In this paper, we propose a queueing model to analyze the performance of an opportunistic spectrum access (OSA) system with service interruptions operating over heterogeneous channels in which the service transmission rate and the service interruption rate after the transmission is resumed are generally different than their value prior to the interruption. We first propose Markov chain models to analyze this system under memoryless service time and availability periods. Based on simplification assumptions, we also provide an analytical z-Transform analysis of the Markov models. The Markov model and approximations are validated with accurate system simulations. We also provide numerical results illustrating the non-convex relations between the traffic metrics and system parameters and that the proposed models are essential for optimal OSA network planning and operation. We further analyze and discuss the OSA queuing model for general distribution of service time and availability periods. The analytical and simulation results indicate that for usual system parameters, the queue average occupancy is similar for different distributions of service time and availability periods and that the memoryless Markov models can be used to accurately predict the heterogeneous OSA system traffic performance.