  Our purpose in this paper is to characterize buffer starvations for streaming
services. The buffer is modeled as an M/M/1 queue, plus the consideration of
bursty arrivals. When the buffer is empty, the service restarts after a certain
amount of packets are \emph{prefetched}. With this goal, we propose two
approaches to obtain the \emph{exact distribution} of the number of buffer
starvations, one of which is based on \emph{Ballot theorem}, and the other uses
recursive equations. The Ballot theorem approach gives an explicit result. We
extend this approach to the scenario with a constant playback rate using
T\`{a}kacs Ballot theorem. The recursive approach, though not offering an
explicit result, can obtain the distribution of starvations with
non-independent and identically distributed (i.i.d.) arrival process in which
an ON/OFF bursty arrival process is considered in this work. We further compute
the starvation probability as a function of the amount of prefetched packets
for a large number of files via a fluid analysis. Among many potential
applications of starvation analysis, we show how to apply it to optimize the
objective quality of experience (QoE) of media streaming, by exploiting the
tradeoff between startup/rebuffering delay and starvations.
