In this work we introduce a novel queueing model with two classes of users in which, instead of accessing a resource, users wait in the system to match with a candidate from the other class. The users are selective and the matchings occur probabilistically. This new model is useful for analysing the traffic in web portals that match people who provide a service with people who demand the same service, e.g. employment portals, matrimonial and dating sites and rental portals. We first provide a Markov chain model for these systems and derive the probability distribution of the number of matches up to some finite time given the number of arrivals. We then prove that if no control mechanism is employed these systems are unstable for any set of parameters. We suggest four different classes of control policies to assure stability and conduct analysis on performance measures under the control policies. Contrary to the intuition that the rejection rate should decrease as the users become more likely to be matched, we show that for certain control policies the rejection rate is insensitive to the matching probability. Even more surprisingly, we show that for reasonable policies the rejection rate may be an increasing function of the matching probability. We also prove insensitivity results related to the average queue lengths and waiting times. Further, to gain more insight into the behaviour of probabilistic matching systems, we propose approximation methods based on fluid and diffusion limits using different scalings. We analyse the basic properties of these approximations and show that some performance measures are insensitive to the matching probability agreeing with the results found by the exact analysis. Finally we study the optimal control and revenue management for the systems with the objective of profit maximization. We formulate mathematical models for both unobservable and observable systems. For an unobservable system we suggest a deterministic optimal control, while for an observable system we develop an optimal myopic state dependent pricing.

In this thesis, by being motivated from the challenges in perinatal networks, we address design, evaluation and flow control of a stochastic healthcare network where there exist multiple levels of hospitals and different types of patients. Patients are supposed urgent; thus they can be rejected and overflow to another facility in the same network if no service capacity is available at their arrival. Rejection of patients due to the lack of service capacity is the common phenomenon in overflow networks. We approach the problem from both strategic and operational perspectives. In strategic part, we address a location & capacity planning problem for adjusting the network to better meet demographic changes. In operational part, we study the optimal patient admission control policies to increase flexibility in allocation of resources and improve the control of patient flow in the network. Finally, in order to evaluate the performance of the network, we develop new approximation methodologies that estimate the rejection probabilities in each hospital for each arriving patient group, thus the overflow probabilities among hospitals. Furthermore, an agent-based discrete-event simulation model is constructed to adequately represent our main applicationarea: Nord Hauts-de-Seine Perinatal Network. The simulation model is used to evaluate the performance of the complex network and more importantly evaluate the strength of the optimal results of our analytical models. The developed methodologies in this thesis are combined in a decision support tool, foreseen under the project "COVER", which aims to assist health system managers to effectively plan strategic and operational decisions of a healthcare network and evaluate the performance of their decisions.

Cette thèse porte sur l’étude d’un réseau de soins hiérarchique stochastique avec rejet où les patients sont transférés lorsque la capacité de l’hôpital d’accueil n’est pas suffisante. Les patients sont alors redirigés vers un autre hôpital, ou hors du réseau. Une application concrète sur les réseaux de périnatalité est proposée, et nous avons identifié plusieurs verrous scientifiques fondamentaux d’un point de vue stratégique et opérationnel. Dans la partie stratégique, nous nous sommes intéressés à un problème de planification de capacité dans le réseau. Nous avons développé un modèle de localisation et de dimensionnement non-linéaire qui tient compte de la nature stochastique du système. La linéarisation du modèle permet de résoudre des problèmes de taille réelle en temps raisonnable. Nous avons développé dans un second temps de nouvelles méthodologies d’approximation permettant d’évaluer la performance du réseau en termes de probabilité de rejet et de transfert entre hôpitaux. Dans la partie opérationnelle, nous avons étudié des politiques de pilotage d’admission optimales pour différentes tailles de réseaux de manière utiliser au mieux les ressources hospitalières. Finalement, nous avons construit un modèle de simulation couplant multi-agents et événements discrets permettant la validation des résultats précédents et l’évaluation de performance du système de manière réaliste. / In this thesis, by being motivated from the challenges in perinatal networks, we address design, evaluation and flow control of a stochastic healthcare network where there exist multiple levels of hospitals and different types of patients. Patients are supposed urgent; thus they can be rejected and overflow to another facility in the same network if no service capacity is available at their arrival. Rejection of patients due to the lack of service capacity is the common phenomenon in overflow networks. We approach the problem from both strategic and operational perspectives. In strategic part, we address a location & capacity planning problem for adjusting the network to better meet demographic changes. In operational part, we study the optimal patient admission control policies to increase flexibility in allocation of resources and improve the control of patient flow in the network. Finally, in order to evaluate the performance of the network, we develop new approximation methodologies that estimate the rejection probabilities in each hospital for each arriving patient group, thus the overflow probabilities among hospitals. Furthermore, an agent-based discrete-event simulation model is constructed to adequately represent our main applicationarea: Nord Hauts-de-Seine Perinatal Network. The simulation model is used to evaluate the performance of the complex network and more importantly evaluate the strength of the optimal results of our analytical models. The developed methodologies in this thesis are combined in a decision support tool, foreseen under the project “COVER”, which aims to assist health system managers to effectively plan strategic and operational decisions of a healthcare network and evaluate the performance of their decisions.