A Concurrent-Push Parallel Server Architecture - Scalable Continuous Media Streaming Systems - page 185

Hence the disk will retrieve N S stripe units in a single transaction. Note that the client continues
to consume video data in blocks of Q bytes and hence the video-block consumption model
in Section 10.3.2 remains valid. However, a video block now contains stripe units transmitted
from all N S servers (Figure 10.6) rather than from a single server as in the original algorithm.
Consequently, the client buffer size Y and Z no longer need to be multiples of N S .
Sub-schedule striping requires no modification to the server as the transaction size remains
the same. Therefore, the server buffer requirement, as well as scheduling delay are the same
as before.
To model the effect on the client buffer requirement, we note that a Q -bytes video block
comprises fragments from all N S servers. Hence, the filling time for a video block would be
affected by the transmission jitter among servers. Specifically, the filling time for video block
i of a video stream started at time t 0 is bounded by
( i

f − ≤ ≤ ( i f + + τ

+ 1) T avg + t 0 + f ( i ) + 1) T avg + t 0 + (10.41)

Using similar derivations, the client buffers needed to prevent underflow and overflow can
be found to be:

f + −

f − − T E + τ

Y > 1 + (10.42)

T avg

f + −

f − +

T L + τ

Z > 1 + (10.43)

T avg

and the time to prefill the first Y client buffers is

f + + τ D P = YT avg + (10.44)

Now both the client buffer requirement and prefill delay no longer depend on the number of
servers in the system.

10.6 Performance Evaluation
In this section, we evaluate the performance of the parallel video server architecture studied in
this chapter using numerical results. Table 10.1 lists the values for the key system parameters
used in the calculation. The parameters T E and T L are determined empirically by collecting
the video block consumption times of a hardware MPEG-1 decoder.

10.6.1 Server Buffer Requirement
Figure 10.7a plots the per-server buffer requirement versus the number of servers in the system.
We can observe that AGSS substantially reduces the buffer requirement. Sub-schedule striping
has no effect on the server buffer requirement. Despite the reduction achieved by AGSS, the
server buffer requirement still increases with the number of servers. This poses one limitation
on the ultimate scalability of the system (to be discussed in Section 10.6.4). Depending on