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Resilient packet ring (RPR) is a new technology to be standardized as IEEE 802.17 for metropolitan area networks (MAN). RPR can be regarded as a buffer (or register) insertion ring. Thus, its delay performance has come to the industry's attention. We have developed a complete model for RPR with three transmit buffers and investigated the delay performance of RPR's three priorities traffic based on queuing theory. It has produced a series of valuable results, such as the delay and throughput performance of RPR's three priorities traffic in two types of transit buffer architectures, the relation between maximum throughput and the number of nodes, the relation between delay and the number of nodes, and so on.