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Two-stage scheduling system with multiple arrival flows is widely used in many quality of service guarantee occasions. However, there is no effective, versatile method to get the performance results for this more complex service rule system. This paper analyses a two-stage scheduling system with strict priority and generalised processor sharing scheduling discipline. By using a vertical decomposition solution method, the statistical performance bounds on the backlog and delay of each flow are derived under the exponentially bounded burstiness input model. Using a discrete time Markov-modulated On-Off process example, the performance bound results are analysed.