In order to deliver innovative and cost-effective IP multimedia applications over mobile devices, there is a need to develop a unified service platform for the future mobile Internet referred as the Next Generation (NG) all-IP network. It is convincingly demonstrated by numerous recent studies that modern multimedia network traffic exhibits long-range dependence (LRD) and self-similarity. These characteristics pose many novel and challenging problems in traffic engineering and network planning. One of the major concerns is how to allocate network resources efficiently to diverse traffic classes with heterogeneous QoS constraints. However, much of the current understanding of wireless traffic modeling is based on classical Poisson distributed traffic, which can yield misleading results and hence poor network planning. Unlike most existing studies that primarily focus on the analysis of single-queue systems based on the simplest FirstCome-First-Serve (FCFS) scheduling policy, in this paper we introduce the first of its kind analytical performance model for multiplequeue systems with self-similar traffic scheduled by priority queueing to support differentiated QoS classes. The proposed model is based on a G/M/1 queueing system that takes into account multiple classes of traffic that exhibit long-range dependence and self-similarity. We analyze the model on the basis of non-preemptive priority and find exact packet delay and packet loss rate of the corresponding classes. We develop a finite queue Markov chain for non-preemptive priority scheduling, extending the previous work on infinite capacity systems. We extract a numerical solution for the proposed analytical framework by formulating and solving the corresponding Markov chain. We further present a comparison of the numerical analysis with comprehensive simulation studies of the same system. We also implement a Cisco-router based test bed, which serves to validate the mathematical, numerical, and simulation results as well as to support in understanding the QoS behaviour of realistic traffic input.