# Cooperative Buffering Schemes for Time-Shifted Live Streaming of Distributed Appliances
## 4 Experimental Results
### Playback Continuity
Thus, it is more likely that the number of neighbor PVRs at the position cannot be greater than \(MIN_{nb}\). It is also evident from Figures 6-8 that the performance can become even worse with smaller buffer sizes due to lack of available chunks required for playback. It is noted that the playback continuity of the _D_DP_-based scheme increases as the \(w\) value decreases. When the buffer size is 150 s, the average playback continuity of the _D_DP_-based scheme with \(w\) values of 0.1 and 0.9 for the first 10 time-shifting hours is 75.4% and 30.6%, respectively. This considerable difference is caused by the fact that the proximity degree from the live broadcast time, i.e., \(PD_{tr_{(j)}}\), is more weighted in Equation (4) as the \(w\) value decreases. Thus, the smallest \(w\) value is best adjusted to the _distribution 1_, whose concentration degree around the live broadcast time is highest in these simulations. On the other hand, Figures 8-10 demonstrate that the performance of the _D_DP_-based scheme is significantly affected by the \(w\) value selected according to the types of playback request distributions. When the \(w\) value is 0.9 in _distribution 1_, 2 and 3, the average playback continuity for the first 16 h is 19.6%, 57.9%, and 75.1%, respectively. This substantial difference is because, as the \(w\) value becomes smaller, the chunks closer to the live broadcast time are more buffered. Thus, when the \(w\) value is 0.9 in _distribution 1_, the _D_DP_-based scheme determines the target time range mainly based on the deficiency degree, reflecting only 10% proportion in the proximity degree even though most of playback requests are concentrated around the live broadcast time. As a result, the average playback continuity is only 19.6% with a \(w\) value of 0.9. On the contrary, when using _distribution 3_, where playback requests are most evenly distributed over time among three types of distributions, the average playback continuity with a \(w\) value of 0.9 is 75.1%, which is almost the same as those with other \(w\) values and the _D_DP_-based scheme. It is noted that the performance of the _R_RC_-based scheme is not significantly affected by the types of playback request distributions. In particular, the difference in the average playback continuity for 16 h between the _distributions 1_ and 2 is only 0.7%. The reason for this is that the _R_RC_-based scheme determines the target time range based on the number of actual requests regardless of how high the request concentration degree is around the live broadcast time. Figure 11 shows the experimental results when the number of participating PVRs is 2400 with the buffer size of 150 s. This experiment doubles the number of PVRs and halves the buffer size compared to the experiment shown in Figure 7. Note that the experimental results from Figures 7 and 11 show a similar performance. This is because a similar data duplication degree can be maintained at most playback positions since the doubled PVRs can compensate for the half-sized buffer. Note that the experiments with the smaller \(w\) values show better performance in all types of distributions. This is because the tendency to watch TV around the live broadcast time is reflected in all types of distributions, even if the concentration degree around that time may differ depending on the types of playback request distributions. Figure 11: Comparison of playback requests between \(D\_DP\) and \(R\_RP\) in _distribution 1_ with a 150 s buffer when the number of PVRs is 2400. Figure 9: Comparison of playback requests between \(D\_DP\) and \(R\_RP\) in _distribution 2_ with a 150 s buffer.