B-ISDN is expected to provide service to diverse traffic such as video, voice and data. These traffics have very different QOS(Quality Of Service). Priority discipline is one of the prevalent method used in a multiplexer which has those traffics requiring different QOS as its traffic input. In this paper, we model the real time traffic using D-BMAP(Discrete-time batch Markov arrival process) and non-real time traffic using D-MMPP(Discrete-time Markov modulated Poisson Process) and hire a nonpreemptive priority discipline. By analyzing the performances of each class of traffic, we can confirm the effectiveness of priority discipline over ordinary FCFS discipline. In order to compute some performance measures, we use not only matrix geometric method but also the PGF(Probability Generating Function) approach.