic flows operating at different time-scales. This time-scale separation can be exploited to reduce considerably the computational cost associated to determine the key performance indicators. Thus, we propose a novel analytical modeling approach based on the transient regime analysis, that we name absorbing Markov chain approximation (AMCA). For a given computational cost, AMCA finds common performance indicators with greater accuracy, when compared to the results obtained by other approximate methods proposed in the literature. / En l'actualitat, la Internet de les Coses (Internet of Things, IoT) és una tecnologia essencial per a la propera generació de sistemes sense fil. La connectivitat és la base d'IoT, i el tipus d'accés requerit dependrà de la naturalesa de l'aplicació. Un dels principals facilitadors de l'entorn IoT és la comunicació machine-to-machine (M2M) i, en particular, el seu enorme potencial per oferir connectivitat ubiqua entre dispositius intel · ligents. Les xarxes mòbils són l'elecció natural per a les aplicacions emergents de IoT i M2M. Un desafiament important en les xarxes mòbils que actualment está rebent molta atenció és aconseguir que la xarxa siga capaç de gestionar escenaris d'accés massiu en què una gran quantitat de dispositius utilitzen comunicacions M2M. D'altra banda, els sistemes mòbils han experimentat un gran desenvolupament en les últimes dècades: incorporen tecnologia sofisticada i nous algoritmes per oferir una àmplia gamma de serveis. El modelatge i análisi del rendiment d'aquestes xarxes multiservei és també un desafiament important que podria requerir un gran esforç computacional. Per abordar els desafiaments anteriors, en aquesta tesi doctoral ens centrem en primer lloc en el disseny i l'avaluació de les prestacions de nous mecanismes de control d'accés per fer front a les comunicacions massives M2M en xarxes cel · lulars. Posteriorment ens ocupem de l'avaluació de prestacions de xarxes multiservei i proposem una nova tècnica analítica que ofereix precisió i eficiència computacional. El nostre principal objectiu és proporcionar solucions per a alleujar la congestió a la xarxa d'accés ràdio quan un gran nombre de dispositius M2M intenten connectar-se a la xarxa. Considerem els dos tipus d'escenaris següents: (i) els dispositius M2M es connecten directament a les estacions base cel · lulars, i (ii) formen grups i les dades s'envien a concentradors de trànsit (gateways) que els proporcionen accés a la infraestructura. En el primer escenari, atès que el nombre de dispositius afegits a la xarxa augmenta contínuament, aquesta hauria de ser capaç de gestionar el considerable increment en les sol · licituds d'accés. El 3rd Generation Partnership Project (3GPP) ha proposat l'access class barring (ACB) com una solució pràctica per al control de congestió a la xarxa d'accès ràdio i la xarxa troncal. L'ajust correcte dels paràmetres d'ACB d'acord amb la intensitat del trànsit és crític, però com fer-ho de forma dinàmica i autònoma és un problema complex, la solució del qual no està recollida en les especificacions del 3GPP. Aquesta tesi doctoral contribueix a l'anàlisi del rendiment i al disseny de nous algoritmes que implementen efectivament aquest mecanisme, i així superar els desafiaments introduïts per les comunicacions massives M2M en les xarxes mòbils actuals i futures. En el segon escenari, atès que l'heterogeneïtat dels dispositius IoT i les arquitectures cel · lulars basades en hardware imposen desafiaments encara més grans per permetre una comunicació flexible i eficient en els sistemes sense fil 5G, aquesta tesi doctoral també contribueix al disseny de software-defined gateways (SD-GWS) en una nova arquitectura proposada per a xarxes sense fils definides per programari que s'anomena SoftAir. Això permet gestionar tant un gran nombre de dispositius com el volum de dades que estaran abocant a la xarxa. Una altra contribució d'aquesta tesi doctoral és la proposta d'una tècnica innovadora per a l'anàlisi de prestacions de xarxes multiservei d'alta capacitat que es basa en un nou enfocament del modelitzat analític de sistemes que operen a diferents escales temporals. Aquest enfocament utilitza l'anàlisi del transitori d'una sèrie de subcadenes absorbents i l'anomenem absorbing Markov chain Approximation (AMCA). Els nostres resultats mostren que per a un cost computacional donat, AMCA calcula els paràmetres de prestacions habituals d / Tello Oquendo, LP. (2018). Design and Performance Analysis of Access Control Mechanisms for Massive Machine-to-Machine Communications in Wireless Cellular Networks [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/107946