Network Calculus (NC) is a powerful means to provide deep insight for flow problems in network performance analysis. Multi-priority scheduling as one of the fundamental models in NC has become an active research topic recently. However, existing works consider neither the arrival interval of the flows nor their arrival orders; thus limiting their applications to only a few delicate scenarios. In this paper, we address these two issues and propose a novel multi-priority model based on the non-preemptive priority scheduling. We derive the theoretical formulation for the service curve under this model, and then obtain the upper bounds of delay and backlog for multi-priority scheduling. We also use two representative case studies to show the correctness and effectiveness of the proposed model. The theoretical analysis is further validated by the numerical experiments. In addition, we discuss the factors that may affect the delay and backlog bounds according to the numerical results.