Workload characterization involves the understanding of the relationship between workload configurations and performance characteristics. To better assess the complexity of workload behavior, a model based approach is needed. Nevertheless, several configuration parameters and performance characteristics exhibit non-linear relationships that prohibit the development of an accurate application behavior model. In this paper, we propose a non-linear model based on an artificial neural network to explore such complex relationship. We achieved high accuracy and good predictability between configurations and performance characteristics when applying such a model to a 3-tier setup with response time restrictions. As shown by our work, a non-linear model and neural networks can increase the understandings of complex multi-tiered workloads, which further provide useful insights for performance engineers to tune their workloads for improving performance