Job Size Stationarity:
Job size distribution is defined as the distribution of
stream requests on video durations during a measurement interval.
We use histogram intersection distance [4]
to measure the change
between two job size distributions, and calculated
the pair-wise histogram intersection distance
of two adjacent data points during the measuremnent.
Figure 1 shows
the CDFs of histogram intersection distance distribution
for 3 time scales.
We can see that within 30-minute and one-hour scale, the
histogram distance is very small for most of the time.
For example, 
of the time it is no more than 0.15.
But from day to day, the
difference of request size distributions is obvious.
This indicates that short-term dynamic provisioning only needs to focus on
request arrival rate dynamics,
while capacity
planning at daily or longer basis has to
take into account both arrival rate
and job size dynamics.
Arrival Rate Predictability: We calculate the autocorrelation coefficient of the arrival rates at the time scale of 30 minutes, and from Figure 2 we can see that the workload is highly correlated in short term. We also use Fourier analysis to discover the possible periodicity in the workload dynamics after removing a few workload spikes. As shown in Figure 3, the maximum value on the figure indicates that the period is one day. With the strong periodicity components, well-known statistical prediction approaches can be applied to further improve the accuracy in capacity planning.
Burstiness: While we can not predict unexpected spikes in the workload, it is necessary to learn the nature of the burstiness and find out an efficient way to handle it once a busrty event happens. The comparison of the request (popularity) distribution during one spike interval and that in the preceding interval is shown in Figure 4. We can see that the workload can be seen as two parts: a base workload similar to the workload in the previous normal period, and an extra workload that is due to several very popular files.
