A Hybrid Architecture - Scalable Continuous Media Streaming Systems - page 344

where M 2 ( ) is the expected number of Type-2 requests in an admission cycle and can be

computed from

δ

M 2 ( δ ) = W C ( δ ) λ D (19.16)

19.3.3 Admission Threshold
In the previous derivations, we have assumed that the admission threshold value is given a pri-
ori . Consequently, the resultant average waiting time for statically-admitted and dynamically-
admitted users may differ. To maintain a uniform average waiting time for both cases, we can
adjust the admission threshold so that the average waiting time difference is within a small
error

ε :

δ = min { x | ( W S ( x ) − W D ( x )) ≤ ε, T R ≥ x ≥ 0 } (19.17)

As adjusting the admission threshold does not affect existing users, the adjustment can
be done dynamically while the system is online. In particular, the system can maintain a
moving average of previous users' waiting time as the reference for threshold adjustment. This
enables the system to maintain a uniform average waiting time for both statically-admitted and
dynamically-admitted users. The term latency in this chapter refers to this uniform average
waiting time.

19.3.4 Channel Partitioning
An important configuration parameter in SS-VoD is the partitioning of available channels for
use as dynamic and static multicast channels. Intuitively, having too many dynamic multicast
channels will increase the traffic intensity at the dynamic multicast channels due to increases in
the service time (cf. equations (19.1) and (19.12)). On the other hand, having too few dynamic
multicast channels may also result in higher load at the dynamic multicast channels. We can
find the optimal channel partitioning policy by enumerating all possibilities, which in this case
is O( N ). Unlike the related Unified Video-on-Demand (UVoD) architecture [3], where the
optimal channel partition policy is arrival-rate dependent, we found that the optimal channel
partitioning policy is relatively independent of the user arrival rate in SS-VoD. This will be
studied in more detail in Section 19.4.2.

19.4 Performance Evaluation
In this section, we present simulation and numerical results to evaluate performance of the
SS-VoD architecture. We first validate the analytical performance model using simulation
results and then proceed to investigate the effect of the channel partitioning policy, to com-
pare latency and channel requirement between TVoD, NVoD, UVoD [3], with SS-VoD, and
finally investigate the performance of SS-VoD under extremely light loads. The focus of the
comparisons is on the server and backbone network resource requirements, represented by
the number of channels required to satisfy a given performance metric such as latency. Note
that for simplicity, we do not distinguish between unicast and multicast channels and assume
they have the same cost. In practice, a multicast channel will incur higher costs in the access