1. Provisioning Content Distribution Networks for Streaming Media Jussara M. Almeida Derek L. Eager Michael Ferris Mary K. Vernon University of Wisconsin-Madison University of Saskatchewan

2. Outline Problem statement and motivation CDN delivery protocols and cost models Key results: –unconstrained proxy servers –Cost-effectiveness of proxy servers –proxy servers with limited space and bandwidth Conclusions and on-going work

3. Problem: Media CDN Design Clients Internet Proxy Server Clients Proxy Server Origin Server Scalable streaming protocol: Bandwidth Skimming [EaVZ00] Each proxy can store a media prefix of size f, 0  f  1 Multicast Multicast or Unicast Goal: insight into value of f that minimizes delivery cost

4. Motivating Example #1 Example: 10 proxy servers, client request rate per proxy = 100 (total client request rate = 1000) cost tradeoff: 10  7  70 proxy streams vs. 12 origin streams bandwidth needed to serve each client immediately:

5. Motivating Example 2 1 proxy, N = 1000, proxy stores prefix of length 10% of file size  request rate to the proxy stored prefix = 100  7 proxy streams to deliver prefix and 5 origin streams for suffix 10% of proxy storage offloads 7/12 of server required bandwidth

6. Scalable Delivery Protocols BWSkim(b): –Proxy and origin use simple Bandwidth Skimming –b: client bandwidth (e.g., b=2 or b=1.2) BWSkim/U(b): –Proxy uses Bandwidth Skimming –Origin uses unicast to the proxy. BWSkim+Batch(b): –If 0  f  1: clients use one unit of bandwidth to batch together for a suffix stream from the origin

7. BWSkim(b): BWSkim(2): Streams Requested by Proxy A Clients B proxy (f,N,P,b) =  ln (1 + f N proxy /  ) B origin (f,N,P,b) =  ln(1+N origin /  ) where: Nproxy = N/P and Proxy B client stream f Prefix merges Suffix merges

8. BWSkim/U(b): BWSkim/U(2): Streams Requested by Proxy A Clients B proxy (f,N,P,b) =  ln (1 + f N proxy /  ) B origin (f,N,P,b) = P  ln(1+ N origin /  ) where: Nproxy = N/P and Proxy B client stream f Prefix merges Suffix merges

9. BWSkim+Batch(b): BWSkim+Batch(3): Streams Requested by Proxy A Clients f Prefix merges Suffix merges Proxy B client stream

10. BWSkim+Batch(b): B proxy =  ln (1 + f N proxy /  ) f  0.25: B origin = origin  (1-f)T where: origin = 1/(fT + 1/N) f  0.25: B origin = origin  (1-f)T + B origin,last_seg (f) where:

11. Delivery Cost Model Each object i: delivery cost i = B origin,i + P   B proxy,i P: number of proxy servers  : average cost of a proxy stream / average cost of one origin stream B origin,i and B proxy,i depend on: f i = fraction of media object i stored at the proxy N = total request rate (avg. # of client arrivals per playback duration) b = client bandwidth

12. Delivery Cost Model Each object i: delivery cost i = B origin,i + P   B proxy,i P: number of proxy servers  : average cost of a proxy stream / average cost of one origin stream B origin,i and B proxy,i depend on: f i = fraction of media object i stored at the proxy N = total request rate (avg. # of client arrivals per playback duration) b = client bandwidth Unconstrained proxy server: find f i that minimizes delivery cost i

13. Delivery Cost Model Each object i: delivery cost i = B origin,i + P   B proxy,i P: number of proxy servers  : average cost of a proxy stream / average cost of one origin stream B origin,i and B proxy,i depend on: f i = fraction of media object i stored at the proxy N = total request rate (avg. # of client arrivals per playback duration) b = client bandwidth Unconstrained proxy server: find f i that minimizes delivery cost i Constrained proxy server: min delivery cost i (n objects) subject to: f i  proxy disk space, B proxy,i  max. proxy bandwidth Mixed Integer Programming, solved using GAMS library {f i }

14. Cost Model Applications Configuring the CDN: –protocol delivery cost comparisons Batching vs. non-batching, Multicast origin vs. unicast origin Client bandwidth, b  2 vs b = 1.2. –proxy content (f) that minimizes delivery cost –Cost-effectiveness of proxy servers Analysis over a wide region of the design space

15. Proxy Servers with Unlimited Bandwidth and Storage Unicast Origin Multicast Origin

16. Protocol Cost Comparison (unconstrained proxies) BWSkim (2) is preferred unless P is large and N/P is very small BWSkim(2) vs BWSkim+Batch(3), each with optimal f: ( large system design space)

17. Optimal f: BWSkim(b) (unconstrained proxies) f=1 or f=0 is optimal Proxy servers are cost-effective (i.e., f=1) only if: Origin uses unicast or P=1 or proxy stream is free or costs a very small fraction of cost of an origin stream.   Multicast Origin, P=1 Unicast Origin, P  1 P=10 Multicast Origin P=100

18. Cache Content: BWSkim+Batch(b) (unconstrained proxies)  Multicast Origin: P=100 BWSkim+Batch[/U](3) outperforms BWSkim[/U](2) and the optimal content is prefix caching only if: –Multicast origin, –Large P (P  10), –Low N/P (N/P  1), –Intermediate values of  (  = 0.1).

19. Protocol Cost Comparison (unconstrained proxies) b=1.2 increases CDN cost by a factor of 1.5 – 3 BWSkim(1.2) compared to best policy with b  2: (P=10) 

20. Cost-Effectiveness of Proxy Servers Proxy servers cost-effective if the origin server uses unicast the file request rate is low cost of proxy stream is small fraction of cost of an origin stream Question: how small? Multicast origin, N  10: Answer:  ~1/P (or less)  = 0.1  = 1/P  = 5/P

21. Proxy Servers with Limited Disk Storage and Bandwidth  ~ 1/P (or less) or Unicast origin

22. Constrained Proxies: Key Parameters M: total client arrival rate, in arrivals per T (all files) P s : proxy storage capacity, as a fraction of all files P b : proxy bandwidth, as a fraction of bandwidth needed if proxy stores all files –P s and P b computed for modern disks, MPEG-2 streams (4 Mb/s) –Each disk: 44 hours of content and 42 concurrent streams –Vary M, number & length of files, file popularity skew, # disks: 0.08  P s  0.68, P b  0.02 –Distribute files across the disks to balance the load

23. Proxy Disk Space & Bandwidth Scenario: –1000 two-hour MPEG-2 (4 Mb/s) movies –1000 requests / hour at each proxy: M/P = 2000 –Zipf distribution of file popularities Average bandwidth needed for all files = 332 streams If proxy has 5 disks: –P s = = 0.11 P b = = 0.63

24. True Optimal (P b =0.32 (bw) Near Optimal (P b =0.32 )(bw) (b =2, P s =34%, M/P =1000, n =128, T =2h) Near Optimal Cache Content (contiguous set of full files) yields delivery cost within 0.05% of true optimal for all CDNs studied. Optimal Caching Policy for BWSkim/U(b) is full-file caching. Optimal vs. Near Optimal BWSkim(b) Proxy Content (unicast origin, constrained proxies)

25. Optimal Content for BWSkim (b) (unicast origin, constrained proxies) P b  1 P=10,  =0.1, (cap), M/P=100 P b  1 P=10,  =0.3, (cap), M/P=100 P b  1, P=100,  =0.1, (cap), M/P=100 P s = 34%, n=128, T=2h P b =0.32 P=10,  =0.1, (both), M/P=1000 Full file caching is the most cost-effective Less popular files are cached as either P b decreases or  or P increases. BWSkim/U(b) is more cost effective than BWSkim+Batch/U(b+1) BWSkim+Batch/U(b+1): prefix caching, cost improves up to 8%

26. (BWSkim/U(2), P b  1, P s =34%, n =128, T =2h) M/P = 1000 (unrealistic P b ) M/P = 100 (realistic P b ) Arbitrarily setting values for proxy bandwidth leads to unrealistic and non-optimal results Unrealistic Proxy Bandwidth Assumption (unicast origin, constrained proxies)

27. BWSkim/U(1.2) increases the delivery cost by up to a factor of three (same for unconstrained proxies) Cost Increase of BWSkim/U(1.2) (unicast origin, constrained proxies) Ratio of delivery cost for BWSkim/U(2) to cost of BWSkim/U(1.2)

28. Cost Increase of BWSkim(2) vs. BWSkim+Batch(3): BWSkim+Batch(3) and prefix caching is preferred only if: large P, moderately small P b a large number of the popular files have N/P  1 and cost of proxy stream is very small or zero In all other scenarios: BWSkim(b) + full file caching is optimal 0.13 11 0.32 11 Pb=Pb= BWSkim(2) vs. BWSkim+Batch(3) (multicast origin, constrained proxies)  = 0, P s =34%

29. Optimal Content for BWSkim+Batch(3) (multicast origin, constrained proxies) P b  1 P=10, (cap) P b =0.32 P=10, (bw) P b  1 P=100, (cap) P s =34%,  = 0 BWSkim+Batch(b) caches primarily prefix files. Less popular data is cached as either P b decreases or  or P increases.

30. Protocol Cost Comparison (constrained proxies) Cost Ratio for Origin Unicast vs. Origin Multicast: (  = 0) Multicast origin significantly reduces delivery cost unless - Total request rate per proxy, M/P, is small or P  1 60 64

31. Conclusions Scalable multicast delivery involves new cost trade-offs Simple delivery cost models can yield significant insight Insights: BWSkim(b) is preferred over BWSkim+Batch(b) unless - P is large and N/P is very small BWSkim+Batch(3) system: prefix caching is optimal BWSkim(b): f=0 or f=1; f=1 only if the origin server uses unicast the file request rate is low (N  1) cost of proxy stream is small, i.e.,  ~1/P (or less) Multicast origin greatly decreases CDN cost if M/P  10