Medium access protocols are needed to resolve the contentions between nodes and to control the traffic flow for satisfying the various Quality of Services(QOS). Among them, Distributed Queue Dual Bus(DQDB) and Asynchronous Transfer Mode Ring(ATMR) protocols have been proposed to be applied in the B-ISDN access networks. In this study, we investigate the waiting time of a cell at the tagged node in the subscriber access network based on the DQDB protocol, assuming that the node has infinite waiting buffer for transmission and the generated cells have two priority types. The result shows that the waiting time is shorter than 10 cell times in the low traffic and the throughput is 0.97. We also compare the performance of the DQDB protocol with that of the ATMR protocol in terms of the waiting time, throughtput, and so on. The waiting time of the higher priority cells under the DQDB protocol are shorter than that of the ATMR protocol and the throughput is higher than that of ATMR. The DQDB protocol is expected to be a more proper solution as a medium access protocol in B-ISDN subscriber access networks especially in case of cell transmissions with different types of priority classes.