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The hierarchical smoothed round robin (HSRR) packet scheduler that improves the performance of the smoothed round robin (SRR) for real-world packet scheduling scenarios is presented. The SRR suffers from an inability to fairly distribute service in highly skewed weight distributions where such distributions often occur in practice. As a result, the transmission behaviour of the SRR can be bursty and non-smooth for the high weighted (or high priority) flows. A novel aggregation strategy is proposed to reshape the sessions' weight distribution that aims to minimise the variance of the high-priority flows' intra-session service times. The aggregation scheme also provides a new capability that supports the provisioning of high-priority service to an arbitrary set of selected flows. The reshaped weight distribution results in guaranteed lower bound in maximum packet delay for the high-priority flows. Furthermore, empirical analyses show that the cumulative average packet delay and jitter of the high-priority flows are significantly reduced from the original SRR and also overall lower for all flows. Along with the enhanced performance in packet delays, the HSRR scheduler attains a worst-case time complexity of O(1).