Enhanced logical tree reconfiguration for reliable multicast

1. Enhanced logical tree reconfiguration for reliable multicast Ko, YangWoo/Lee, Soojeon May 20th, 2003 CDS& N Lab.

2. Table of contents • Logical tree and error bitmap • Objective • What we have done • Basic approaches • Penalty • Lazy move • Conclusion CDS& N Lab.

3. What is logical tree ? sender Transport layer Parent node Child node Network layer (b) Trees (a) Protocol layers CDS& N Lab.

4. Ideal logical tree S Logical tree Original multicast distribution tree S source routers D E D E A hosts A B C B C CDS& N Lab.

5. Problem is … • Logical tree is built at transport or upper layer where routing topology information is not available. • Then, how to configure logical tree ? • RTT • The faster, the nearer • Error bitmap • The more stable, the nearer CDS& N Lab.

6. Example of logical tree repair Bit-wise comparison S S 11111 A B A B E 11011 10110 01011 C E C D 11000 01001 D CDS& N Lab.

7. Objective • As of midterm presentation • To enhance logical tree reconfiguration by use of longer error bitmap while minimizing overhead due to increase in size of error bitmap. • Now • To enhance logical tree reconfiguration with minimum (or no, or even less) overhead. CDS& N Lab.

8. What we have done so far • Implementation (programming) • Error bitmap generator (Java) • Physical tree generator (Java) • Logical tree constructor (C++) • Logical tree similarity evaluator (C++) • Idea building • Various construction enhancement • Logical tree evaluation metric CDS& N Lab.

9. Logical tree evaluation • There has been no proper metric to evaluate logical trees. • Results from simulation and simple counting of mismatching parent-child relationships. • Newly proposed metric (called “penalty”) • Similarity of two trees based on number of “additional” links. • It is not perfect but far better than “rule of thumb”. CDS& N Lab.

10. Logical tree evaluation (contd.) • Penalty • Sum of numbers of additional links for all nodes. • For each node, it can be derived by one full traverse of tree at most. CDS& N Lab.

11. Basic approaches • Full (cumulative) history • Best result but impractical because; • Each node has different life time. • It requires more memory space. • Limited history • Practical but … (see next slide) • Superimposed history • It may add more historical “flavor” to history but … (see next slide) CDS& N Lab.

12. Basic approaches (64bit) No convergence ! CDS& N Lab.

13. Convergence rate of cumulative approach CDS& N Lab.

14. New approach : Lazy move • How can we memorize “rough history” without saving error bitmap ? • Time period during which one node stays under a sub-tree can be an indicator for “proximity” of that node against the tree. • Interpretation • As I have lived here so long, I would not move somewhere else though I heard warning signal that “you are misplaced”. • If warning signal repeats, then I will move. CDS& N Lab.

15. Lazy vs. non-lazy move (32bit) We may converge without cumulative history bitmap ! CDS& N Lab.

16. Lazy vs. non-lazy (16bit) CDS& N Lab.

17. Lazy vs. non-lazy (8bit) CDS& N Lab.

18. Rate of laziness doesn’t matter CDS& N Lab.

19. Sanity check of lazy move Lazy move with 32bit 1x history (10 different sequences) CDS& N Lab.

20. No laziness, no convergence Non-lazy move with 32bit 1x history (5 different error bitmaps) CDS& N Lab.

21. Convergence by lazy move Lazy move with 32bit 1x history (5 different error bitmaps) Not always converge ! CDS& N Lab.

22. Comparison in 10 samples Average of 10 error bitmap samples with 32bit 1x history No lazy : μ = 7.61, σ2 = 12.77 Lazy : μ = 2.93, σ2 = 6.08 CDS& N Lab.

23. Concluding remarks • Our contributions • Penalty is proposed as a formal metric for logical tree evaluation • Lazy move can enhance quality of logical tree with proper size of error bitmap. • (Just two of many) future works • Penalty does not consider number of intermediate routers. • Evaluation of overhead incurred to each node by implementation of lazy move is necessary. CDS& N Lab.