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Contemporary communication networks are expected to support multimedia services which require differentiated quality-of-services (QoS). To this end, many traffic scheduling schemes have been proposed and extensively studied. Recently, a hybrid scheduling discipline which integrates priority queueing and generalized processor sharing (GPS) has been emerging as a promising scheme for QoS differentiation. In this paper, we present an analytical performance model for the integrated scheduling system under Markov modulated Poisson processes (MMPPs), which can qualitatively model the time-varying arrival rate and capture the important correlation between the inter-arrival times. We decompose the complex system into a group of single-server single-queue (SSSQ) systems at two steps. The first step is to divide the priority queueing level into a SSSQ system and a GPS system. At the second step, we adopt a bounding approach to decompose the GPS system into two SSSQ systems and derive the performance bounds for their queue length distributions. The comparison between analytical and simulation results validates the accuracy of the analytical model.