We present here an exact method for analyzing the queueing behavior of packet-switched data in a new basic rate user-network interface of ISDN. The new interface of ISDN in this paper adopts statistical multiplexing for providing integrated voice and data services. In order to properly represent the arrival of multirate data service, this interface assumes that the data packet input process is in batch Poisson. Furthermore, it is modeled by multiple synchronous servers with priority queues and finite waiting room with complete rejection strategy. The analytical method, with an application of the residue theorem in complex variable, can accurately obtain the data performance measures.>