1. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein1 The Impact of Multicast Layering on Network Fairness Dan Rubenstein Jim Kurose Don Towsley

2. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein2 Motivation How should multicast flows share bandwidth “fairly” within a network? S1S1 S2S2 r 1,1 r 2,1 r 2,2 router

3. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein3 Layered Multicast Layering permits multi-rate sessions –receivers in same session receive at differing rates Q: How can multi-rate sessions affect fairness within a network? Used for – multicast video [MJV’96/’97] – (reliable) data via FEC [RV’98, BLMR’98] S1S1 S2S2 r 1,1 r 2,1 r 2,2

4. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein4 Paper Contributions Formally extend max-min fair (MMF) definition to cover multi-rate (i.e., layered) sessions Demonstrate that desirable fairness properties hold in multi-rate max-min fair rate allocations Quantify a practical coordination problem within multi-rate sessions: redundancy Examine how redundancy impacts fairness of a practical congestion control protocol Talk Overview

5. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein5 Unicast MMF [H ‘81, …, BG ‘92] When possible, take from the rich, give to the poor... “rates” are max-min fair when for all rates B, either –B uses all link bandwidth on some link – increasing B causes a decrease in some other rate A, where initially A B S1S1 S2S2 S3S3 r1r1 r2r2 r3r3 S1S1 S2S2 S3S3 r1r1 r2r2 r3r3 Not MMF!

6. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein6 Unicast MMF [H ’81, …, BG ’92] When possible, take from the rich, give to the poor... “rates” are max-min fair when for all rates B, either –B uses all link bandwidth on some link – increasing B causes a decrease in some other rate A, where initially A B S1S1 S2S2 S3S3 r1r1 r2r2 r3r3 S1S1 S2S2 S3S3 r1r1 r2r2 r3r3 Not MMF! MMF! Hayden proves: For any unicast network, there is a unique max-min fair allocation.

7. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein7 Single-rate Multicast MMF [TS’97] all receivers in session must receive at same rate “fairness” applies to session rates a session’s link BW is identical on all utilized links TS’97 proves: for any single-rate multicast network there is a unique max-min fair allocation S1S1 S2S2 r 1,1 r 2,1 r 2,2

8. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein8 Multi-rate MMF receivers in a session can receive at differing rates make receiving rates “fair” session’s link BW is the maximum used on downstream links (like layered protocols) We prove: for any multi-rate multicast network, there is a unique max-min fair allocation (Proofs extend to networks w/ mix of single-rate & multi-rate sessions) S1S1 S2S2 r 1,1 r 2,1 r 2,2

9. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein9 Why is multi-rate MMF “desirable”? We identify desirable fairness properties –Derived from desirable properties of unicast max-min fair allocations –e.g., Same-path-receiver-fairness (SPRF): 2 rcvrs with same paths from sources should receive at identical rates. Same paths Multi-rate MMF Single-rate MMF No SPRF! SPRF!

10. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein10 The other fairness properties... Deal with competing session’s rates & link utilizations (give from richer to poorer)... –Fully-Utilized-Receiver-Fairness: Each receiving rate should be no “poorer” than other rates over some competing link –Per-Session-Link-Fairness: Each session should be no “poorer” than other sessions on some link over some branch of the session’s multicast tree. –Per-Receiver-Link-Fairness: Each session should be no “poorer” than other sessions on some link over every branch of the session’s multicast tree.

11. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein11 Multi-rate MMF is “desirable” We prove these “desirable” properties hold within the multi-rate MMF allocation in any network. We show these properties need not hold within the single-rate MMF allocation (e.g., Same-path-receiver-fairness) We measure “desirability” of the MMF allocation as individual session types (single- or multi-rate) vary –construct allocation ordering relation –show “desirability” increases as sessions switch to multi-rate.

12. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein12 In practice: finite # of layers small set of available rates Problem: fixed set of layers might not yield fair rate Solution: join and leave layers to achieve desired (fair) average rate Leads to another problem... Practicalities... Layer 2 Layer 1 MMF rate } } time

13. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein13 Redundancy Lack of intra-session join/leave coordination increases shared link usage r 1,1 coorduncoord Link usage r 1,1 r 1,2 session’s link redundancy = s/M s: session’s shared link rate M: session’s max rcvr rate on link session’s link redundancy = s/M s: session’s shared link rate M: session’s max rcvr rate on link Redundancy of 1 is optimal Redundancy > 1: some desired fairness properties don’t hold

14. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein14 Redundancy in Practice Simple example –one layer –Unsynched (random) joins and leaves redundancy highest when all receivers “touch” a layer Also find: using multiple layers reduces redundancy

15. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein15 Redundancy vs. Fair rates E.g., single bottleneck link: redundancy lowers fair rates Less impact on rates when fraction, f, of sessions with redundancy is small. f likely to be small

16. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein16 Redundancy in Practice What is the redundancy of a practical, layered, congestion control protocol? Protocol we consider: (simple model based on the work of [VCR’98]): –Lose a packet, leave a layer –Join layer, 2 versions: uncoordinated points in time coordinated by sender Markov models and simulation on mod-star topology Shared-loss link Independent-loss links

17. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein17 A practical CC protocol: redundancy Results w/ 100 rcvrs: –allocations are “close” to multi-rate max-min fair –sender-coordinated joins keeps redundancy smaller than 3 Redundancy < 3 means fair rate within.9 of optimal!

18. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein18 Conclusion Multi-rate sessions change “the rules” for fairness –can achieve desirable fairness properties Keep redundancy low –simple techniques likely to do quite well in practice

19. Sep. 1, 1999 - SIGCOMM '99 Dan Rubenstein19 Open Issues Extensions to other fairness definitions: –TCP fairness –Proportional fairness Eliminating redundancy –Network support (router filters) –Prioritized layers –Effects of join/leave latencies Stability –How fast should/can protocols join/leave layers