This paper presents a performance analysis of slotted rings based on a register-insertion method which is proposed for broadband ring topology networks. The analysis is carried out under the assumption that each node contains a finite buffer space. A Markovian model is developed for the ring. The arrival process of packets from upstream nodes is determined from the model. Then, the probability of buffer overflow and the probability distribution of the number of packets in a buffer are calculated using the model. The analytical results are shown to be accurate by comparing them with simulation results.