In video streaming, feedback-based rate control is utilized for guaranteeing video quality on an end-to-end basis. In this paper, we consider the effect of feed-back based rate controls on video streaming service. Focusing on the receiver buffer of a client node, we model it as a finite-capacity single-server queue with a state-dependent arrival process. The buffer-overflow and starvation probabilities are analyzed with a discrete-time Markov chain. Numerical examples show the effectiveness of the feedback-based rate controls for improving both the starvation and overflow probabilities. In particular, it is observed that the rate control which is sensitive to the number of data blocks in the receiver buffer makes the buffer-overflow and starvation probabilities significantly small. Numerical examples also show that buffer-size enhancement is important for the use of the rate control with moderate rate variations.