Threshold adjustment - balancing the scalability and viewing quality

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 $P_d$, 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, $P_d$, 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 $P_d$, 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.