A numerical example

1. A numerical example • Update frequency : 12

2. Simulation Setup • Inet topology generator, • http://topology.eecs.umich.edu/inet/ • Default n = 3037 • r(v) randomly generated in [0,100] • w : number of update operation • α : read-write ratio

3. Performance comparisons • Traffic reduction ratio • 3 algorithm: • Greedy • Optimal • random

4. Performance comparisons (R vs. k) • α = 0 • Difference between opt and greedy usually within 10% • R rises sharply at a small number of proxies • R does not change much as the access frequency changes.

5. Performance comparisons (Bell Lab) • Why different? • Traffic even or uneven

6. Performance comparisons (R vs. k ) • ρ (hit ratio) : fixed 40%

7. Performance comparisons (R vs. α) • ρ (hit ratio) : fixed 40%

8. Observation • Randomly placing the proxy just makes the things worse. • R increases sharply when k is small and becomes saturated when k reaches about 5. • Placing too many proxies would degenerate the system performance • If the update frequency is relatively high.

9. Performance comparisons ( R vs. ρ) • R improves significantly as ρ increases

10. Finding the optimal number of proxies • Depends on n, α and ρ • For the next 3 figures, 2 y-axis are used: • LHS : the optimal number of proxies required in the system (denoted by k) • RHS : the corresponding traffic reduction ratio (denoted by R)

11. The optimal number of proxies ( diff. n ) • ρ = 40% • α = 0.001 and 0.0001 • k-curve for α= 0.001 remains almost flat • The k-curve for α= 0.0001 shows a stable increase • Two R-curves are quite flat

12. The optimal number of proxies (diff. α) • ρ = 40% • the need of proxies drops dramatically as the update to the Web data frequency increases. • We could predict k-curve would eventually reach 0.

13. The optimal number of proxies (diff. ρ) • The k-curve and R-curve both show a stable increase of k as the hit-ratio increases • Placing more proxies should come together with the improvement of cache hit-ratio

14. Discussion • Stability of routing • If routes are stable, the routes used to access the Web server would form a SPT; root=server. • In reality: • 80% of routes change less often than 1/day • 93% of the routes are actually stable (from Bell Lab’s Web server to 13,533 destinations ) • Reduce the arbitrary network to a tree

15. Discussion (cont.) • The placement of en-route proxies in the routers requires static configuration work. • although the client population changes significantly from time to time, the outgoing traffic remains pretty stable. • the optimal locations for the proxies do not change by much as time progresses

16. Discussion (cont.) • Multicast model and not considering building and maintenance cost. • Once a proxy is placed at node u, the nodes on the π(u, s) path can have a proxy without increasing the cost, but just decrease read cost on those nodes. • Solution : Consider the monetary cost and maintenance cost.

17. Conclusion • placing k proxies problem • Time complexity : O(n3k2), where k is the number of proxies and n the number of nodes in the system. • The optimal number of proxies problem • given the read frequencies of all clients and the update frequency of the server. • Time complexity : O(n3),

18. Web-Server Proxies Placement of with Consideration of 2007 COMMUNICATION OPTIMIZATION FOR PARALLEL PROCESSING Read 李苡嬋 and Update Operations 張又仁 the 莊謹譽 on Internet