In this paper, we present an analysis of a high-speed slotted ring with a single packet buffer at each station. Assuming that distances between stations affect the network performance only through the sum of themselves (this will be called the "lumpability assumption"), we introduce a model system called the lumped model in which stations are aggregated at a single point on the ring with their relative positions preserved. At the instant when each slot visits the aggregated point of the lumped model, we build a Markov chain by recording the system state of buffers and slots. From the steady state probabilities of the Markov chain, we obtain the mean waiting time and the blocking probability of each station. It will be shown analytically and by simulation that the analysis based on the lumped model yields accurate results for various network conditions.