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In this paper, we propose and analyze a methodology for providing absolute differentiated services for real-time applications. We develop a method that can be used to derive delay bounds without specific information on flow population. With this new method, we are able to successfully employ a utilization-based admission control approach for flow admission. This approach does not require explicit delay computation at admission time and, hence, is scalable to large systems. We assume the underlying network to use static-priority schedulers. We design and analyze several priority assignment algorithms and investigate their ability to achieve higher utilization bounds. Traditionally, schedulers in differentiated services networks assign priorities on a class-by-class basis, with the same priority for each class on each router. In this paper, we show that relaxing this requirement, that is, allowing different routers to assign different priorities to classes, achieves significantly higher utilization bounds.