Reliable and Fault-Tolerant Storage Systems - Scalable Continuous Media Streaming Systems - page 90

discussed in this chapter can be directly extended to these clustered schemes and hence we
will focus on single-cluster disk arrays in the rest of the chapter.

5.3.3 Disk Performance Model
Tomodel the disk, we extend the diskmodel introduced inChapter 3 by incorporating additional
details such as head-switching time and retrieval across track boundary. Let N trk be the number
of tracks per recording surface (or number of cylinders), N suf be the number recording surfaces,
W be the disk rotation speed in rounds per second, S be the sector size in bytes, N zone be the
number of zones, Y i ( i N zone ) be the number of sectors per track in zone i . Note

the disk transfer rate, denoted by X i ( i

= 1 , 2 ,...,

= 1 , 2 ,..., N zone ), is also zone dependent and is given

by

X i = SY i W (5.3)

To simplify notations in later sections, we define

X min = min { X i | i = 1 , 2 ,..., N zone } (5.4)

Y min = min { Y i | i = 1 , 2 ,..., N zone } (5.5)

Y max = max { Y i | i = 1 , 2 ,..., N zone } (5.6)

and we shall leave out the subscript i in X i and Y i when representing random variables (i.e.,
X , Y ) instead of system parameters.
To model disk performance, we first consider the time it takes to serve a request. Specifically,
disk time for retrieving a single request can be broken down into four components, namely,
fixed overhead (e.g., head-switching time, settling time, etc.) denoted by , seek time denoted

by t seek , rotational latency denoted by t rot , and transfer time denoted by t xfr :

α

t req = α + t seek + t rot + t xfr (5.7)

Seek time depends on the seek distance and can be modeled by a seek function f seek ( n )
where n is the number of tracks to seek. For rotational latency, the random variable t rot will
be uniformly distributed between 0 and W − 1 . Finally, the transfer time t xfr comprises three
components:

Q
X +

t xfr = t hsw + t track (5.8)

where the first term is the time it takes to read the media block of Q bytes from the disk surface;
the second term is the total head-switching time incurred if the media block spans more than
one track in the cylinder; the last term is the total track-to-track seek time incurred if the media
block spans more than one consecutive cylinder.
Take the Quantum Atlas-10K disk model as an example, transfer time for retrieving a 64KB
media block ranges from 4.59ms to 6.69ms depending on the zone, head-switching time is
0.176ms, and track-to-track seek time is 1.25ms. Therefore, unless one sacrifices some storage
(7-10% depending on zone) to prevent a media block spanning two tracks, the effect of track-
crossing should not be ignored.