Coordinated multi-point transmission (CoMP) is considered to be a promising technique to improve the throughput for LTE-Advanced systems. One important approach for CoMP is Joint Transmission (JT). However, the analytical model of JT has not been fully studied, as user equipments (UEs) receiving the desired signals from an adjacent base station (BS) as well as serving BS, or only serving BS were not distinguished. We derive a new analytical model to describe the call admission control in JT based systems. The performance measures of interest are the call blocking probability, and resource utilization. Furthermore, we compare the performance of JT-based systems and non-JT- based systems. The analytical results are in reasonable agreement with the simulation results.