1. Optimal Multicast Smoothing of Streaming Video Over the Internet Subhabrata Sen, Don Towsley, Zhi-Li Zhang, and Jayanta K. Dey IEEE J. Selected Areas in Communications, No. 7, Sept. 2002

2. Outline Single link smoothing Video multicast distribution tree model Optimal multicast smoothing Performance evaluation Conclusion

3. Basics Variable-bit-rate (VBR) Higher quality Combine video, audio, and text sources in a stream. Smoothing Reduce network requirements without degradation in video quality.

4. Overview Server Client Buffer Server Decoder Unsmoothed Smoothed

5. Single link smoothing model

6. Definitions w : startup delay b : playback buffer size Arrival vector A = (A 0, …, A N ) A N : The cumulative amount of data from the stream which has arrived at node 0 (root) by time k = 0, 1, …, N. A k ≥ A k-1, 1 ≤ k ≤ N. Client playback vector D = (D 0, …, D N ) D N : The cumulative amount of data from the stream that must be removed at leaf i by k = 0, 1, …, N. D k ≥ D k-1, 1 ≤ k ≤ N. Lower constraint L t = max{D t (w), A t – b 0 } Upper constraint U t = min{D t-1 (w) + b 1, A t }

7. Transmission schedules U L

8. Majorize X=[x 1, …, x n ] and Y=[y 1, …, y n ] Let x [1], …, x [n] and y [1], …, y [n] denote the nonincreasing orders of X and Y. X is said to be majorized (more smooth) by Y if Ex: [4 4 2] is majorized by [8 1 1]

9. Design of the algorithm Piecewise-CBR transmission schedule Policies Consider CBR transmission segments which are as long as possible. Change the rate as early as possible. The rate change is as small as possible.

10. Algorithm U L

11. Multicast smoothing

12. Multicast smoothing model leaves (clients)

13. Example L-size Buffer M-size Buffer S-size Buffer

14. Constraints Upper constraints Effective buffer overflow constraint Lower constraints

15. Configurations Videos Blues Brothers : mean rate = 1.48 Mb/s, peak rate = 44.5 Mb/s Space Jam: mean rate = 3.6 Mb/s, peak rate = 17.5 Mb/s Network topology A full 3-ary tree of depth 4. Internal nodes With identical buffer space. Client (leaves) The buffers are randomly selected from the set {0.512, 1, 2, 4, 8, 16, 32} MB. Only one leaf has 32 MB buffer. Only one leaf has 512 KB buffer. 32 MB buffer is large enough to smooth the video stream into a CBR stream.

16. Definitions SUM_MAX(i) : the sum of the worst case bandwidth allocation (based on the peak rate of the video stream) along each link on the entire path to the leaf i. SUM(i) : the sum of the peak rates of the smoothed transmission schedules along each link on the path from the source to the leaf i.

17. Bandwidth reservation Blues BrothersSpace Jam

18. Total bandwidth If internal buffers are small, the multicast smoothing algorithm can not perform well.

19. Conclusion A novel technique integrating workahead smoothing with application- level multicasting and temporal caching to efficiently stream VBR video from a server to multiple heterogeneous clients is developed. Their future work is to explore actual implementation issues.