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Transmission for new stream
starts at round i+1.
U+1
U+1
U+1
u
u
u
u
2
2
2
2
Transmission
1
1
1
1
. . .
. . .
. . .
Disk Retrieval
New stream arrives
during round i.
Retrieval for new stream
starts at current round i.
Figure 4.2
Early-Admission Scheduling in soft scheduling
simplify notations, let
f
seek
(
k
),
k
1, be the seek function that includes both
seek time and fixed overhead. Let there be
u
existing streams (i.e., retrieving
u
data blocks per
round) when the new request arrives. Let
t
new
be the time the new request arrives and
t
due
be
the latest time when the current service round must end.
Suppose the disk is retrieving data block for stream
=
1
,
2
,...,
N
−
when the new request arrives and the
data block for the new request is located in the scanning direction of the disk head, i.e., the
track number of the data block for stream
u
w
+
1 is equal to or larger than the track number of
data block for stream
. In this case, we can simply insert the new data block into the list of
remaining data blocks to be retrieved, sort it by their track number
w
{
v
w
,v
w
+
1
,...,v
u
+
1
}
, and
then compute the residual service time, denoted by
, to complete the service round:
f
seek
(
u
Q
r
j
+
1
+
t
j
+
1
latency
=
v
j
+
1
−
v
j
)
+
j
=
w
(4.13)
+
f
seek
(
N
−
v
u
+
1
)
+
t
residual
where the first summation term is the service time to retrieve the remaining data blocks; the
second term is the head-repositioning time; and the last term is the time to complete retrieving
the current data block
.
In the worst case equation (4.13) is bounded by
w
f
seek
(
W
−
1
u
Q
r
j
+
1
+
max
{} =
v
j
+
1
−
v
j
)
+
j
=
w
−
1
(4.14)
+
f
seek
(
N
−
v
u
+
1
)
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