Some oil and gas companies are drilling and developing fields in the Arctic Ocean, which has an environment with sea ice called ice floes. These companies must protect their platforms from ice floe collisions. One proposal is to use a system that consists of autonomous underwater vehicles (AUVs) and docking stations. The AUVs measure the under-water topography of the ice floes, while the docking stations launch the AUVs and recharge their batteries. Given resource constraints, we optimize quantities and locations for the docking stations and the AUVs, as well as the AUV scheduling policies, in order to provide the maximum protection level for the platform. We first use an queueing approach to model the problem as a queueing system with abandonments, with the objective to minimize the abandonment probability. Both M/M/k+M and M/G/k+G queueing approximations are applied and we also develop a detailed simulation model based on the queueing approximation. In a complementary approach, we model the system using a multi-stage stochastic facility location problem in order to optimize the docking station locations, the AUV allocations, and the scheduling policies of the AUVs. A two-stage stochastic facility location problem and several efficient online scheduling heuristics are developed to provide lower bounds and upper bounds for the multi-stage model, and also to solve large-scale instances of the optimization model. Even though the model is motivated by an oil industry project, most of the modeling and optimization methods apply more broadly to any radial detection problems with queueing dynamics. / text

Most departments of education and school boards do not identify nor compile data reasons for public school abandonments. Public schools are anchors, vital components, and “heartbeats” of communities that contribute to the growth or decline of neighborhoods. Despite the influences that public schools have on the development and sustainability of neighborhoods, public school abandonments are increasing. School systems use abandonments to address challenges of poor academic achievements, decreasing budgets, declining enrollments, and deteriorating and underutilized facilities. However, absent from literature are comprehensive data and analyses that identify the number of public school abandonments, their locations, or the contributing factors for these abandonments. In this dissertation, I argue that this lack of information creates a critical gap to effective urban and school planning and neighborhood preservation. I confirm this gap and provide a foundation for future research. First, I analyze demographic data for ten of the nation’s most populous metropolitan areas. Second, I survey inner-city school district administrators to obtain primary data about school abandonments. I confirm through my data analyses that abandonments occur most often in poverty and minority concentrated inner-city neighborhoods. I conclude that the findings of my research support the need for comprehensive data and analyses specific to public school abandonments and the need for urban and school planners to evaluate and incorporate the analyses of these data in strategic neighborhood and school planning and development decisions, thereby, minimizing additional adverse impacts on communities that are already in social, economical, and physical distress.

Dans cette thèse, nous étudions le contrôle dynamique des systèmes de partage de ressources qui se posent dans divers domaines : réseaux de gestion des stocks, services de santé, réseaux de communication, etc. Nous visons à allouer efficacement les ressources disponibles entre des projets concurrents, selon certains critères de performance. Ce type de problème est de nature stochastique et peut être très complexe à résoudre. Nous nous concentrons donc sur le développement de méthodes heuristiques performantes. Dans la partie I, nous nous plaçons dans le cadre des Restless Bandit Problems, qui est une classe générale de problèmes d’optimisation dynamique stochastique. Relaxer la contrainte de trajectoire dans le problème d’optimisation permet de définir une politique d’index comme heuristique pour le modèle contraint d’origine, aussi appelée politique d’index de Whittle. Nous dérivons une expression analytique pour l’index de Whittle en fonction des probabilités stationnaires de l’état dans le cas où les bandits (ou projets) suivent un processus de naissance et de mort. D’une part, cette expression nécessite la vérification de plusieurs conditions techniques, d’autre part elle ne peut être calculée explicitement que dans certains cas spécifiques. Nous prouvons ensuite, que dans le cas particulier d’une file d’attente multi-classe avec abandon, la politique d’index de Whittle est asymptotiquement optimale aussi bien pour les régimes à faible trafic comme pour ceux à fort trafic. Dans la partie II, nous dérivons des heuristiques issues de l’approximation des systèmes stochastiques de partage de ressources par des modèles fluides déterministes. Nous formulons dans un premier temps une version fluide du problème d’optimisation relaxé que nous avons introduit dans la partie I, et développons une politique d’index fluide. L’index fluide peut toujours être calculé explicitement et surmonte donc les questions techniques qui se posent lors du calcul de l’index de Whittle. Nous appliquons les politiques d’index de Whittle et de l’index fluide à plusieurs cas : les fermes de serveurs éco-conscients, l’ordonnancement opportuniste dans les systèmes sans fil, et la gestion de stockage de produits périssables. Nous montrons numériquement que ces politiques d’index sont presque optimales. Dans un second temps, nous étudions l’ordonnancement optimal de la version fluide d’une file d’attente multi-classe avec abandon. Nous obtenons le contrôle optimal du modèle fluide en présence de deux classes de clients en concurrence pour une même ressource. En nous appuyant sur ces derniers résultats, nous proposons une heuristique pour le cas général de plusieurs classes. Cette heuristique montre une performance quasi-optimale lorsqu’elle est appliquée au modèle stochastique original pour des charges de travail élevées. Enfin, dans la partie III, nous étudions les phénomènes d’abandon dans le contexte d’un problème de distribution de contenu. Nous caractérisons une politique optimale de regroupement afin que des demandes issues d’utilisateurs impatients puissent être servies efficacement en mode diffusion. / In this thesis we study the dynamic control of resource-sharing systems that arise in various domains: e.g. inventory management, healthcare and communication networks. We aim at efficiently allocating the available resources among competing projects according to a certain performance criteria. These type of problems have a stochastic nature and may be very complex to solve. We therefore focus on developing well-performing heuristics. In Part I, we consider the framework of Restless Bandit Problems, which is a general class of dynamic stochastic optimization problems. Relaxing the sample-path constraint in the optimization problem enables to define an index-based heuristic for the original constrained model, the so-called Whittle index policy. We derive a closed-form expression for the Whittle index as a function of the steady-state probabilities for the case in which bandits (projects) evolve in a birth-and-death fashion. This expression requires several technical conditions to be verified, and in addition, it can only be computed explicitly in specific cases. In the particular case of a multi-class abandonment queue, we further prove that the Whittle index policy is asymptotically optimal in the light-traffic and heavy-traffic regimes. In Part II, we derive heuristics by approximating the stochastic resource-sharing systems with deterministic fluid models. We first formulate a fluid version of the relaxed optimization problem introduced in Part I, and we develop a fluid index policy. The fluid index can always be computed explicitly and hence overcomes the technical issues that arise when calculating the Whittle index. We apply the Whittle index and the fluid index policies to several systems: e.g. power-aware server-farms, opportunistic scheduling in wireless systems, and make-to-stock problems with perishable items. We show numerically that both index policies are nearly optimal. Secondly, we study the optimal scheduling control for the fluid version of a multi-class abandonment queue. We derive the fluid optimal control when there are two classes of customers competing for a single resource. Based on the insights provided by this result we build a heuristic for the general multi-class setting. This heuristic shows near-optimal performance when applied to the original stochastic model for high workloads. In Part III, we further investigate the abandonment phenomena in the context of a content delivery problem. We characterize an optimal grouping policy so that requests, which are impatient, are efficiently transmitted in a multi-cast mode.