Cognitive radio technology enables secondary users (SUs) to opportunistically access the unused or sparsely utilized spectrum by primary users (PUs) without causing any harmful interference to PUs. Consequently, spectrum occupancy modeling appears as an essential task in cognitive radio networks (CRNs). In this paper, we model spectrum occupancy using a queueing theory based approach in order to evaluate the performance of CRNs in terms of network capacity and number of cognitive radio users waiting for services etc. The queue adopted in this model has variable service capacity and can be considered as a multi-service queue with server failure where each channel acts as a server. When a channel is occupied by a PU, it is regarded as a server failure. Using the probability generating function, the closed-form expressions for various performance parameters are derived. Numerical results on the remaining services for SUs and the expected number of SUs as the CRN capacity varies are illustrated.