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Traffic self-similarity has been discovered to be a ubiquitous phenomenon in communication networks and multimedia systems. Due to its fractal-like nature, performance modelling of self-similar traffic poses greater challenges and exhibits more complexity than that of traditional non-bursty traffic. As a result, most existing studies on analytical modelling of priority queueing systems with self-similar inputs have been restricted to a simplified scenario where only two traffic flows are taken into account. This study contributes to performance modelling of priority queueing systems by proposing a novel queue-decomposition approach, which offers several potential advantages and unique innovations. Specifically, we extend the well-known empty buffer approximation (EBA) method to model priority queueing systems with multiple traffic flows and decompose the original priority queueing system into a group of single-server single-queue systems, which can make the challenging performance modelling problem tractable. We further develop an analytical model to investigate the queue length distributions of individual traffic flows. The validity and accuracy of the model demonstrated through extensive simulation experiments make it a practical and cost-effective evaluation tool for quantitatively evaluating the performance behavior of priority queueing systems with multi-class self-similar traffic under various working conditions.