This paper propose a novel analysis of hierarchical packet scheduling algorithm, HDDRR, enhanced from the existing dynamic deficit round-robin (DDRR) to provide relative differentiated service that enables support of delay-sensitive applications over the Internet. The level of service differentiation can be adjusted with parameter. The HDDRR scheduler fully utilizes the property of DDRR, therefore it can achieve high throughput efficiently and simultaneously provide smaller delay for short packets of each class. Simulation results showing the effectiveness of HDDRR are also presented.