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The threshold value can be used as a knob to adjust the balance between
scalability and viewing quality in P2Cast. As illustrated in Section
4, a larger threshold in P2Cast usually leads to the admission
of more clients. However, a smaller threshold would help to provide better
quality of the played out video  it is more likely that clients get continuous
playback without a glitch.
A smaller threshold makes the patch size
smaller, thus the patch disruption is less likely.
Furthermore, a small threshold reduces the number of clients
in a session. Hence the probability that the clients' base stream gets
disrupted decreases. For instance,
Fig. 17 depicts the
probability that the base stream
encounters at least one disruption during the playback if the base
tree is a balanced binary tree. We assume that a node can leave with
probability , and a departure will affect all its descendant nodes. We
note that the curve is concave and the probability decreases as the number of
nodes decreases.
In the extreme, when the threshold is zero, the P2Cast reverts to the
unicast service model, where clients' early departures do not affect
each other and
the continuous playback is guaranteed
once a client is admitted. Therefore the threshold in P2Cast gives the
service provider a knob to adjust the balance between the scalability
and the clients' viewing quality.
Figure 17:
Probability that the base stream
encounters at least one disruption during the playback (balanced binary tree).

We also examine the probability that a client is forced to stop in the
middle of video playback due to some other clients' early departure. This
happens when a client cannot successfully recover from the disruption.
For instance, a disrupted client cannot rejoin the base
tree successfully.
Fig. 18 depicts the probability of such forced
early departure vs. clients' departure probability, ,
with the threshold equal to 10% of the video
length and the arrival rate set to be 1 arrival/min. Although this probability
increases along , overall the probability
of forced early departure is
small. Intuitively, although early departures disrupt other
clients, their used bandwidth is released. Thus it is likely that
disrupted clients can rejoin the base tree and find a new parent node.
Figure 18:
Probability of forced early departure due to disruption.

Next: Related Work
Up: Failure Recovery  Providing
Previous: Disruption effect on continuous
Yang Guo
20030327