In this paper, the cell loss rate is analyzed in terms of the input traffic stream of different speed in ATM network. The cell loss rate is calculated by birth-death process of Leaky-Bucket mechanism as the representative algorithm of usage parameter control. The cell loss rate assumed 2-state MMPP input process to be birth-death process by considering the character of token pool about finite capacity queue. The results from numerical analysis show that the cell loss rate decreases abruptly according to the buffer size increase. The computer simulation by SIMSCRIPT II.5 has been done and compared with on/off input source case to verify the analysis results.