A Dynamic Caching Algorithm Based on Internal Popularity Distribution of Streaming Media

1. A Dynamic Caching Algorithm Based on Internal PopularityDistribution of Streaming Media 資料來源:Multimedia Systems (2006) 12:135–149 DOI 10.1007/s00530-006-0045-x 作 者:Jiang Yu , Chun Tung Chou , ZongKai Yang , Xu Du ,Tai Wang 指導老師:游象甫 教授 學 生:梁凱鈞 學 號:109832008 日 期:98/09/15

2. Outline • Introduction • Internal Popularity Based Caching Algorithm • Methodology and Comparison • Conclusions and Future Work

3. Introduction • Most caching algorithms • Divide the video into segments • The caching unit is video segment rather than the entire video. • In order to make a caching decision, these schemes collect statistics on the access frequencies of the video segments. • But it cost too much memory space to record all segments of a video.

4. Introduction (cont.) • We address the following two questions. • Can the internal popularity of streaming videos be described by some parametric statistical distribution? • If such statistical distribution can be found, how can we exploit that for caching? • Observations • The internal popularity of the majority of the most popular videos obeys a k-transformed Zipf-like distribution. • The segment popularity versus segment sequence number is a straight line in the logarithm of the transformed variables.

5. Introduction (cont.) • This means that the popularity of all segments can be predicted by only knowing the state information of few points on this straight line. • We design internal-popularity-based (IPB) caching algorithm. • This algorithm will estimate the segment popularity based on an empirical model for segment popularity. • This algorithm requires only to store a small amount of segment popularity information.

6. Introduction (cont.)

7. Internal Popularity Based Caching Algorithm • Internal Popularity Analysis • IPB Caching Algorithm Design

8. Internal Popularity Analysis(cont.) • Let x denote video segment sequence number. • Let y denote the popularity of the segment.

9. Internal Popularity Analysis(cont.)

10. Internal Popularity Analysis(cont.)

11. IPB Caching Algorithm Design • It chooses the appropriate segments to cache to minimize the bandwidth consumption of backbone network. • Updating kx and ky dynamically • Recording and updating user access information • Window-based model in IPB caching algorithm • Updating the value of a and b • Finding the optimal popularity threshold

12. Updating kx and ky dynamically • Initially, both kx and ky are set to one. ( Here w is the weight for the R value of video i , and n denotes the number of videos. ) • In our algorithm, the (kx, ky) which achieves the largestWARwill be chosen in each update.

13. Recording and updating user access information • We will need to store some user access information. • We will choose some segments from each video for this purpose and call these chosen segments as record segments

14. Recording and updating user access information(cont.) • Let M denote the number of record segments. • Let L denote the total number of segments in a video. • The i-th record segment will be the j-th segment in the video.

15. Recording and updating user access information(cont.)

16. Window-based model in IPB caching algorithm • We introduce a window-based model in IPB caching algorithm for the purpose of forgetting the out-of-date information.

17. Window-based model in IPB caching algorithm(cont.) • Triggered Update • Periodic Update

18. Updating the value of a and b • The IPB caching algorithm will update a and b in differentways. • All the segments whose popularity is larger than or equal to the optimal popularity threshold will be cached. • The IPB algorithm will decide whether the model parameters of a and b of video i should be re-calculated.

19. Updating the value of a and b(cont.) • We calculate the goodness of fit of video i, denoted by Di. • If Di value is larger than or equal to 0.90, it means that the existing ai and bi can model theinternal popularity of video i well even under the video has received a new request.

21. Finding the optimal popularity threshold

22. Finding the optimal popularity threshold(cont.) • Each video segment uses r units of bandwidth • It requires s units of storage space

23. Finding the optimal popularity threshold(cont.) • Lagrange multiplier method • Let λ > 0 be the Lagrange multiplier • Consider the unconstrained optimization problem: • Let p∗(λ) be the optimalN-tuple (p1, p2, . . . pN) that maximizes (P2)

24. Finding the optimal popularity threshold(cont.) • Proved that p∗(λ) maximizes f (p1, . . . , pN) subjected tothe constraint g(p1, . . . , pN) ≤ g(p∗(λ)) • If we can find a value of λ such that the corresponding p∗(λ)hasthe property g(p∗(λ)) = C • Then p∗(λ) is the optimal solution to (P1)

25. Finding the optimal popularity threshold(cont.) • However, there may not exist p∗(λ) such that the equality g(p∗(λ)) = C holds • In order to solve (P1), we must search for a suitable value of λ. • The problem (P2) can be decomposed into N independent optimization problems, one for each value of pi (i = 1, . . . ,N)

26. Finding the optimal popularity threshold(cont.) • The optimal solution to the above problem is given by the highest index j such that yij*b−λs ≥ 0 • The quality λs/b will be referred to the optimal popularity threshold

27. Methodology and Comparison Compared with four caching algorithm Fine-grained caching algorithm Exponential caching algorithm Zipf-like caching algorithm IPB caching algorithm

28. Methodology and Comparison(cont.)

29. Conclusions and future work • The analysis and simulation results show that. • The internal popularity of the majority of the most popular streaming videos obeys a Zipf-like distribution after k-transformation • The internal popularity distribution based caching algorithm performs well in different conditions with little user access information