# Cooperative Buffering Schemes for Time-Shifted Live Streaming of Distributed Appliances
## 4 Experimental Results
### Playback Continuity  
First of all, we can see from Figures 6-8 that our proposed buffering schemes can substantially extend effective time-shifting hours compared with when PVRs buffer the same broadcast programs independently of each other. In Figure 6, each independent PVR can store only the parts of the programs corresponding to 450 s, whereas our buffering schemes extend effective time-shifting hours whose playback continuities are over 90% to 7.4, 6.8, 4.5, and 3.2 h for the \(R\_RC\)-based scheme and the \(D\_DP\)-based scheme with \(w\) values of 0.1, 0.5, and 0.9, respectively. This significant improvement is possible because PVRs playing back at the live broadcast time work together to buffer for each other's time-shifting. It is also evident that, as we use the larger buffer, we can obtain more time-shifting hours. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Default Value** \\ \hline Number of participating PVRs & 1200 \\ Backbone network bandwidth & 10 Gbps \\ Bandwidth between router and PVR & 100 Mbps: 10\% \\  & 50 Mbps: 50\% \\  & 20 Mbps: 20\% \\  & 10 Mbps: 20\% \\ Maximum number of neighbor PVRs & 6 \\ \(MIN_{nb}\) & 4 \\ Average inter-arrival and inter-leaving rate & 3400 s \\ Video playback rate & 720 Kbps \\ Number of chunks per second & 3 \\ Chunk size & 30 KB \\ Buffer size in seconds & 150 \\ Number of buffered chunks required for initial playback & 45 chunks (15 s) \\ Simulation duration & 36,000 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 5: Three types of playback request distributions according to the concentration degree around the live broadcast time. Figure 6-8 show the playback continuity of the \(R\_RC\)-based scheme and the \(D\_DP\)-based scheme with \(w\) values of 0.1, 0.5, and 0.9 while changing the buffer size to 150, 300, and 450 s in _distribution 1_. We can see that the playback continuity of the \(R\_RC\)-based scheme is higher than the \(D\_DP\)-based scheme with all \(w\) values in all buffer sizes. When the buffer size is 300 s, the average playback continuity of the \(R\_RC\)-based scheme for  
Figure 8: Comparison of playback requests between \(D\_DP\) and \(R\_RP\) in _distribution 1_ with a 150 s buffer. Figure 6: Comparison of playback requests between \(D\_DP\) and \(R\_RP\) in _distribution 1_ with a 450 s buffer. Figure 7: Comparison of playback requests between \(D\_DP\) and \(R\_RP\) in _distribution 1_ with a 300 s buffer. 16 time-shifting hours is 84.1%, whereas those of the _D_DP_-based scheme with \(w\) values of 0.1, 0.5, and 0.9 are 81.1%, 72.9%, and 51.2%, respectively. In particular, when the buffer size is 300 s, the average playback continuity of the _R_RC_-based scheme for the first two time-shifting hours is 95.6%, while that of the _D_DP_-based scheme with \(w\) values of 0.9 is 70.0%, which indicates a 25.6% performance difference. The reason for this is that the _R_RC_-based scheme can adjust the number of chunk copies required immediately more accurately by evaluating the number of actual requests. It can be also seen that the playback continuity in all the schemes improves as the buffer size increases. The average playback continuity of the _R_RC_-based scheme with buffer sizes of 450 s and 150 s for 10 time-shifting hours is 91.5% and 78.1%, respectively, which is a 13.4% improvement. The difference in the _D_DP_-based scheme with the \(w\) value of 0.9 between two buffer sizes is 49.7%. It is obvious that more chunks can be shared among PVRs with larger buffers since a larger buffer can accommodate more chunks. We can also see that the performance degrades as playback positions go further from the live broadcast time. The playback continuities of the _R_RC_-based scheme with a buffer size of 300 s are 95.6% and 68.0% at the 2 nd and 15 th hour positions after the live broadcast time, respectively. The reason for this is that the number of playback requests decreases due to the reduced popularity as the playback position becomes further away from the live broadcast time.