1. A Dynamic Caching Algorithm Based on Internal Popularity Distribution 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.)

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 largestWAR will 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 different ways. 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 the internal 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 to the constraint g(p1,..., pN) ≤ g(p ∗ (λ)) If we can find a value of λ such that the corresponding p ∗ (λ) has the 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