Strict priority scheduling scheme is a good candidate for the implementation of service differentiation in an Internet because of simplicity in implementation and the capability to guarantee the delay requirement of the highest class of traffic. However, it is also blown that strict priority starves the lower-class traffic at the cost of prioritizing the higher-class traffic. The purpose of this work is to propose an analytic method which can estimate the average delay performance of Diffserv service architecture and shows that strict priority scheme does not sacrifice the lower class traffic over a diverse condition of the load. From the numerical experiments for three-class Diffserv network we validate our argument that strict priority scheme may be applied to a service differentiation scheme for the future Internet.