Cloud RAN (C-RAN) is a very promising architecture for future mobile network deployment, where the cloud-centric approach is useful in improving total processing load. In this context, radio and baseband network functions processing pose interesting problems that we try to expose and solve in this paper. A novel architecture for C-RAN and a first modeling of the system are proposed. Furthermore, we study the impact of many radio parameters on the processing time. Moreover, a mathematical and a deep learning model are proposed and evaluated for processing time prediction. Results show the feasibility of the proposed approaches.