While the results for scenarios 1 and 2 are good, and we feel that with
more investigation, scenario 3 can be handled as well, there is more to
the story. Yuang's buffer analysis does not hold for short clips for arbitrary 
and 
durations. Imagine if
and
are allowed to grow arbitrarily long. Then with high probability, during
a short clip the channel will either be in one state or the other for the
entire clip. Thus, over the length of the short clip, the channel does
not behave ergodically. While the time average of the channel over the
thirty second clip is likely to be either 
or 
the ensemble average is
For instance, in figure 9, we see
that for 
secs, 
the curve in figure 3 flattens in the
experimental data. In the analysis, however, it remains much the same as
shown in scenario 1.
Figure 9: Simulation data for scenario 1 with 
sec, 
sec,
. We see a flattening out of the curves as the durations of the channel
states become comparable to the duration of the clips
We have explored methods to handle this situation but have not been
able to verify that these match well with simulation results. The approach
is to have two analyses running in parallel, one assuming that the channel
begins in the good state, and the other assuming the channel begins in
the bad state. The buffer state probabilities are then the weighted average
of the buffer states in each of the two paths.