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Abstract-Generalized Processor Sharing (GPS) is an important scheduling discipline because it enables bandwidth sharing with work conservation and traffic isolation properties. While Markov Modulated Fluid Processes (MMFP) capture the dynamics of the sources, the analysis of such sources with a GPS server is difficult because of the large state space. In this paper, we study a multi-queue GPS system with MMFP classes and propose a scalable, low complexity algorithm for the tail distributions of the logical queues. The effective bandwidth of the classes and a simple Connection Admission Control (CAC) scheme are derived. Numerical results illustrate the efficiency and accuracy of the technique. The application to an example system of classes consisting of voice and variable-bitrate (VBR) video traffic is included.