With the growing demand of data processing/storage from Internet of Things (IoT) users and the increasing maturity of Cloud-Edge technologies, it becomes more and more critical to develop an effective and efficient performance evaluation approach in order to enhance the performance of Cloud-Edge services. Analytic modeling is an effective evaluation approach. The existing modeling researches on edge and/or cloud computing either ignored workload heterogeneity or ignored delay constraint of IoT tasks. This paper develops a hierarchical model for capturing the behaviors of Cloud-Edge datacenters, which provides service to tasks with different service priorities and requesting different number of service resources. Formulas for calculating performance measures of interest are also developed. The approximate accuracy of the proposed analytic model is verified through comparing numerical results and discrete-event simulation results.