Information Technology Reference
In-Depth Information
Assume
X
(
t
) has lower buffer requirement than the MDR transmission schedule
S
(
t
), then
∃
t
0
such that
S
(
t
0
)
>
X
(
t
0
)
≥
A
(
t
0
)
(7.20)
We know that
S
(
t
) must coincide
A
(
t
) at the bit-rate reduction points, i.e.,
S
(
T
i
)
=
A
(
T
i
)
,
for
i
=
1
,
2
,...,
n
(7.21)
where
n
is the number of bit-rate reduction points. Now
X
(
t
) cannot be lower than
S
(
t
) at the
bit-rate reduction points
{
T
i
|
i
=
0
,
1
,
2
...
n
}
. This implies that the
t
0
in equation (7.20)
cannot be the bit-rate reduction points:
t
0
=
T
i
,
for
i
=
1
,
2
,...,
n
(7.22)
However, as
S
(
t
) is constructed with straight lines connecting the bit-rate reduction points,
X
(
t
) cannot be lower than
S
(
t
) in between two consecutive bit-rate reduction points either:
t
0
∈
(
T
i
−
1
,
T
i
)
,
for
i
=
2
,
3
,...,
n
(7.23)
Otherwise
X
(
t
) will be convex in the range (
T
i
−
1
,
T
i
), which contradicts with the assumption
that
X
(
t
) has monotonic decreasing rates. From equations (7.21) and (7.22), we conclude that
t
0
does not exist and the result follows.
7.4 Performance Evaluation
We evaluate performance of the MDR scheduler and compare it to Optimal Smoothing [1] in
this section. To obtain realistic performance results, we collected the video bit-rate traces of
274 different videos from DVD movies for simulation. These are full-length (average 5,781
seconds long and 4,348 MB in size), MPEG-2 encoded videos with an average bit-rate of
6.02 Mbps. The bit-rate varies from below 0.5 Mbps to over 18 Mbps. Long-range (minutes to
tens of minutes) bit-rate variations are common in these real-world MPEG-2 encoded videos.
We implemented the MDR scheduler presented in Section 7.3.1 in software and used it to
compute the transmission schedule for the videos.We also implemented theOptimal Smoothing
algorithm [1] for comparison purposes. The generated transmission schedules are then fed into
a simulator developed using CNCL [16] to obtain simulation results.
The simulationmodel consists of a systemwith clients connecting through a 1Gbps backbone
network to a server storing the 274 VBR videos. We assume that the backbone network is the
bottleneck of the system. For simplicity, we ignore delay and loss in the network. New stream
requests are generated according to a Poisson process with various mean inter-arrival times
to simulate different system utilization. A new stream request randomly selects a video from
the 274-video collection with uniform probability. Note that we adopt the uniform popularity
instead of the Zipf popularity model [17] because the video titles have varying bandwidth
requirements and lengths. Consequently, using the Zipf popularity will result in large variations
in the simulation results, depending on which of the video titles happened to be picked as the
hot titles. To obtain more consistent results for comparison, we therefore adopt the uniform
popularity model.
Search WWH ::
Custom Search