CDMA-based technologies deserve assiduous analysis and evaluation. We study the performance, at call-level, of a CDMA cell with interference cancellation capabilities, while assuming that the cell accommodates different service-classes of batched Poisson arriving calls. The partial batch blocking discipline is applied for Call Admission Control (CAC). To guarantee certain Quality of Service (QoS) for each service-class, the Bandwidth Reservation (BR) policy is incorporated in the CAC; i.e., a fraction of system resources is reserved for highspeed service-classes. We propose a new multirate loss model for the calculation of time and call congestion probabilities. The notion of local (soft) and hard blocking, users activity, interference cancellation, as well as the BR policy, are incorporated in the model. Although the steady state probabilities of the system do not have a product form solution, time and call congestion probabilities can be efficiently determined via approximate but recursive formulas. Simulation verified the high accuracy of the new formulas. We also show the consistency of the proposed model in respect of its parameters, while comparison of the proposed model with that of Poisson input shows its necessity.