We consider a novel traffic model, and an associated parameter fitting procedure, that jointly describes the packet arrival and the packet size processes, allowing for the incorporation of multifractal scaling behavior in both characteristics. The model is based on so-called stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. We provide a detailed comparison with a related multifractal model based on conservative cascades. Our results, that include applying the fitting procedure to real observed data with multifractal scaling behavior on both the packet arrival and packet size processes, show that L-System based models can achieve excellent fitting performance in terms of first and second order statistics and queuing behavior.