In SDN, as the control channel becomes a performance bottleneck, modeling the control channel traffic is important. Such a model is useful in predicting the control channel traffic for network provisioning. However, previously proposed models are quite limited in that they assume only the forwarding function of a specific controller for their models. To overcome the limitations, first, this paper analyzes the control traffic by seven functions (including forwarding function) of a controller. Then, we build a seven-function model to predict control channel usage and evaluate the prediction accuracy that achieves as high as 94%. Note that previous models did not have any quantitative evaluation. Our model is built with the Open Network Operating System (ONOS) controller and extended to Floodlight and POX controllers. We show that the extended model also achieves similar prediction accuracy (95%). Furthermore, we compare three controllers in terms of control channel usage through our model.