We propose a multilevel (hierarchical) ON/OFF model to simultaneously capture the mono/multifractal behavior of Internet traffic. Parameter estimation methods are developed and applied to estimate the model parameters from real traces. Wavelet analysis and simulation results show that the synthetic traffic (using this new model with estimated parameters) and real traffic share the same statistical properties and queuing behaviors. Based on this model and its statistical properties, as described by the Logscale diagram of traces, we propose an efficient method to predict the queuing behavior of FIFO and RED queues. In order to satisfy a given delay and jitter requirement for real time connections, and to provide high goodput and low packet loss for non-real time connections, we also propose a parallel virtual queue control structure to offer differential quality of services. This new queue control structure is modeled and analyzed as a regular nonlinear dynamic system. The conditions for system stability and optimization are found (under certain simplifying assumptions) and discussed. The theoretical stationary distribution of queue length is validated by simulation.