One of the key radio resource management functions in mobile broadband networks is radio scheduling (also called MAC scheduling), which coordinates the access to shared radio resources. In Long Term Evolution (LTE), advanced scheduling algorithms are needed to provide proper QoS for multi-services and optimize the trade-off between QoS and resource efficiency. Moreover, in order to reduce the overall operation effort and costs, it is also more and more desired by the mobile network operators to develop a self-optimization function which can automatically adapt the optimized settings of the MAC scheduler in accordance with the traffic and network changes during the continuing operations. In this paper we use a novel OSA (Optimized Service Aware) scheduling algorithm for LTE, which provides a good balance between multi-QoS provisioning to support mixes of real-time/non-real-time traffic and system performance maximization in a proportionally fair manner. We present extensive simulation results to investigate the impact of the parameter settings of the OSA scheduler on the service and system performance, and further compare with the well known Proportional Fair (PF) scheduler. In addition, we explore the sensitivity of the optimal setting of the OSA scheduler with respect to different traffic scenarios. Then based on the investigations, we discuss the potential gain of applying SON (Self-Organizing Networks) functions to the OSA scheduler.