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caching media segments [D
6
,D
7
] from the R-stream
S
a
. Note that the client also continues
to receive media segments [D
3
,D
5
] from the P-stream
S
b
. Finally, in Phase 3 the remaining
P-stream
S
b
is released and the client simply continues playback using cached data and data
received from the R-stream
S
a
.
This transition patching technique differs from simple patching in two aspects. First, the P-
stream
S
c
allocated for client
r
c
is occupied for a duration of (
t
c
−
t
b
) seconds, which is shorter
than the duration when simple patching is used, i.e., (
t
c
−
t
a
) seconds. Second, the P-stream
S
b
is extended from (
t
b
−
t
b
) seconds to support client
r
c
. This stream
is called a
transition stream
(T-stream) [11]. Thus, the net gain in resource reduction is equal
to (((
t
c
−
t
a
) seconds to (2
t
c
−
t
a
−
t
a
.
For example, suppose
L
,
t
a
,
t
b
and
t
c
equal to 7200, 0, 200 and 250 seconds respectively.
Then the costs of supporting
r
a
,
r
b
and
r
c
are 7200
R
, 200
R
and 150
R
respectively, representing
resource savings of 97.22% and 97.92% for clients
r
b
and
r
c
.
t
a
)
−
(
t
c
−
t
b
))
−
((2
t
c
−
t
a
−
t
b
)
−
(
t
b
−
t
a
)))
=
3
t
b
−
2
t
c
−
17.3.2 Recursive Patching
In transition patching we allow a client to share data from an existing patching stream in
addition to a full stream. If there are multiple on-going patching streams it is possible to
further reduce resource consumption by allowing the client to share data from more than one
patching streams -
recursive patching
. Figure 17.7 illustrates the recursive patching technique
using a fourth client
r
d
which arrives at the system at time
t
d
in addition to the three clients
r
a
,
r
b
, and
r
c
considered in Figure 17.6. To facilitate discussion, we divide the whole media
stream into 6 segments denoted by D
1
to D
6
.
As client
r
d
has already missed the initial (
t
d
−
t
a
) seconds of the media stream, the cost
of serving this client using simple patching will be equal to (
t
d
−
t
a
)
R
bytes. If we apply
transition patching by sharing data from the patching stream
S
b
then the cost will become
(3
t
d
−
t
b
)
R
bytes.
Now consider the use of recursive patching, which in this case is divided into four phases as
shown in Figure 17.7. In Phase 1, the client caches media segment D
2
from
S
c
while playing
2
t
c
−
t
a
t
b
t
c
t
d
Full Stream -
S
a
Patching Stream -
S
b
Patching Stream -
S
c
Patching Stream -
S
d
D
1
D
2
D
3
D
4
D
5
D
6
D
1
D
2
D
3
D
4
D
5
D
1
D
2
D
3
D
1
Client
r
d
's
reception -
r
d
schedule
D
6
D
4
D
5
D
2
D
3
D
1
Phase 1
Phase
2
Phase
3
Phase
4
Client
r
d
's
playback -
r
d
schedule
D
1
D
2
D
3
D
4
D
5
D
6
t
d
-
t
c
2
t
d
-
t
c
-
t
b
2
t
d
-
t
b
-
t
a
Figure 17.7
Operation of 4-phase recursive patching
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