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Differentiation service (Diffserv) is regarded as one of the practical architectures to realize quality of service (QoS) on the Internet. Relative differentiated service, which achieves relative QoS differentiation between traffic classes, is a simple and easily-deployed service model. Based on the concept of relative differentiated service, Dovrolis et al. (ACM SIGMETRICS Performance Evaluation Review vol.27, no.1, pp.204-5, 1999; IEEE Network, September 1999; ACM SIGCOMM-99, September 1999) proposed a proportional differentiation service model which guarantees the ratios of service differences between classes. They claimed that weighted fair queuing (WFQ) is not suitable for implementing relative differentiation service and employed priority-based scheduling algorithms in their model. In this paper, we extend WFQ and apply it to proportional delay differentiation service. The extended WFQ algorithm adjusts …