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In this paper, we propose and analyze a methodology for providing statistical guarantees within the diffserv model in a network, that uses static-priority schedulers. We extend the previous work on statistical delay analysis and 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 systematically analyze the performance of our approaches in terms of system utilization. As expected, our experimental data show that statistical services can achieve much higher utilization than deterministic services.