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Random access channel (RACH) is the uplink common channel defined in the universal mobile telecommunication system (UMTS). For a better utilization of UMTS resources is very important to predict the performance of this channel. In this paper we analyze RACH throughput, considering multiple demodulation resources in the Node B. New expressions to compute the success and collision probabilities in the channel are presented in this work. Also, a modification in RACH procedure is proposed to improve the throughput performance.