The Impact of Multicast Layering on Network Fairness

1. The Impact of Multicast Layering on Network Fairness Dan Rubenstein Jim Kurose Don Towsley Dan Rubenstein

2. S1 r2,2 r1,1 S2 router r2,1 Motivation • How should multicast flows share bandwidth “fairly” within a network? Dan Rubenstein

3. r2,2 S1 r1,1 S2 r2,1 Layered Multicast • Layering permits multi-rate sessions • receivers in same session receive at differing rates • Used for • multicast video [MJV’96/’97] • (reliable) data via FEC [RV’98, BLMR’98] Q: How can multi-rate sessions affect fairness within a network? Dan Rubenstein

4. Talk Overview 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 Dan Rubenstein

5. 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 r1 r1 r2 r2 S1 S1 S2 S2 S3 S3 r3 r3 Not MMF! Dan Rubenstein

6. 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 r1 r1 r2 r2 S1 S1 S2 S2 S3 S3 r3 r3 MMF! Not MMF! • Hayden proves: For any unicast network, there is a unique max-min fair allocation. Dan Rubenstein

7. Single-rate Multicast MMF [TS’97] r2,2 S1 • 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 r1,1 S2 r2,1 • TS’97 proves: for any single-rate multicast network • there is a unique max-min fair allocation Dan Rubenstein

8. r2,2 S1 r1,1 S2 r2,1 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) Dan Rubenstein

9. No SPRF! Same paths Single-rate MMF 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. SPRF! Multi-rate MMF Dan Rubenstein

10. 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. Dan Rubenstein

11. 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. Dan Rubenstein

12. Practicalities... • In practice: finite # of layers smallset 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... } MMF rate Layer 2 } Layer 1 time Dan Rubenstein

13. r1,1 r1,2 r1,2 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 Redundancy • Lack of intra-session join/leave coordination increases shared link usage Link usage r1,1 coord uncoord Dan Rubenstein

14. 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 Dan Rubenstein

15. 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 Dan Rubenstein

16. 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 Independent-loss links • Markov models and simulation on mod-star topology Shared-loss link Dan Rubenstein

17. 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! Dan Rubenstein

18. 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 Dan Rubenstein

19. 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 Dan Rubenstein