The purpose of this paper is to model quality of experience (QoE) of media streaming service in a shared fast-fading channel. In this context, the arrival and the service processes of the playout buffer do not have the same job size. We present an analytical framework based on Takács Ballot theorem to compute the probability of buffer starvation and the distribution of playback intervals. We model the arrival processes of Proportional Fair and Round Robin schedulers, and feed them into this framework to study the impact of prefetching on the starvation behavior. Our simulations match the developed model very well if the base station knows the playback rate and the channel gain. Furthermore, we make an important observation that QoE metrics predicted by users are very sensitive to the measurement error of arrival process.