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Traffic self-similarity has been discovered to be a ubiquitous phenomenon in modern communication networks and multimedia systems. Due to its scale-invariant bursty 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 and analysis of priority queueing systems by proposing a novel and efficient queue-decomposition approach to handle multi-class self-similar traffic. Specifically, we extend the well-known method of empty buffer approximation in order to decompose the priority queueing system equivalently into a group of single-server single-queue systems. We further obtain the analytical upper and lower bounds of the queue length distributions for individual traffic flows.