We consider a two-class Generalized Processor Sharing (GPS) queueing system, in which each class has its specific traffic characteristics and quality-of-service (QoS) requirements. Traffic of both classes is assumed to be Gaussian (a versatile family of models that covers both long-range dependent and short-range dependent traffic). In this paper we address the question how to select the GPS weight values. To do so, we first characterize the admissible region of the system for fixed weights. Then we obtain the realizable region by taking the union of the admissible regions over all possible weight values. The results indicate that, under a broad variety of traffic characteristics and QoS requirements, nearly the entire realizable region can be obtained by strict priority scheduling disciplines. In addition, we indicate how the buffer thresholds, QoS requirements and the traffic characteristics of the two classes determine which class should get high priority.