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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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