Modeling Global Multicast Tree Efficiency

1. Modeling the Branching Characteristics and Efficiency Gains in Global Multicast Trees Robert C. Chalmers and Kevin C. Almeroth UC Santa Barbara, Computer Science {robertc,almeroth}@cs.ucsb.edu http://www.nmsl.cs.ucsb.edu/mwalk Infocom 2001

2. Goals • goal: to characterize multicast efficiency • efficiency in relation to duplicate unicast streams • goal: to accurately model tree topologies • do inter-domain trees share common properties? • requirement: a clear understanding of the shape of multicast trees web site - http://www.nmsl.cs.ucsb.edu/mwalk/

3. Key Factors of Shape • height • increase in shared links • breadth • near bottom - sharing • near top - duplication • number of receivers • more likely to share web site - http://www.nmsl.cs.ucsb.edu/mwalk/

4. Key Factors of Shape • height • increase in shared links • breadth • near bottom - sharing • near top - duplication • number of receivers • more likely to share web site - http://www.nmsl.cs.ucsb.edu/mwalk/

5. Key Factors of Shape • height • increase in shared links • breadth • near bottom - sharing • near top - duplication • number of receivers • more likely to share web site - http://www.nmsl.cs.ucsb.edu/mwalk/

6. Key Factors of Shape • height • increase in shared links • breadth • near bottom - sharing • near top - duplication • number of receivers • more likely to share web site - http://www.nmsl.cs.ucsb.edu/mwalk/

7. Key Factors of Shape • height • increase in shared links • breadth • near bottom - sharing • near top - duplication • number of receivers • more likely to share • branching • where does it occur • how does it affect sharing web site - http://www.nmsl.cs.ucsb.edu/mwalk/

8. Measuring Efficiency • compare total mcast and ucast hops •  = 1 - Lm / Lu • % gain using mcast • Lm = 18, Lu = 38 •  = 1 - 18 / 38 = .52 • 52% reduction in links traversed (3) (3) (7) (1) (1) (1) (1) (1) (1) (7) (1) (1) (5) (1) (1) (1) (1) (1) web site - http://www.nmsl.cs.ucsb.edu/mwalk/

9. Estimating Efficiency • expands on work to price mcast (Chuang-98) Lm / Lu = Nk • k  0.8 for a range of generated networks • assuming Lu= Lu / N  = 1 - N • where  = k - 1  0.8 - 1 = -0.2 web site - http://www.nmsl.cs.ucsb.edu/mwalk/

10. Estimating Efficiency (cont’d) • 20-40 receivers  60-70% improved efficiency • 80% savings for 150 users, 90% for 1,000 web site - http://www.nmsl.cs.ucsb.edu/mwalk/

11. Efficiency Analysis web site - http://www.nmsl.cs.ucsb.edu/mwalk/

12. Receiver Duration early clustering 1-minute timeout 20-minute timeout infinite timeout web site - http://www.nmsl.cs.ucsb.edu/mwalk/

13. Inter-Arrival Times random receiver activity || drops from 0.34 to 0.30 web site - http://www.nmsl.cs.ucsb.edu/mwalk/

14. Receiver Distribution synthesized group distribution || still lower than for real groups web site - http://www.nmsl.cs.ucsb.edu/mwalk/

15. Efficiency and Shape • do consistent efficiencies imply similar shapes? • global mcast trees share common properties • long paths from source to backbone • branching in backbone only occurs at a limited number of peering points • long paths from backbone to receiver • the range of tree shapes are constrained by the underlying network connectivity web site - http://www.nmsl.cs.ucsb.edu/mwalk/

16. Out-degree Frequencies • most nodes have a very low out-degree • result is chains of relay nodes (Pansiot-98) • degree frequencies in Internet routers follow a skewed distribution (Faloutsos-99) web site - http://www.nmsl.cs.ucsb.edu/mwalk/

17. Average Degree average degree grows with N internal degree tapers off near 1.5 web site - http://www.nmsl.cs.ucsb.edu/mwalk/

18. Conclusions • accurately characterized mcast efficiency • over a range of receiver dynamics and distributions • useful in effort to deploy multicast • identified common properties of mcast trees • useful to improve tree generation techniques • shape is constrained by network connectivity • http://www.nmsl.cs.ucsb.edu/mwalk • for more information web site - http://www.nmsl.cs.ucsb.edu/mwalk/

19. Addendum

20. Unicast vs. Multicast • ratio of ucast to mcast path lengths for 1198 receivers in the SYNTH-1 dataset • majority of mcast paths are 0.7-1.2 times the ucast path length web site - http://www.nmsl.cs.ucsb.edu/mwalk/