Information Technology Reference
In-Depth Information
L
Overflow Limit,
B
(
t
)
Cumulative Data
Consumption Function,
A
(
t
)
Transmission
Schedule,
S
(
t
)
Client Buffer Size
Time
Figure 7.1
A feasible piecewise-smooth transmission schedule for VBR video delivery
The principle of smoothing is
work-ahead
, i.e., by transmitting data at a bit-rate higher than the
playback bit-rate during periods of lower playback rates. Excess video data are then buffered at
the client side so that the transmission bit-rate can be reduced during periods of high playback
rates by consuming video data from the buffer for playback. Note that smoothing not only
reduces bit-rate variations, but also reduces the peak data rate as well.
Let
A
(
t
) be the cumulative data consumption function for a video (see Figure 7.1), defined
as the amount of data that needs to be accumulated at the client for playback
t
seconds after
playback starts. Let
S
(
t
) be the transmission schedule for the video, defined as the amount of
data transmitted to the client
t
seconds after playback starts. Ignoring network delay, processing
delay, and interactive playback controls, it is clear that a feasible transmission schedule must
not be lower than
A
(
t
) for all
t
so that the client will not run out of video data during playback:
S
(
t
)
≥
A
(
t
)
(7.1)
On the other hand, if the client buffer size is limited to, say,
b
bytes, then the transmission
schedule cannot be too aggressive either, or else client buffer overflow will occur. This buffer
constraint can be represented by a function
B
(
t
) defined as
B
(
t
)
=
A
(
t
)
+
b
(7.2)
and thus to prevent buffer overflow we must ensure that
S
(
t
)
≤
B
(
t
)
(7.3)
Together, the two curves
A
(
t
) and
B
(
t
) define the feasible region for all feasible transmission
schedules:
B
(
t
)
≥
S
(
t
)
≥
A
(
t
)
(7.4)
Clearly, there is an infinite number of feasible transmission schedules than can fit within
the feasible region. Thus, one can pick a transmission schedule to optimize various measures
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