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Server 0
Server 1
δ
Disk Read
New Request
Transmission
Server 0
Server 1
δ
New Request
Figure 10.4 Transmission jitter depends on both clock jitter and request arrival time
Theorem 10.1. Assume that new-session requests arrive at all servers at the same time, then
the transmission jitter is bounded by
δ
T F
(10.3)
Proof. Please refer to the Appendix.
This bound on transmission jitter will be used to derive the amount of buffer required at the
client to prevent buffer underflow and overflow respectively.
10.3.2 Video Block Consumption Model
Many studies on VoD systems assume that video data are consumed periodically by the video
decoder. However, our experience in programming some off-the-shelf hardware and soft-
ware video decoders reveals that the decoder consumes fixed-size data blocks only quasi-
periodically.
Given the average video data rate, R V , and block size, Q , the average time for a video
decoder to consume a single block is
Q
R V
T avg =
(10.4)
To quantify the randomness of video block consumption time, we first define a few notations.
Definition 10.1. (a) Let T i be the time the video decoder start decoding the ith video block,
then the decoding-time deviation of video block i is defined as
T DV ( i )
=
T i
iT avg
T 0
(10.5)
and decoding is late if T DV (i)
>
0 and early if T DV ( i )
<
0
.
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