Streaming Variable Bit-Rate Media Streams - Scalable Continuous Media Streaming Systems - page 134

7.5.3 Performance Evaluation
We evaluate the AMDR scheduler's performance in this section using simulation. The sim-
ulation set-up is identical to the one in Section 7.4 except for two differences: (a) the MDR
scheduler is replaced by the AMDR scheduler; and (b) the client buffer size is fixed.
Table 7.2 shows the admission complexity for theAMDR scheduler and theOptimal Smooth-
ing scheduler. Comparing the results with those in Table 7.1, we observe that the AMDR sched-
uler requires more computations than the MDR scheduler. This is because we have set a client
buffer size constraint of 32 MB for the AMDR scheduler and consequently a proportion of the
videos are scheduled using the Optimal Smoothing scheduler, which requires more admission
computations. Nevertheless, the resultant admission complexity is still less than the Optimal
Smoothing scheduler for both successful and unsuccessful admissions.
Next we investigate the impact on the client waiting time. Figure 7.7 plots the mean and
worst-case client waiting times versus client buffer size for a system utilization of 90%. We
also simulated lower system utilization settings of 60% to 80% but both schedulers perform
nearly identically and so the results are not shown here. From Figure 7.7, we observe that with
smaller buffer sizes, both AMDR and Optimal Smoothing achieve similar waiting time. At
larger buffer sizes, AMDR slightly outperforms Optimal Smoothing and ultimately converges
to the MDR curve that has no buffer size constraint. The performance difference between
AMDR and Optimal Smoothing is due to the fact that MDR schedules are more aggressive at
the beginning of the video stream, where the transmission bit-rate is highest. This results in
more work-ahead as compared to Optimal Smoothing and thus the MDR scheduler is able to
utilize any unused bandwidth to reduce the bit-rate requirements down the road.
As the AMDR scheduler over-allocates bandwidth to maintain a MDR schedule, it may
become less efficient when the system capacity is small. To investigate this issue, we repeat

Table 7.2 Comparison of admission complexity between the Optimal Smoothing and the AMDR
schedulers (client buffer size fixed at 32MB)

Unsuccessfull Admission # Successfull Admission

Scheduler Comparisons Additions Comparisons Additions

Temporal smoothing
complexity at ρ = 0 . 6 ∗ 0.00 (0.00) 0.00 (0.00) 5782.52 5782.52

complexity at ρ = 0 . 7 ∗ 0.01 (0.00) 0.01 (0.00) 5782.20 5782.20

complexity at ρ = 0 . 8 ∗ 4.15 (0.20) 4.15 (0.20) 5782.04 5782.04

complexity at ρ = 0 . 9 ∗ 74.00 (5.15) 74.00 (5.15) 5782.08 5782.08

AMDR scheduler
complexity at ρ = 0 . 6 ∗

0.00 (0.00) 0.00 (0.00) 5008.15 5781.70

complexity at ρ = 0 . 7 ∗ 0.00 (0.00) 0.00 (0.00) 5007.47 5781.38

complexity at ρ = 0 . 8 ∗

0.20 (0.20) 0.20 (0.20) 5007.15 5781.22

complexity at ρ = 0 . 9 ∗ 5.19 (5.17) 5.19 (5.17) 5007.08 5781.26

Notes : *Numerical results are measured as the average number of computations required to admit a
client at a given average network utilization ( ρ ), averaged over requests for all 274 videos.
# Numbers in parentheses are the average number of unsuccessful admission tests performed for each
request.