Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 1

The Impact of Multicast Layering on Network Fairness

Dan RubensteinJim Kurose

Don Towsley

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 2

Motivation

• How should multicast flows share bandwidth “fairly” within a network?

S1

S2

r1,1r2,1

r2,2

router

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 3

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]

S1

S2r1,1r2,1

r2,2

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 4

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

Sep. 1, 1999 - SIGCOMM '99

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

S1

S2

S3

r1r2

r3

S1

S2

S3

r1r2

r3Not MMF!

Sep. 1, 1999 - SIGCOMM '99

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

S1

S2

S3

r1r2

r3

S1

S2

S3

r1r2

r3Not MMF! MMF!

• Hayden proves: For any unicast network, there is a unique max-min fair allocation.

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 7

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

S1

S2r1,1r2,1

r2,2

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 8

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)

S1

S2r1,1r2,1

r2,2

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 9

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 MMFSingle-rate MMF

No SPRF! SPRF!

Sep. 1, 1999 - SIGCOMM '99

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.

Sep. 1, 1999 - SIGCOMM '99

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.

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 12

• 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

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 13

Redundancy• Lack of intra-session join/leave coordination increases shared link usage

r1,1coord uncoord

Link usage

r1,1

r1,2 r1,2

session’s link redundancy = s/Ms: session’s shared link rate M: session’s max rcvr rate on link

session’s link redundancy = s/Ms: 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

Sep. 1, 1999 - SIGCOMM '99

Dan Rubenstein 14

1

10

1 10 100Receivers

All 0.1

All 0.5

All 0.9

1st 0.5, rest 0.1

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

Sep. 1, 1999 - SIGCOMM '99

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 small0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10Redundancy

f = 0.01

f = 0.05

f = 0.1

f = 1

Sep. 1, 1999 - SIGCOMM '99

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

• Markov models and simulation on mod-star topology Shared-loss link

Independent-loss links

Sep. 1, 1999 - SIGCOMM '99

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!1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.02 0.04 0.06 0.08 0.1Independent Link Loss Rates

uncoord low shared

uncoord high shared

coord low shared

coord high shared

Sep. 1, 1999 - SIGCOMM '99

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

Sep. 1, 1999 - SIGCOMM '99

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