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that the maximum clock jitter between any two servers in the system is bounded and is denoted
by
. For simplicity, we ignore network delay jitter in this study. Assuming that network delay
jitter is bounded (which is true in ATM networks with QoS guarantees), it is easy to see that
the effect of network delay jitter can be incorporated into our performance model in the same
way as clock jitter, and the same derivations are still valid.
In the following sections, we derive three key performance metrics for evaluating the parallel
video server architecture, namely, server buffer requirement, client buffer requirement, and
system response time.
τ
10.3.1 Server Scheduling
Under concurrent push, the client will be receiving
N
S
video blocks simultaneously at an
aggregate rate of
R
V
. The average filling time, defined as the time to completely transmit a
video block of
Q
bytes, is given by
N
S
Q
R
V
T
F
=
(10.1)
On the other hand, each server will be serving at most
N
S
concurrent video sessions.
Under the SCAN disk scheduler,
N
S
video blocks will be retrieved in each service round
for transmission at a rate of
R
V
/
N
S
per video stream. Hence the duration of a service round is
equal to
T
F
in equation (10.1) and two buffers are needed for each video stream for a total of
2
N
S
Q
bytes buffers at each server.
As server clocks are not synchronous, the service round of the servers may not be aligned
(see Figure 10.3). Without loss of generality, we assume a video title is striped with block
zero storing at server zero. Let
T
i
,
j
be the time server
i
(0
≤
i
<
N
S
) starts transmitting the
(
jN
S
+
i
)th block of a video stream. Then we can formally define
transmission jitter
as:
max
T
i
,
j
−
T
k
,
j
|∀
j
δ
=
i
,
k
,
(10.2)
It may appear that the maximum clock jitter
also bounds the transmission jitter. However, it
turns out that the transmission jitter not only depends on the clock jitter, but also depends on
the arrival time of a new video session request as depicted in Figure 10-4. We derive the upper
bound for the transmission jitter in Theorem 10.1:
τ
. . .
Transmission
Server 0
. . .
Retrieval
. . .
Transmission
Server 1
. . .
Retrieval
δ
Figure 10.3
Service round misalignment between different servers
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