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disk model in Section 5.3.3, the modified service round length is bounded from above by
u
t
hsw
+
Q
SY
min
N
suf
f
seek
(1)
Q
SY
min
t
r
(
u
,v
)
=
α
+
f
seek
(
N
trk
/
(
u
+
2))
+
Q
SY
min
W
−
1
+
v
α
+
W
−
1
+
+
f
seek
(
N
trk
/
(
u
+
2))
t
hsw
+
v
−
t
seek
(1)
1
+
+
f
seek
(
N
trk
/
(
u
+
2))
(5.30)
N
s
The first term is the service time for reading
u
media blocks; the second term is the additional
seek time due to rebuild; the third term is the time for reading
tracks, the fourth term is the
track-to-track seek time for reading rebuild tracks, and the last term is the head-repositioning
delay.
Now invoking the continuity condition in equation (5.17), we can determine the maximum
number of tracks that can be retrieved for rebuild given there are already
u
data requests in a
round, denoted by
V
(
u
), from
v
max
(
N
D
−
1)
Q
V
(
u
)
=
v
|
t
r
(
u
,v
)
≤
,v
=
0
,
1
,...
(5.31)
R
v
Given a disk with
N
suf
recording surfaces and
N
trk
tracks per surface, the rebuild time can then
be computed from
N
trk
N
suf
V
(
u
)
(
N
D
−
1)
Q
T
rebuild
=
·
(5.32)
R
v
5.5.3 Buffer Requirement
Under track-based rebuild, tracks retrieved in a service round will be consumed by the recon-
struction process to compute the lost tracks for writing to the spare disk in the next service
round. With a sector size of
S
bytes and up to
Y
max
sectors per track, the maximum buffer
requirement for rebuild can be obtained from
B
r
=
V
(0)(
N
D
−
1)
SY
max
+
V
(0)
SY
max
(5.33)
where the first term is the buffer for reading from the (
N
D
−
1) working disks and the second
term is the buffer for writing to the spare disk.
Without buffer sharing, the total buffer requirement would be the sum of equations (5.2) and
(5.33):
B
sum
=
B
p
+
B
r
=
K
(2
N
D
−
1)
Q
+
V
(0)
N
D
SY
max
(5.34)
Using buffer-sharing technique, we can compute the combined buffer requirement at a given
server utilization from
B
share
(
u
)
=
u
(2
N
D
−
1)
Q
+
V
(
u
)
N
D
SY
max
(5.35)
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