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It is well known that traditional analytic methods of queueing systems, are based on the distributions of interarrival time and service time. However, it is quite inconvenient to, employ these methods directly to the analysis of current self-similar traffic models. In this paper, we first derive a novel analytic model based on the arrival rate and the service rate for single-class steady-state queueing systems. Then the derivations are extended to provide upper and, lower boundary conditions for multipriority queues in networks deploying differentiated services (DS). In addition, the analytical model is also applied to the analysis of DS effects on self-similar traffic. The results illustrate the performance gain in queue length of the priority classes that DS can provide compared to a network that does not deploy DS. Additionally, the upper lower boundary conditions of the queue lengths for each priority class also, serves as a system design guideline.