In ATM switching system link bandwidth is one of the improtant resources. Thus ATM switching system must allocate the bandwidth to the users efficiently and guarantee the QoS. Especially to guarantee the QoS of the VBR traffic source such as video, users must declare the traffic characteristics and QoS expectations using UPC parameters. The CAC can use two multiplexig models in variation to link capacity and connection number. One is loseless multiplexing model; the second is a statistical multiplexing model. The loseless multiplexing model performs best when the number of mutiplexed sources is small, but as the number of multiplexed sources is increase the CAC must use the statistical multiplexing model. In this paper, the statistical multiplexing models are studied, which are suitable for high capacity ATM link on VBR traffic sources. The satistical multiplexing model and the loseless multiplexing model are combined. In statistical model we map the UPC parameters provided by new VBR connection to appropriate source traffic model. In the high capacity ATM link, as the connection number increases, the statical multiplexing gain increases.