Continuous Media Storage and Retrieval - Scalable Continuous Media Streaming Systems - page 58

empty buffers after transmission, the buffer requirement for data retrieval is also reduced from
d 2 kQ bytes to dkQ bytes, and the total buffer requirement becomes 2 dkQ bytes, or 2 kQ bytes
per disk - same as the single-disk case.
Therefore from the scalability perspective, a split schedule is linearly scalable in terms of
buffer requirement. Start-up delay is more complicated as it also depends on the utilization of
the disk array. Similar to the GSS scheduler discussed earlier in Section 3.4, a new user can
join any one of the d groups to receive service. Thus, if the disk array is lightly utilized (e.g.,
with fewer than k on-going streams), then the new stream can simply join the next service
round and the average delay will be the same as in the single-disk case, i.e., equal to 1.5 T a v g .
At higher utilization some of the groups may be fully occupied and in that case the delay will
be longer. We will revisit this issue in Chapter 11 where we derive the average admission delay
at a given system utilization.
3.6 Disk Zoning
So far in this chapter we havemodeled a hard disk to be composed of multiple disk platters, each
further divided into tracks, and finally each track sub-divided into a fixed number of sectors.
This last assumption, however, is not necessarily true in practice. In the race to increase the
disk storage capacity, disk drive manufacturers have developed a technique called Zoned-Bit-
Recording (ZBR), which breaks the constant-size track assumption.
If we reconsider the physical disk geometry in Figure 3.1 we can easily see that an outer
track at the edge of the disk platter will have a larger circumference than the inner track closer
to the center of the disk platter. Therefore, if the same number of sectors are used (i.e., same
track size), then the recording density of the outer tracks will be lower than the inner tracks.
Disk drive manufacturer exploits this by allocating more sectors to outer tracks than the inner
tracks. In most cases the tracks are divided into multiple zones , with tracks in the same zone
having the same number of sectors per track - disk zoning. The number of sectors per track
increases as we go from the innermost zone to the outermost zone. This effectively increases
the storage capacity of the outer zones/tracks.
The immediate impact of disk zoning is that the disk transfer rate R disk is no longer a constant
parameter. As the disk spins at a constant angular velocity (e.g., 10,000 rpm), the transfer rate
will be higher for the outer tracks than the inner tracks due to the larger track size. Take Seagate
31200W, as an example. Its disk platter is divided into 23 zones with transfer rates ranging from
2.33 MBps for the innermost zone to 4.17 MBps for the outermost zone. Thus, the difference
in transfer rates can be quite substantial.
This creates a problem in disk capacity dimensioning as the disk transfer rate is one of
the parameters previously assumed to be a given constant. For worst-case capacity dimen-
sioning the obvious solution is to use the lowest transfer rate among all disk zones as the
parameter value in dimensioning the disk capacity. This guarantees that the continuity re-
quirement will be satisfied no matter which zone the requested data happen to be located.
However, this obviously will under-utilize the disk as the outer zones, due to their larger
storage capacity, account for a larger proportion of the disk's storage. Over the years re-
searchers have come up with clever solutions to tackle this problem, principally by trading
off some storage and/or buffer for higher throughput. Interested readers are referred to the
works by Birk [8], Mourad [9], Ghandeharizadeh et al . [10], and Nerjes et al . [11] for more
detail.