In this paper, a cloud radio access network (C-RAN) is considered where the baseband units form a pool of computational resource units (RUs) and are separated from the remote radio heads (RRHs). The RRHs are grouped into clusters based on their capacity in radio RUs. Each RRH serves different service-classes whose calls have different requirements in terms of radio and computational RUs and follow a compound Poisson process. This means that calls arrive in batches while each batch of calls follows a Poisson process. If the RUs’ requirements of an arriving call are met, then the call is accepted in the serving RRH for an exponentially distributed service time. Otherwise, call blocking occurs. We initially start our analysis with a single-cluster C-RAN and model it as a multiservice loss system, prove that the model has a product form solution, and determine time and call congestion probabilities via a convolution algorithm. Furthermore, the previous model is extended to include the more complex case of many clusters of RRHs.