Information Technology Reference
In-Depth Information
Add
S
(
T
i
−
1
)
T
i
−
1
to both sides and we obtain:
S
(
T
i
)
T
i
+
1
−
S
(
T
i
−
1
)
T
i
+
1
−
S
(
T
i
)
T
i
−
1
−
S
(
T
i
−
1
)
T
i
−
1
<
S
(
T
i
+
1
)
T
i
−
S
(
T
i
+
1
)
T
i
−
1
−
S
(
T
i
−
1
)
T
i
−
S
(
T
i
−
1
)
T
i
−
1
(7.33)
Then factorize equation (7.33) to get:
[
S
(
T
i
)
−
S
(
T
i
−
1
)](
T
i
+
1
−
T
i
−
1
)
<
[
S
(
T
i
+
1
)
−
S
(
T
i
−
1
)](
T
i
−
T
i
−
1
)
(7.34)
which is equivalent to
S
(
T
i
)
−
S
(
T
i
−
1
)
S
(
T
i
+
1
)
−
S
(
T
i
−
1
)
r
<
=
(7.35)
T
i
−
T
i
−
1
T
i
+
1
−
T
i
−
1
Since the transmission schedule coincides with the data consumption curve at bit-rate re-
duction points, i.e.,
S
(
T
i
)
=
A
(
T
i
) for all
i
,wehave
A
(
T
i
)
−
A
(
T
i
−
1
)
A
(
T
i
+
1
)
−
A
(
T
i
−
1
)
<
(7.36)
T
i
−
T
i
−
1
T
i
+
1
−
T
i
−
1
Now according to the MDR scheduler (cf. equation (7.6)):
max
A
(
t
)
∀
T
i
−
1
−
A
(
T
i
−
1
)
r
i
=
t
>
(7.37)
t
−
T
i
−
1
From equation (7.36), we must have
r
i
equal to
−
A
(
T
i
+
1
)
A
(
T
i
−
1
)
r
i
=
(7.38)
T
i
+
1
−
T
i
−
1
which violates the definition of
r
i
. This contradicts the assumption that the schedule
S
(
t
)is
generated by the MDR scheduler and therefore the schedule with increasing rates cannot be
generated by the MDR scheduler and the result follows.
References
[1] T.V. Lakshman, A. Ortega, and A.R. Reibman, VBR Video: Tradeoffs and Potentials,
Proceedings of the IEEE
,
vol. 86, no. 5, May 1998, pp. 952-973.
[2] J. McManus and K. Ross, Video on Demand over ATM: Constant-Rate Transmission and Transport,
Proceedings
of IEEE INFOCOM
, Mar. 1996, pp. 1357-1362.
[3] W. Feng and S. Sechrest, Critical Bandwidth Allocation for the Delivery of Compressed Video,
Computer
Communications
, vol. 18, no. 10, Oct. 1995, pp. 709-717.
[4] W. Feng, F. Jahanian, and S. Sechrest, Optimal Buffering for the Delivery of Compressed Prerecorded Video,
ACM Multimedia Systems Journal
, Sep. 1997, pp.
[5] W. Feng, Rate-constrained Bandwidth Smoothing for the Delivery of Stored Video,
Proceedings of SPIE Multi-
media Networking and Computing
, Feb. 1997, pp. 58-66.
[6] W. Feng, Time Constrained Bandwidth Smoothing for Interactive Video-on-Demand Systems,
Proceedings of
International Conference on Computer Communications
, Nov. 1997, pp. 291-302.
[7] R.I. Chang, M.C. Chen, J.M. Ho, andM.T. Ko, Designing the ON-OFFCBRTransmission Schedule for Jitter-free
VBR Media Playback in Real-time Networks,
Proceedings of the Fourth International Workshop on Real-Time
Computing Systems and Applications
, Oct. 1997, pp. 2-9.
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