Soft Scheduling - Scalable Continuous Media Streaming Systems - page 74

distributions all resemble the normal distribution. The same observation holds for all five disk
models simulated. In retrospect, this is expected since the round length is a summation of
multiple random variables and hence would approach normal according to the central limit
theorem.
We take advantage of this observation and use the normal distribution in place of F round ( t , k )
to compute numerical results in the following sections. As shown in Figure 4.4, the normal
approximation curves closely overlap with their simulated counterparts and hence justify their
use for computing numerical results.

4.6.2 Statistical Streaming Capacity
Once the round length distribution is known, we can compute the usable disk capacity from
equation (4.3). The first set of results is obtained from simulation with media bit-rates of
150KB/s (e.g., MPEG-1 video). Figures 4.5a and 4.5b show the normalized gains in disk
capacity versus overflow probability constraint for bit-rate of 150KB/s and block sizes of
64KB and 128KB respectively. Figures 4.6a and 4.6b show a similar set of results for bit-rate
of 600KB/s (e.g., MPEG-2 video) and block size of 256KB and 512KB respectively. Note that
the normalized capacity gain is defined as

C ( ε ) − C

G = (4.29)

C

where C ( and C

is the usable disk capacity under hard scheduling. The lowest overflow probability constraint is
set to 1

ε ) is the usable disk capacity under soft scheduling with overflow constraint ε

10 − 10 , equivalent to a mean-time-between-overflow of 138.5 years assuming the disk
is operated continuously at full capacity 24 hours a day. Depending on the overflow probability
constraint, the block size, and the particular disk model, the capacity gains ranges from around
20% to over 40%.
To further investigate the effect of media block size on capacity gains, we plot in Fig-
ure 4.7 the capacity gains versus media block sizes for media bit-rate of 150KB/s and overflow
probability constraint of 10 − 6 . We observe that while the capacity gains vary according to
the chosen block size, the gains remain substantial for all block sizes, with all but one case
exceeding 25%.

×

4.6.3 Dual-Round Scheduling
To investigate the additional gains achievable using Dual-Round Scheduling, we compute the
normalized additional capacity gain from

C DRS ( ε ) − C ( ε )

= (4.30)

C ( ε ) − C

and plot the results in Figure 4.8 for block size of 64KB and bit-rate of 150KB/s. The results
clearly show that DRS can further improve capacity gains over single-round scheduling. Note
that there are ups and downs in the curves due to variations of the factor C ( ) in equation

(4.30). We also observe that, in general, DRS is more effective for smaller overflow probability

ε