Rate-based flow control plays an important role for efficient traffic management of Available Bit Rate(ABR) services. We deal with the problem of the buffer dimension for rate-based ABR control. In this paper, we analyze the Allowed Cell Rate(ACR) of a source and the queue size in a steady state. First, we investigate the effect of the number of active sources on the behavior of the ACR and the maximum queue size. Reflecting the effect of this real scenes, we determine the optimal buffer size and buffer threshold. Furthermore, our analytic results are compared with the case when the effect of the number of active sources is disregarded.