Soft Scheduling - Scalable Continuous Media Streaming Systems - page 66

Finally, we can compute the usable disk capacity under DRS from

C DRS ( ε ) = max { k | ( k ) ≤ ε, k = 0 , 1 ,... } (4.8)

4.3.3 Buffer Requirement
To achieve the capacity gains, there is also a trade-off in DRS - the additional buffers used
to store the early-retrieved media blocks. To obtain an upper bound for the extra buffer re-
quirement, we note that in the worst case, the second disk service round will have a length of
t max

round ( k ) as given in equation (3.5). To prevent overflow, the server will have to start the service
round earlier by

t max

T early =

round ( k )

− T r (4.9)

Note that DRS cannot compensate for overflowed rounds with length longer than 2 T r as the
slack time for the previous round is bounded by T r .
Now the time to retrieve a media block of size Q bytes is bounded from below by

Q
r max

t min
read

= (4.10)

where r max is the maximum transfer rate (e.g., at the outer-most zone). Hence during the time
interval T early , we need at most

min T early
t min
read

) B early = , C DRS ( ε (4.11)

extra buffers to store the early-retrieved media blocks.
To be fair, the extra buffers may also be used to increase the media block size Q , which also
increases disk efficiency, instead of using DRS. However, increasing the media block size will
result in longer service round length and, consequently, will increase the admission delay for
new streams. In practice, a system is likely to have been dimensioned to use the largest media
block size for maximum disk efficiency and hence increasing the block size further will not
be feasible. By contrast, DRS does not affect the scheduling delay as the media-block size is
unchanged and hence we can employ DRS to further increase the usable disk capacity in a
system with an already optimized media block size.

4.4 Early-Admission Scheduling
In conventional round-based scheduler such as SCAN and CSCAN, the media block size is one
of the key parameters in determining the achievable disk utilization. As current memory costs
continue to drop due to rapid increases in memory density, it may appear that one can keep in-
creasing disk utilization simply by choosing larger block sizes. However, in addition tomemory
cost, the usable block size is also limited by the admission delay, as discussed in Section 3.3.
For example, in conventional round-based scheduler a new request arriving mid-way in
round i will receive service beginning in the next round ( i + 1). Due to double-buffering, the

retrieved block will be transmitted in round ( i + 2). Hence, the worst-case admission delay is