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Relay stations are an important component of heterogeneous networks introduced in the LTE-Advanced technology as a means to provide very high capacity and QoS all over the cell area. This paper develops a self-organizing network (SON) feature to optimally allocate resources between backhaul and station to mobile links. Static and dynamic resource sharing mechanisms are investigated. For stationary ergodic traffic we provide a queuing model to calculate the optimal resource sharing strategy and the maximal capacity of the network analytically. When traffic is not stationary, we propose a load balancing algorithm to adapt both the resource sharing and the zones covered by the relays based on measurements. Convergence to an optimal configuration is proven using stochastic approximation techniques. Self-optimizing dynamic resource allocation is tackled using a Markov Decision Process model. Stability in the infinite buffer case and blocking rate and file transfer time in the finite buffer case are considered. For a scalable solution with a large number of relays, a well-chosen parameterized family of policies is considered, to be used as expert knowledge. Finally, a model-free approach is shown in which the network can derive the optimal parameterized policy, and the convergence to a local optimum is proven.