This article considers Gaussian flows which are fed into a GPS (Generalized Processor Sharing) scheduler. The system is analyzed using a most probable path approach. This method gives quite good approximations for performance measures, like queue length distributions in the full range of queue levels. The approximations are based on the distinction whether it is more probable that an aggregated queue consists of traffic from one class only or whether it is a combination of several classes. The approximate queue length distribution for a specific flow is then calculated either using the Empty Buffer Approximation or the authors' Rough Full Link Approximation, respectively.