The outbreak of the coronavirus disease 2019 (COVID-19) has seen the world scramble for effective countermeasures to limit infection spread in society. Understanding how infection spreads in places where strangers meet in relatively high numbers and proximity to one another is especially important. Supermarkets are one such place where strangers inevitably gather in close proximity indoors. In particular, the checkout area where people queue up to pay tends to be densely populated, making it especially hazardous. One approach to understanding the infection spread is to use agent-based computer simulations to model different scenarios. This paper describes one such simulation of a supermarket checkout area using the Unity 3D engine, including the effect of checkout types and quantity, customer load and COVID-19 countermeasures, i.e., masking and distancing, on infection spread. Using the results from one default scenario and eleven variations, the relative impact of aforementioned factors on exposure in the simulation is discussed. Results indicate that for this simulation the most important factor is preventing queue buildup via having sufficient customer throughput capacity, with potent effects also resulting from operating service registers in such a way that the distance between each queue is maximized as well as increasing distances between agents within queues. Including a self-checkout area was found to be a viable approach to reducing queue times and consequently exposure rates. Comparatively, masking did not yield as notable reductions in exposure rates in the simulation. Similarities in exposure patterns to previous work in the context of supermarkets are discussed, as well as limitations of simulations in capturing the real world. / Utbrottet av coronavirus disease 2019 (COVID-19) föranledde införandet av smittskyddsåtgärder världen över i ett försök att begränsa smittspridningen i samhället. Särskilt viktigt är att förstå hur smittspridning äger rum i trånga utrymmen där ett förhållandevis stort antal främmande människor samlas. Ett exempel på en inomhusmiljö där stora folksamlingar oundvikligen uppstår är mataffärer, där kassaområdena är högriskområden för smittspridning eftersom kunder köar för att betala i dessa områden. Ett tillvägagångssätt för att erhålla kunskap kring smittspridning är att använda agentbaserade datorsimuleringar för att modellera olika scenarion. Den här publikationen beskriver en sådan simulering av en mataffärs kassaområde i spelmotorn Unity 3D. Simuleringen används för att undersöka betydelsen av kassaområdets utformning för smittspridningen, samt inverkan av besökstryck och smittskyddsåtgärder, härvidlag användning av munskydd och social distansering. Som diskussionsunderlag för att fastställa vilken effekt dessa faktorer har på smittspridningen används ett grundscenario och elva simuleringsvarianter. Resultaten visar att den enskilt viktigaste faktorn i denna simulering är att hålla tillräckligt många kassor öppna, vilket förhindrar kötillväxt. Att hålla maximalt avstånd mellan öppna kassor, samt anamma social distansering mellan köande agenter bidrar också påtagligt till minskad smittspridning. Vidare förefaller inkludering av självskanningskassor vara ett effektivt tillvägagångssätt för att minska kötid och därmed även smittspridning. Användande av munskydd har jämförelsevis en mindre påtaglig effekt i simuleringen. I publikationen diskuteras även likheter i exponeringsmönster gentemot tidigare forskning rörande simulering av smittspridning i mataffärskontext, samt vilka begränsningar simuleringar kan uppvisa när det kommer till att replikera verkligheten.

Queueing theory is widely used in practical queuing applications. It can be applied for specific models of queuing systems, especially the ones that follow the Markovian property. Its purpose is to predict system behaviour in order to be used for performance optimization. In this case study, it was used to evaluate an extended queuing model with agents serving multiple queues. The purpose was to try to capture more variability and input factors into the theoretical model and test its applicability on more extended models. The main objective was to use relevant queuing theory models to estimate the wait time using real contact center data. Different from the theoretical model, the service rates of the system model depended on how many queues an agent served concurrently, which increased the complexity of the model. The obtained results demonstrated some limitations that made the models too restrictive to be applied to a model with multi-skilled agents that were not equally available. Moreover, it was shown that heuristical approaches might be more suitable for more complex queuing systems that are not covered in queueing theory models. / Köteori används i stor utsträckning i praktiska kö-applikationer. Den kan tillämpas för specifika modeller av kö-system, speciellt de som följer Markovegenskapen. Dess syfte är att förutse systembeteende för att kunna användas för prestandaoptimering. I denna fallstudie användes den för att utvärdera en utökad kömodell med agenter som betjänade flera köer. Syftet var att försöka fånga mer variabilitet och inputfaktorer i den teoretiska modellen och testa dess tillämplighet för mer utökade modeller. Huvudmålet var att använda relevanta kö-teorimodeller för att estimera väntetiden med användning av riktiga contact center data. Till skillnad från den teoretiska modellen, betjäningsintensiteten för systemmodellen berodde på hur många köer en agent betjänade samtidigt, vilket ökade komplexiteten av modellen. De erhållna resultaten visade begränsningar som gjorde modellen för restriktiv för att appliceras på en modell med fler-kvalificerade agenter som inte var lika tillgängliga. Utöver detta så visade det sig att heuristiska metoder kan vara mer lämpliga för mer komplicerade system som inte täcks av kö-teori modeller.

A CONWIP (Constant Work-In-Progress) system is basically a hybrid system with a PUSH-PULL interface at the first machine in the line. This research addresses the most general case of a cyclic CONWIP system by incorporating two additional constraints over earlier studies namely; stochastic processing times and limited intermediate storage. One of the main issues in the design of a CONWIP system is the WIP level 'M', to be maintained. This research proposes an iterative procedure to determine this optimal level. The second main issue is the optimization of the line by determining an appropriate job sequence. This research assumes a 'permutational' scheduling policy and proposes an iterative approach to find the best sequence. The approach utilizes a controlled enumerative approach called the Fast Insertion Heuristic (FIH) coupled with a method to appraise the quality of every enumeration at each iteration. This is done by using a modified version of the Floyd's algorithm, to determine the cycle time (or Flow time) of a partial/full solution. The performance measures considered are the Flow time and the Interdeparture time (inverse of throughput). Finally, both the methods suggested for the two subproblems, are tested through computer implementations to reveal their proficiency. / Master of Science

最近，金融科技(FinTech)和行動金融服務，吸引越來越多的目光。新的創新金融科技服務，改變了金融服務的消費行為。行動網路的發展使人們能夠隨時隨地的享受行動銀行的服務已經是個不爭的事實。然而，由於無線網路先天的特性以及行動裝置的移動性，使行動金融的服務品質受到網路不穩定的影響。而且，隨著Bank 3.0時代的來臨，將會有大量的使用者同時使用行動金融服務，特別是在股市開盤以及重大訊息揭露的時候。因著大量使用者瞬間湧入，以及無線網路不穩定的影響，交易系統的效能很可能會時好時壞，所以無法滿足即時金融市場的需求。 本論文中，我們提出「行動銀行訊息即服務」的框架，使系統能夠很容易的水平擴充，並且能夠輕易的實現雙向通訊和雙向交易等多項行動金融服務。為了達到最少成本追求最大利益的目的，我們發展了能夠適應突發流量以及網路不穩定性的任務分配演算法，使得不用增加額外硬體成本的前提下改善系統效能。然後，為了實驗欲模擬大量行動裝置的使用者，我們觀察真實網路的特性並發明了網路延遲自相關模型來驗證我們提出的任務分配演算法。結果顯示，透過此任務分配演算法，確實能夠有效改善系統資源管理的能力。最後，本研究將系統佈署於真實網路環境當中，並且發現進行同樣實驗的結果與採用網路延遲自相關模型的實驗結果一致。因此，本研究間接驗證了網路自相關模型的正確性，以及證明本任務分配演算法，在突發流量和網路不穩定的即時行動金融服務環境下，能有效降低系統響應時間。 / FinTech (financial technology) and mobile financial services are getting more and more attention recently. New innovative FinTech services change the consumption behavior for financial services. It is an indisputable fact development of the mobile Internet allows people to enjoy mobile banking everywhere and anytime. However, due to the nature of wireless networking and the mobility of the mobile device, the quality of mobile financial service will be affected by network instability. Moreover, with the coming of Bank 3.0, a huge amount of users would be in the mobile service of finance simultaneously, especially when the instances of the stock market opening or disclosure of highly important financial message. As the result of bursty traffic and network instability, the performance of transaction system is up and down, making it tough to satisfy the demand of real-time financial markets. In this thesis, we propose a “Mobile Banking Messaging as a Service Framework” that can easily scale out and fulfill functions comprising Bilateral Communication, Bilateral Trading, and many other mobile financial services. To pursuit of the greatest benefit along with investment of the least resources, we develop the task assignment algorithm which can adapt the system to bursty traffic and unstable networks to improve performance for free. Then, in order to simulate a large number of mobile users, we observe the characteristic of real-world network delay and propose a network delay autocorrelation model to verify our task assignment algorithm. The results of experiment show that we could actually use our task assignment algorithm to improve the ability of the system to manage resource. Finally, we deploy our system in a real-world network delay environment and find that the results obtained in the real condition are the same with our simulation results. Therefore, this research can indirectly verify the correctness of the network delay autocorrelation model, and prove that our task assignment algorithm can effectively reduce the system response time for real-time mobile financial service system under bursty traffic and unstable networks.

In many optimization problems, the relationship between the objective and parameters is not known. The objective function itself may be stochastic such as a long-run average over some random cost samples. In such cases finding the gradient of the objective is not possible. It is in this setting that stochastic approximation algorithms are used. These algorithms use some estimates of the gradient and are stochastic in nature. Amongst gradient estimation techniques, Simultaneous Perturbation Stochastic Approximation (SPSA) and Smoothed Functional(SF) scheme are widely used. In this thesis we have proposed a novel multi-time scale quasi-Newton based smoothed functional (QN-SF) algorithm for unconstrained as well as constrained optimization. The algorithm uses the smoothed functional scheme for estimating the gradient and the quasi-Newton method to solve the optimization problem. The algorithm is shown to converge with probability one. We have also provided here experimental results on the problem of optimal routing in a multi-stage network of queues. Policies like Join the Shortest Queue or Least Work Left assume knowledge of the queue length values that can change rapidly or hard to estimate. If the only information available is the expected end-to-end delay as with our case, such policies cannot be used. The QN-SF based probabilistic routing algorithm uses only the total end-to-end delay for tuning the probabilities. We observe from the experiments that the QN-SF algorithm has better performance than the gradient and Jacobi versions of Newton based smoothed functional algorithms. Next we consider constrained routing in a similar queueing network. We extend the QN-SF algorithm to this case. We study the convergence behavior of the algorithm and observe that the constraints are satisfied at the point of convergence. We provide experimental results for the constrained routing setup as well. Next we study reinforcement learning algorithms which are useful for solving Markov Decision Process(MDP) when the precise information on transition probabilities is not known. When the state, and action sets are very large, it is not possible to store all the state-action tuples. In such cases, function approximators like neural networks have been used. The popular Q-learning algorithm is known to diverge when used with linear function approximation due to the ’off-policy’ problem. Hence developing stable learning algorithms when used with function approximation is an important problem. We present in this thesis a variant of Q-learning with linear function approximation that is based on two-timescale stochastic approximation. The Q-value parameters for a given policy in our algorithm are updated on the slower timescale while the policy parameters themselves are updated on the faster scale. We perform a gradient search in the space of policy parameters. Since the objective function and hence the gradient are not analytically known, we employ the efficient one-simulation simultaneous perturbation stochastic approximation(SPSA) gradient estimates that employ Hadamard matrix based deterministic perturbations. Our algorithm has the advantage that, unlike Q-learning, it does not suffer from high oscillations due to the off-policy problem when using function approximators. Whereas it is difficult to prove convergence of regular Q-learning with linear function approximation because of the off-policy problem, we prove that our algorithm which is on-policy is convergent. Numerical results on a multi-stage stochastic shortest path problem show that our algorithm exhibits significantly better performance and is more robust as compared to Q-learning. Future work would be to compare it with other policy-based reinforcement learning algorithms. Finally, we develop an online actor-critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process(MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multistage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.

Les files d'attente fluides sont des processus markoviens à deux dimensions, où la première composante, appelée le niveau, représente le contenu d'un réservoir et prend des valeurs continues, et la deuxième composante, appelée la phase, est l'état d'un processus markovien dont l'évolution contrôle celle du niveau. Le niveau de la file fluide varie linéairement avec un taux qui dépend de la phase et qui peut prendre n'importe quelle valeur réelle.<p><p>Dans cette thèse, nous explorons le lien entre les files fluides et les processus QBD, et nous appliquons des arguments utilisés en théorie des processus de renouvellement pour obtenir la distribution stationnaire de plusieurs modèles fluides.<p><p>Nous commençons par l'étude d'une file fluide avec un réservoir de taille infinie; nous déterminons sa distribution stationnaire, et nous présentons un algorithme permettant de calculer cette distribution de manière très efficace. Nous observons que la distribution stationnaire de la file fluide de capacité infinie est très semblable à celle d'un processus QBD avec une infinité de niveaux. Nous poursuivons la recherche des similarités entre les files fluides et les processus QBD, et nous étudions ensuite la distribution stationnaire d'une file fluide de capacité finie. Nous montrons que l'algorithme valable pour le cas du réservoir infini permet de calculer toutes les quantités importantes du modèle avec un réservoir fini.<p><p>Nous considérons ensuite des modèles fluides plus complexes, de capacité finie ou infinie, où le comportement du processus markovien des phases peut changer lorsque le niveau du réservoir atteint certaines valeurs seuils. Nous montrons que les méthodes développées pour des modèles classiques s'étendent de manière naturelle à ces modèles plus complexes.<p><p>Pour terminer, nous étudions les conditions nécessaires et suffisantes qui mènent à l'indépendance du niveau et de la phase d'une file fluide de capacité infinie en régime stationnaire. Ces résultats s'appuient sur des résultats semblables concernant des processus QBD.<p><p>Markov modulated fluid queues are two-dimensional Markov processes, of which the first component, called the level, represents the content of a buffer or reservoir and takes real values; the second component, called the phase, is the state of a Markov process which controls the evolution of the level in the following manner: the level varies linearly at a rate which depends on the phase and which can take any real value.<p><p>In this thesis, we explore the link between fluid queues and Quasi Birth-and-Death (QBD) processes, and we apply Markov renewal techniques in order to derive the stationary distribution of various fluid models.<p><p>To begin with, we study a fluid queue with an infinite capacity buffer; we determine its stationary distribution and we present an algorithm which performs very efficiently in the determination of this distribution. We observe that the equilibrium distribution of the fluid queue is very similar to that of a QBD process with infinitely many levels. We further exploit the similarity between the two processes, and we determine the stationary distribution of a finite capacity fluid queue. We show that the algorithm available in the infinite case allows for the computation of all the important quantities entering in the expression of this distribution.<p><p>We then consider more complex models, of either finite or infinite capacities, in which the behaviour ff the phase process may change whenever the buffer is empty or full, or when it reaches certain thresholds. We show that the techniques that we develop for the simpler models can be extended quite naturally in this context.<p><p>Finally, we study the necessary and sufficient conditions that lead to the independence between the level and the phase of an infinite capacity fluid queue in the stationary regime. These results are based on similar developments for QBD processes. / Doctorat en sciences, Spécialisation mathématiques / info:eu-repo/semantics/nonPublished

El mundo de las telecomunicaciones está cambiando de un escenario donde únicamente las personas estaban conectadas a un modelo donde prácticamente todos los dispositivos y sensores se encuentran conectados, también conocido como Internet de las cosas (IoT), donde miles de millones de dispositivos se conectarán a Internet a través de conexiones móviles y redes fijas. En este contexto, hay muchos retos que superar, desde el desarrollo de nuevos estándares de comunicación al estudio de la viabilidad económica de los posibles escenarios futuros. En esta tesis nos hemos centrado en el estudio de la viabilidad económica de diferentes escenarios mediante el uso de conceptos de microeconomía, teoría de juegos, optimización no lineal, economía de redes y redes inalámbricas. La tesis analiza la transición desde redes centradas en el servicio de tráfico HTC a redes centradas en tráfico MTC desde un punto de vista económico. El primer escenario ha sido diseñado para centrarse en las primeras etapas de la transición, en la que ambos tipos de tráfico son servidos bajo la misma infraestructura de red. En el segundo escenario analizamos la siguiente etapa, en la que el servicio a los usuarios MTC se realiza mediante una infraestructura dedicada. Finalmente, el tercer escenario analiza la provisión de servicios basados en MTC a usuarios finales, mediante la infraestructura analizada en el escenario anterior. Gracias al análisis de todos los escenarios, hemos observado que la transición de redes centradas en usuarios HTC a redes MTC es posible y que la provisión de servicios en tales escenarios es viable. Además, hemos observado que el comportamiento de los usuarios es esencial para determinar la viabilidad de los diferentes modelos de negocio, y por tanto, es necesario estudiar el comportamiento y las preferencias de los usuarios en profundidad en estudios futuros. Específicamente, los factores más relevantes son la sensibilidad de los usuarios al retardo en los datos recopilados por los sensores y la cantidad de los mismos. También hemos observado que la diferenciación del tráfico en categorías mejora el uso de las redes y permite crear nuevos servicios empleando datos que, de otro modo, no se aprovecharían, lo cual nos permite mejorar la monetización de la infraestructura. También hemos demostrado que la provisión de capacidad es un mecanismo válido, alternativo a la fijación de precios, para la optimización de los beneficios de los proveedores de servicio. Finalmente, se ha demostrado que es posible crear roles específicos para ofrecer servicios IoT en el mercado de las telecomunicaciones, específicamente, los IoT-SPs, que proporcionan servicios basados en sensores inalámbricos utilizando infraestructuras de acceso de terceros y sus propias redes de sensores. En resumen, en esta tesis hemos intentado demostrar la viabilidad económica de modelos de negocio basados en redes futuras IoT, así como la aparición de nuevas oportunidades y roles de negocio, lo cual nos permite justificar económicamente el desarrollo y la implementación de las tecnologías necesarias para ofrecer servicios de acceso inalámbrico masivo a dispositivos MTC. / The communications world is moving from a standalone devices scenario to a all-connected scenario known as Internet of Things (IoT), where billions of devices will be connected to the Internet through mobile and fixed networks. In this context, there are several challenges to face, from the development of new standards to the study of the economical viability of the different future scenarios. In this dissertation we have focused on the study of the economic viability of different scenarios using concepts of microeconomics, game theory, non-linear optimization, network economics and wireless networks. The dissertation analyzes the transition from a Human Type Communications (HTC) to a Machine Type Communications (MTC) centered network from an economic point of view. The first scenario is designed to focus on the first stages of the transition, where HTC and MTC traffic are served on a common network infrastructure. The second scenario analyzes the provision of connectivity service to MTC users using a dedicated network infrastructure, while the third stage is centered in the analysis of the provision of services based on the MTC data over the infrastructure studied in the previous scenario. Thanks to the analysis of all the scenarios we have observed that the transition from HTC users-centered networks to MTC networks is possible and that the provision of services in such scenarios is viable. In addition, we have observed that the behavior of the users is essential in order to determine the viability of a business model, and therefore, it is needed to study their behavior and preferences in depth in future studios. Specifically, the most relevant factors are the sensitivity of the users to the delay and to the amount of data gathered by the sensors. We also have observed that the differentiation of the traffic in categories improves the usage of the networks and allows to create new services thanks to the data that otherwise would not be used, improving the monetization of the infrastructure and the data. In addition, we have shown that the capacity provision is a valid mechanism for providers' profit optimization, as an alternative to the pricing mechanisms. Finally, it has been demonstrated that it is possible to create dedicated roles to offer IoT services in the telecommunications market, specifically, the IoT-SPs, which provide wireless-sensor-based services to the final users using a third party infrastructure. Summarizing, this dissertation tries to demonstrate the economic viability of the future IoT networks business models as well as the emergence of new business opportunities and roles in order to justify economically the development and implementation of the new technologies required to offer massive wireless access to machine devices. / El món de les telecomunicacions està canviant d'un escenari on únicament les persones estaven connectades a un model on pràcticament tots els dispositius i sensors es troben connectats, també conegut com a Internet de les Coses (IoT) , on milers de milions de dispositius es connectaran a Internet a través de connexions mòbils i xarxes fixes. En aquest context, hi ha molts reptes que superar, des del desenrotllament de nous estàndards de comunicació a l'estudi de la viabilitat econòmica dels possibles escenaris futurs. En aquesta tesi ens hem centrat en l'estudi de la viabilitat econòmica de diferents escenaris per mitjà de l'ús de conceptes de microeconomia, teoria de jocs, optimització no lineal, economia de xarxes i xarxes inalàmbriques. La tesi analitza la transició des de xarxes centrades en el servici de tràfic HTC a xarxes centrades en tràfic MTC des d'un punt de vista econòmic. El primer escenari ha sigut dissenyat per a centrar-se en les primeres etapes de la transició, en la que ambdós tipus de tràfic són servits davall la mateixa infraestructura de xarxa. En el segon escenari analitzem la següent etapa, en la que el servici als usuaris MTC es realitza per mitjà d'una infraestructura dedicada. Finalment, el tercer escenari analitza la provisió de servicis basats en MTC a usuaris finals, per mitjà de la infraestructura analitzada en l'escenari anterior. Als paràgrafs següents es descriu amb més detall cada escenari. Gràcies a l'anàlisi de tots els escenaris, hem observat que la transició de xarxes centrades en usuaris HTC a xarxes MTC és possible i que la provisió de servicis en tals escenaris és viable. A més a més, hem observat que el comportament dels usuaris és essencial per a determinar la viabilitat dels diferents models de negoci, i per tant, és necessari estudiar el comportament i les preferències dels usuaris en profunditat en estudis futurs. Específicament, els factors més rellevants són la sensibilitat dels usuaris al retard en les dades recopilats pels sensors i la quantitat dels mateixos. També hem observat que la diferenciació del tràfic en categories millora l'ús de les xarxes i permet crear nous servicis emprant dades que, d'una altra manera, no s'aprofitarien, la qual cosa ens permet millorar la monetització de la infraestructura. També hem demostrat que la provisió de capacitat és un mecanisme vàlid, alternatiu a la fixació de preus, per a l'optimització dels beneficis dels proveïdors de servici. Finalment, s'ha demostrat que és possible crear rols específics per a oferir servicis IoT en el mercat de les telecomunicacions, específicament, els IoT-SPs, que proporcionen servicis basats en sensors inalàmbrics utilitzant infraestructures d'accés de tercers i les seues pròpies xarxes de sensors. En resum, en aquesta tesi hem intentat demostrar la viabilitat econòmica de models de negoci basats en xarxes futures IoT, així com l'aparició de noves oportunitats i rols de negoci, la qual cosa ens permet justificar econòmicament el desenrotllament i la implementació de les tecnologies necessàries per a oferir servicis d'accés inalàmbric massiu a dispositius MTC. / Sanchis Cano, Á. (2018). Economic analysis of wireless sensor-based services in the framework of the Internet of Things. A game-theoretical approach [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/102642 / TESIS

Cette thèse étudie les communications directes entre les mobiles, appelées communications D2D, en tant que technique prometteuse pour améliorer les futurs réseaux cellulaires. Cette technologie permet une communication directe entre deux terminaux mobiles sans passer par la station de base. La modélisation, l'évaluation et l'optimisation des différents aspects des communications D2D constituent les objectifs fondamentaux de cette thèse et sont réalisés principalement à l'aide des outils mathématiques suivants: la théorie des files d'attente, l'optimisation de Lyapunov et les processus de décision markovien partiellement observable POMDP. Les résultats de cette étude sont présentés en trois parties. Dans la première partie, nous étudions un schéma de sélection entre mode cellulaire et mode D2D. Nous dérivons les régions de stabilité des scénarios suivants: réseaux cellulaires purs et réseaux cellulaires où les communications D2D sont activées. Une comparaison entre ces deux scénarios conduit à l'élaboration d'un algorithme de sélection entre le mode cellulaire et le mode D2D qui permet d'améliorer la capacité du réseau. Dans la deuxième partie, nous développons un algorithme d'allocation de ressources des communications D2D. Les utilisateurs D2D sont en mesure d'estimer leur propre qualité de canal, cependant la station de base a besoin de recevoir des messages de signalisation pour acquérir cette information. Sur la base de cette connaissance disponibles au niveau des utilisateurs D2D, une approche d'allocation des ressources est proposée afin d'améliorer l'efficacité énergétique des communications D2D. La version distribuée de cet algorithme s'avère plus performante que celle centralisée. Dans le schéma distribué des collisions peuvent se produire durant la transmission de l'état des canaux D2D ; ainsi un algorithme de réduction des collisions est élaboré. En outre, la mise en œuvre des algorithmes centralisé et distribué dans un réseau cellulaire, type LTE, est décrite en détails. Dans la troisième partie, nous étudions une politique de sélection des relais D2D mobiles. La mobilité des relais représente un des principaux défis que rencontre toute stratégie de sélection de relais. Le problème est modélisé par un processus contraint de décision markovien partiellement observable qui prend en compte le dynamisme des relais et vise à trouver la politique de sélection de relais qui optimise la performance du réseau cellulaire sous des contraintes de coût. / This thesis considers Device-to-Device (D2D) communications as a promising technique for enhancing future cellular networks. Modeling, evaluating and optimizing D2D features are the fundamental goals of this thesis and are mainly achieved using the following mathematical tools: queuing theory, Lyapunov optimization and Partially Observed Markov Decision Process (POMDP). The findings of this study are presented in three parts. In the first part, we investigate a D2D mode selection scheme. We derive the queuing stability regions of both scenarios: pure cellular networks and D2D-enabled cellular networks. Comparing both scenarios leads us to elaborate a D2D vs cellular mode selection design that improves the capacity of the network. In the second part, we develop a D2D resource allocation algorithm. We observe that D2D users are able to estimate their local Channel State Information (CSI), however the base station needs some signaling exchange to acquire this information. Based on the D2D users' knowledge of their local CSI, we provide an energy efficient resource allocation framework that shows how distributed scheduling outperforms centralized one. In the distributed approach, collisions may occur between the different CSI reporting; thus, we propose a collision reduction algorithm. Moreover, we give a detailed description on how both centralized and distributed algorithms can be implemented in practice. In the third part, we propose a mobile relay selection policy in a D2D relay-aided network. Relays' mobility appears as a crucial challenge for defining the strategy of selecting the optimal D2D relays. The problem is formulated as a constrained POMDP which captures the dynamism of the relays and aims to find the optimal relay selection policy that maximizes the performance of the network under cost constraints.

Le réseau mobile d’Orange France comprend plus de 100 000 antennes 2G, 3G et 4G sur plusieurs bandes de fréquences sans compter les nombreuses femto-cells fournies aux clients pour résoudre les problèmes de couverture. Ces chiffres ne feront que s’accroître pour répondre à la demande sans cesse croissante des clients pour les données mobiles. Cela illustre le défi énorme que rencontrent les opérateurs de téléphonie mobile en général à savoir gérer un réseau aussi complexe tout en limitant les coûts d’opération pour rester compétitifs. Cette thèse s’attache à utiliser le concept SON (réseaux auto-organisants) pour réduire cette complexité en automatisant les tâches répétitives ou complexes. Plus spécifiquement, nous proposons des algorithmes d’optimisation automatique pour des scénarios liés à la densification par les small cells ou les antennes actives. Nous abordons les problèmes classiques d’équilibrage de charge mais avec un lien backhaul à capacité limitée et de coordination d’interférence que ce soit dans le domaine temporel (notamment avec le eICIC) ou le domaine fréquentiel. Nous proposons aussi des algorithmes d’activation optimale de certaines fonctionnalités lorsque cette activation n’est pas toujours bénéfique. Pour la formulation mathématique et la résolution de tous ces algorithmes, nous nous appuyons sur les résultats de l’approximation stochastique et de l’optimisation convexe. Nous proposons aussi une méthodologie systématique pour la coordination de multiples fonctionnalités SON qui seraient exécutées en parallèle. Cette méthodologie est basée sur les jeux concaves et l’optimisation convexe avec comme contraintes des inégalités matricielles linéaires. / The mobile network of Orange in France comprises more than 100 000 2G, 3G and 4G antennas with severalfrequency bands, not to mention many femto-cells for deep-indoor coverage. These numbers will continue toincrease in order to address the customers’ exponentially increasing need for mobile data. This is an illustrationof the challenge faced by the mobile operators for operating such a complex network with low OperationalExpenditures (OPEX) in order to stay competitive. This thesis is about leveraging the Self-Organizing Network(SON) concept to reduce this complexity by automating repetitive or complex tasks. We specifically proposeautomatic optimization algorithms for scenarios related to network densification using either small cells orActive Antenna Systems (AASs) used for Vertical Sectorization (VeSn), Virtual Sectorization (ViSn) and multilevelbeamforming. Problems such as load balancing with limited-capacity backhaul and interference coordination eitherin time-domain (eICIC) or in frequency-domain are tackled. We also propose optimal activation algorithms forVeSn and ViSn when their activation is not always beneficial. We make use of results from stochastic approximationand convex optimization for the mathematical formulation of the problems and their solutions. We also proposea generic methodology for the coordination of multiple SON algorithms running in parallel using results fromconcave game theory and Linear Matrix Inequality (LMI)-constrained optimization.