This paper proposes a novel multifractal traffic model, and an associated parameter fitting procedure, based on stochastic L-systems, which were introduced by biologist A. Lindenmayer (1968) 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, show that L-system based models can achieve excellent fitting performance in terms of first and second order statistics and queuing behavior.