Traffic patterns generated by multimedia services are different from traditional Poisson traffic. It has been shown in numerous studies that multimedia network traffic exhibits self-similarity and burstiness over a large range of time-scales. The area of wireless IP traffic modeling for the purpose of providing assured QoS to the end-user is still immature and the majority of existing work is based on characterization of wireless IP traffic without any coupling of the behaviour of queueing systems under such traffic conditions. Work in this area has either been limited to simplified models of FIFO queueing systems which do not accurately reflect likely queueing system implementations or the results have been limited to simplified numerical analysis studies. In this paper, we advance the knowledge of queueing systems by example of traffic engineering of different UMTS service classes. Specifically, we examine QoS mapping using three common queueing disciplines; Priority Queuing (PQ), Low Latency Queuing (LLQ) and Custom Queueing (CQ), which are likely to be used in future all-IP based packet transport networks. The present study is based on a long-range dependent traffic model, which is second order self-similar. We consider three different classes of self-similar traffic fed into a G/M/1 queueing system and construct analytical models on the basis of non-preemptive priority, low-latency queueing and custom queueing respectively. In each case, expressions are derived for the expected waiting times and packet loss rates of different traffic classes. We have developed a comprehensive discrete-event simulator for a G/M/1 queueing system in order to understand and evaluate the QoS behaviour of self-similar traffic and carried out performance evaluations of multiple classes of input traffic in terms of expected queue length, packet delay and packet loss rate. Furthermore, we have developed a traffic generator based on the self-similar traffic model and fed the generated traffic through a CISCO router-based test bed. The results obtained from the three different queueing schemes (PQ, CQ and LLQ) are then compared with the simulation results in order to validate our analytical models.