With online social networks such as Facebook and Twitter becoming globally popular, there is renewed interest in understanding the structural and dynamical properties of social networks. In this thesis we study several stochastic models arising in the context of the spread of influence or information in social networks. Our objective is to provide compact and accurate quantitative descriptions of the spread processes, to understand the effects of various system parameters, and to design policies for the control of such diffusions. One of the well established models for influence spread in social networks is the threshold model. An individual’s threshold indicates the minimum level of “influence” that must be exerted, by other members of the population engaged in some activity, before the individual will join the activity. We begin with the well-known Linear Threshold (LT) model introduced by Kempe et al. [1]. We analytically characterize the expected influence for a given initial set under the LT model, and provide an equivalent interpretation in terms of acyclic path probabilities in a Markov chain. We derive explicit optimal initial sets for some simple networks and also study the effectiveness of the Pagerank [2] algorithm for the problem of influence maximization. Using insights from our analytical characterization, we then propose a computationally efficient G1-sieving algorithm for influence maximization and show that it performs on par with the greedy algorithm, through experiments on a coauthorship dataset. The Markov chain characterisation gives only limited insights into the dynamics of influence spread and the effects of the various parameters. We next provide such insights in a restricted setting, namely that of a homogeneous version of the LT model but with a general threshold distribution, by taking the fluid limit of a probabilistically scaled version of the spread Markov process. We observe that the threshold distribution features in the fluid limit via its hazard function. We study the effect of various threshold distributions and show that the influence evolution can exhibit qualitatively different behaviors, depending on the threshold distribution, even in a homogeneous setting. We show that under the exponential threshold distribution, the LT model becomes equivalent to the SIR (Susceptible-Infected-Recovered) epidemic model [3]. We also show how our approach is easily amenable to networks with heterogeneous community structures. Hundreds of millions of people today interact with social networks via their mobile devices. If the peer-to-peer radios on such devices are used, then influence spread and information spread can take place opportunistically when pairs of such devices come in proximity. In this context, we develop a framework for content delivery in mobile opportunistic networks with joint evolution of content popularity and availability. We model the evolution of influence and content spread using a multi-layer controlled epidemic model, and, using the monotonicity properties of the o.d.e.s, prove that a time-threshold policy for copying to relay nodes is delay-cost optimal. Information spread occurs seldom in isolation on online social networks. Several contents might spread simultaneously, competing for the common resource of user attention. Hence, we turn our attention to the study of competition between content creators for a common population, across multiple social networks, as a non-cooperative game. We characterize the best response function, and observe that it has a threshold structure. We obtain the Nash equilibria and study the effect of cost parameters on the equilibrium budget allocation by the content creators. Another key aspect to capturing competition between contents, is to understand how a single end-user receives and processes content. Most social networks’ interface involves a timeline, a reverse chronological list of contents displayed to the user, similar to an email inbox. We study competition between content creators for visibility on a social network user’s timeline. We study a non-cooperative game among content creators over timelines of fixed size, show that the equilibrium rate of operation under a symmetric setting, exhibits a non-monotonic behavior with increasing number of players. We then consider timelines of infinite size, along with a behavioral model for user’s scanning behavior, while also accounting for variability in quality (influence weight) among content creators. We obtain integral equations, that capture the evolution of average influence of competing contents on a social network user’s timeline, and study various content competition formulations involving quality and quantity.

Cette thèse apporte des contributions à la modélisation, compréhension ainsi qu'à la communication efficace d'information dans les réseaux dynamiques peuplant la périphérie de l'Internet. Par réseaux dynamiques, nous signifions les réseaux pouvant être modélisés par des graphes dynamiques dans lesquels noeuds et liens évoluent temporellement. Dans la première partie de la thèse, nous proposons un nouveau modèle de mobilité - STEPS - qui permet de capturer un large spectre de comportement de mobilité humains. STEPS mets en oeuvre deux principes fondamentaux de la mobilité humaine : l'attachement préférentiel à une zone de prédilection et l'attraction vers une zone de prédilection. Nous proposons une modélisation markovienne de ce modèle de mobilité. Nous montrons que ce simple modèle paramétrique est capable de capturer les caractéristiques statistiques saillantes de la mobilité humaine comme la distribution des temps d'inter-contacts et de contacts. Dans la deuxième partie, en utilisant STEPS, nous analysons les propriétés comportementales et structurelles fondamentales des réseaux opportunistes. Nous redéfinissons dans le contexte des réseaux dynamiques la notion de structure petit monde et montrons comment une telle structure peut émerger. En particulier, nous montrons que les noeuds fortement dynamiques peuvent jouer le rôle de ponts entre les composants déconnectés, aident à réduire significativement la longueur du chemin caractéristique du réseau et contribuent à l'émergence du phénomène petit-monde dans les réseaux dynamiques. Nous proposons une façon de modéliser ce phénomène sous STEPS. À partir d'un réseau dynamique régulier dans lequel les noeuds limitent leur mobilité à leurs zones préférentielles respectives. Nous recablons ce réseau en injectant progressivement des noeuds nomades se déplaçant entre plusieurs zones. Nous montrons que le pourcentage de tels nœuds nomades est de 10%, le réseau possède une structure petit monde avec un fort taux de clusterisation et un faible longueur du chemin caractéristique. La troisième contribution de cette thèse porte sur l'étude de l'impact du désordre et de l'irrégularité des contacts sur la capacité de communication d'un réseau dynamique. Nous analysons le degré de désordre de réseaux opportunistes réels et montrons que si exploité correctement, celui-ci peut améliorer significativement les performances du routage. Nous introduisons ensuite un modèle permettant de capturer le niveau de désordre d'un réseau dynamique. Nous proposons deux algorithmes simples et efficaces qui exploitent la structure temporelle d'un réseau dynamique pour délivrer les messages avec un bon compromis entre l'usage des ressources et les performances. Les résultats de simulations et analytiques montrent que ce type d'algorithme est plus performant que les approches classiques. Nous mettons également en évidence aussi la structure de réseau pour laquelle ce type d'algorithme atteint ses performances optimum. Basé sur ce résultat théorique nous proposons un nouveau protocole de routage efficace pour les réseaux opportunistes centré sur le contenu. Dans ce protocole, les noeuds maintiennent, via leurs contacts opportunistes, une fonction d'utilité qui résume leur proximité spatio-temporelle par rapport aux autres noeuds. En conséquence, router dans un tel contexte se résume à suivre le gradient de plus grande pente conduisant vers le noeud destination. Cette propriété induit un algorithme de routage simple et efficace qui peut être utilisé aussi bien dans un contexte d'adressage IP que de réseau centré sur les contenus. Les résultats de simulation montrent que ce protocole superforme les protocoles de routage classiques déjà définis pour les réseaux opportunistes. La dernière contribution de cette thèse consiste à mettre en évidence une application potentielle des réseaux dynamiques dans le contexte du " mobile cloud computing ". En utilisant les techniques d'optimisation particulaires, nous montrons que la mobilité peut augmenter considérablement la capacité de calcul des réseaux dynamiques. De plus, nous montrons que la structure dynamique du réseau a un fort impact sur sa capacité de calcul.

In this thesis we study several resource management problems in two classes of wireless networks. The thesis is in two parts, the first being concerned with game theoretic approaches for cellular networks, and the second with control theoretic approaches for mobile opportunistic networks. In Part I of the thesis, we first investigate optimal association and power control for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one base station (BS) (i.e., cell). Users have minimum signal to interference ratio(SINR) requirements and associate with BSs where least transmission powers are required. We formulate the problem as a non-cooperative game among users. We propose a distributed association and power update algorithm, and show its convergence to a Nash equilibrium of the game. We consider network models with discrete mobiles(yielding an atomic congestion game),as well as a continuum of mobiles(yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. We show that these prices weakly enforce system optimality in general, and strongly enforce it in special settings. We also show that these mechanisms can be implemented in distributed fashions. Next, we consider the hierarchical problems of user association and BS placement, where BSs may belong to the same(or, cooperating) or to competing service providers. Users transmit with constant power, and associate with base stations that yield better SINRs. We formulate the association problem as a game among users; it determines the cell corresponding to each BS. Some intriguing observations we report are:(i)displacing a BS a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction;(ii)A cell corresponding to a BS may be the union of disconnected sub-cells. We then study the problem of the placement of BSs so as to maximize service providers’ revenues. The service providers need to take into account the mobiles’ behavior that will be induced by the placement decisions. We consider the cases of single frequency band and disjoint frequency bands of operation. We also consider the networks in which BSs employ successive interference cancellation(SIC) decoding. We observe that the BS locations are closer to each other in the competitive case than in the cooperative case, in all scenarios considered. Finally, we study cooperation among cellular service providers. We consider networks in which communications involving different BSs do not interfere. If service providers jointly deploy and pool their resources, such as spectrum and BSs, and agree to serve each others’ customers, their aggregate payoff substantially increases. The potential of such cooperation can, however ,be realized only if the service providers intelligently determine who they would cooperate with, how they would deploy and share their resources, and how they would share the aggregate payoff. We first assume that the service providers can arbitrarily share the aggregate payoff. A rational basis for payoff sharing is imperative for the stability of the coalitions. We study cooperation using the theory of transferable payoff coalitional games. We show that the optimum cooperation strategy, which involves the acquisition of channels, and deployment and allocation of BSs to customers, is the solution of a concave or an integer optimization problem. We then show that the grand coalition is stable, i.e., if all the service providers cooperate, there is an operating point offering each service provider a share that eliminates the possibility of a subset of service providers splitting from the grand coalition; this operating point also maximizes the service providers’ aggregate payoff. These stabilizing payoff shares are computed by solving the dual of the above optimization problem. Moreover, the optimal cooperation strategy and the stabilizing payoff shares can be obtained in polynomial time using distributed computations and limited exchange of confidential information among the service providers. We then extend the analysis to the scenario where service providers may not be able to share their payoffs. We now model cooperation as a nontransferable payoff coalitional game. We again show that there exists a cooperation strategy that leaves no incentive for any subset of service providers to split from the grand coalition. To compute this cooperation strategy and the corresponding payoffs, we relate this game and its core to an exchange market and its equilibrium. Finally, we extend the formulations and the results to the case when customers are also decision makers in coalition formation. In Part II of this thesis, we consider the problem of optimal message forwarding in mobile opportunistic wireless networks. A message originates at a node(source), and has to be delivered to another node (destination). In the network, there are several other nodes that can assist in relaying the message at the expense of additional transmission energies. We study the trade-off between delivery delay and energy consumption. First, we consider mobile opportunistic networks employing two-hop relaying. Because of the intermittent connectivity, the source may not have perfect knowledge of the delivery status at every instant. We formulate the problem as a stochastic control problem with partial information, and study structural properties of the optimal policy. We also propose a simple suboptimal policy. We then compare the performance of the suboptimal policy against that of the optimal control with perfect information. These are bounds on the performance of the proposed policy with partial information. We also discuss a few other related open loop policies. Finally, we investigate the case where a message has to be delivered to several destinations, but we are concerned with delay until a certain fraction of them receive the message. The network employs epidemic relaying. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain, and derive the optimal forwarding policy. As observed earlier, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we then obtain an ODE(i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal deterministic policy. We evaluate the performance of this policy over finite networks, and demonstrate that this policy performs close to the optimal closed loop policy. We also briefly discuss the case where message forwarding is accomplished via two-hop relaying.