Example: 25 transmissions to be carried out T2 T3 T4 T5 T1 T1 - PowerPoint PPT Presentation

ICON 2004 - IEEE International Conference On Networks November 16-19, 2004, Singapore, Hilton E FFICIENT L IQUID S CHEDULE S EARCH S TRATEGIES FOR C OLLECTIVE C OMMUNICATIONS Emin Gabrielyan, Roger D. Hersch Swiss Federal Institute of Technology - Lausanne -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Example: 25 transmissions to be carried out T2 T3 T4 T5 T1 T1 T2 T3 T4 T5 l 2 l 3 l 5 l 4 l 1 l 11 l 12 l 6 l 7 l 10 l 9 l 8 R1 R3 R4 R2 R5 R1 R3 R4 R5 R2 -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Round-robin schedule T1 T2 T3 T4 T5 T1 T2 T3 T4 T5 R1 R1 R2 R3 R4 R5 R2 R3 R4 R5 T2 T3 T4 T5 T4 T5 T1 T2 T3 T4 T5 T1 T2 T3 T1 R1 R3 R4 R5 R1 R3 R4 R5 R2 R1 R3 R4 R5 R2 R2 -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Round-robin Throughput phase 4.1 phase 1 phase 3.1 n n o o i i t t s s e e g g n n o o c c phase 5 phase 3.2 phase 2 phase 4.2 ⁄ ⋅ T roundrobin = 25 7 1 Gbps = 3.57 Gbps -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Liquid schedule time frame 2 time frame 3 time frame 1 time frame 6 time frame 4 time frame 5 ⁄ ⋅ T liquid = 25 6 1 Gbps = 4.16 Gbps -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Transfers and Load of Links T2 T3 T4 T5 T1 T2 T3 T4 T5 T1 5 5 5 5 5 6 s k c e X = n e l t t o b 6 5 5 5 5 5 R1 R1 R3 R4 R5 R2 R3 R4 R5 R2 The 25 transfer traffic λ l 1 X ( , ) , …λ l 12 X ( , ) = 5 = 6 { , } … l 1 l 12 l 9 , { , , } … , l 1 l 6 Transfers: -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Duration of Traffic T2 T3 T4 T5 T1 λ l 1 X ( , ) , …λ l 10 X ( , ) = 5 = 5 l 2 l 3 l 5 l 4 l 1 l 11 λ l 11 X ( , ) , …λ l 12 X ( , ) = 5 = 6 l 12 l 6 l 7 l 10 l 9 l 8 Λ X ( ) = 6 R1 R2 R3 R4 R5 {l 1 , l 6 }, {l 1 , l 7 }, {l 1 , l 8 }, {l 1 , l 12 , l 9 }, {l 1 , l 12 , l 10 }, {l 2 , l 6 }, {l 2 , l 7 }, {l 2 , l 8 }, {l 2 , l 12 , l 9 }, {l 2 , l 12 , l 10 }, X= {l 3 , l 6 }, {l 3 , l 7 }, {l 3 , l 8 }, {l 3 , l 12 , l 9 }, {l 3 , l 12 , l 10 }, {l 4 , l 11 , l 6 }, {l 4 , l 11 , l 7 }, {l 4 , l 11 , l 8 }, {l 4 , l 9 }, {l 4 , l 10 }, {l 5 , l 11 , l 6 }, {l 5 , l 11 , l 7 }, {l 5 , l 11 , l 8 }, {l 5 , l 9 }, {l 5 , l 10 } -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Liquid Throughput {l 1 , l 6 }, {l 1 , l 7 }, {l 1 , l 8 }, {l 1 , l 12 , l 9 }, {l 1 , l 12 , l 10 }, {l 2 , l 6 }, {l 2 , l 7 }, {l 2 , l 8 }, {l 2 , l 12 , l 9 }, {l 2 , l 12 , l 10 }, X= {l 3 , l 6 }, {l 3 , l 7 }, {l 3 , l 8 }, {l 3 , l 12 , l 9 }, {l 3 , l 12 , l 10 }, {l 4 , l 11 , l 6 }, {l 4 , l 11 , l 7 }, {l 4 , l 11 , l 8 }, {l 4 , l 9 }, {l 4 , l 10 }, {l 5 , l 11 , l 6 }, {l 5 , l 11 , l 7 }, {l 5 , l 11 , l 8 }, {l 5 , l 9 }, {l 5 , l 10 } the throughput of a single link total number of transfers ( ) # X 25 ⋅ ⋅ - - - - - - - - - - - - T link - - - - - 1 Gbps - T liquid = = = 4.17 Gbps Λ X ( ) 6 traffic’s duration (the load of its bottlenecks) -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Schedules yielding the liquid throughput {l 1 , l 6 }, {l 1 , l 7 }, {l 1 , l 8 }, {l 1 , l 12 , l 9 }, {l 1 , l 12 , l 10 }, {l 2 , l 6 }, {l 2 , l 7 }, {l 2 , l 8 }, {l 2 , l 12 , l 9 }, {l 2 , l 12 , l 10 }, X= {l 3 , l 6 }, {l 3 , l 7 }, {l 3 , l 8 }, {l 3 , l 12 , l 9 }, {l 3 , l 12 , l 10 }, {l 4 , l 11 , l 6 }, {l 4 , l 11 , l 7 }, {l 4 , l 11 , l 8 }, {l 4 , l 9 }, {l 4 , l 10 }, {l 5 , l 11 , l 6 }, {l 5 , l 11 , l 7 }, {l 5 , l 11 , l 8 }, {l 5 , l 9 }, {l 5 , l 10 } • Without a right schedule we may have intervals when the access to the bottleneck links is blocked by other transmissions. • Our goal is to schedule the transfers such that all bot- tlenecks are always kept occupied ensuring that the liquid throughput is obtained. • A schedule yielding the liquid throughput we call as a liquid schedule and our objective is to find a liquid schedule whenever it exists. -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Swiss-T1 Cluster N07 N08 6 N 0 0 N 9 PR15 PR16 P P 5 PR13 PR18 N10 0 R PR12 R PR19 N PR11 1 PR20 1 4 7 N04 PR21 N11 PR10 PR22 PR09 PR23 PR08 N03 N12 PR07 PR24 PR06 PR25 2 1 N02 N PR26 PR05 1 3 PR04 PR27 N01 PR03 PR28 N 1 4 PR29 PR02 N00 3 0 Node P P R 3 R 0 0 1 N00 N15 PR31 PR00 Switch 0 PR32 PR63 1 N16 3 3 3 2 R 6 R P N P PR34 PR61 4 7 Rx Proc N N30 PR35 PR01 PR60 1 7 PR36 PR59 PR37 PR58 N29 N18 PR38 PR57 Tx Proc PR00 6 5 PR39 PR56 PR40 PR55 N19 N28 PR41 PR54 PR42 PR53 Routing PR52 PR43 N20 N27 PR51 PR44 PR45 PR50 6 9 PR47 PR48 4 4 N N26 R 2 R 1 P P N 5 2 2 N Link 2 N23 N24 -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

363 Communication Patterns Liquid throughput (MB/s) 1800 1600 1400 1200 1000 800 600 400 200 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Number of contributing nodes -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

363 Topology Test-bed 2800 Aggregate throughput (MB/s) 2400 Crossbar throughput 2000 1600 1200 Liquid throughput 800 400 0 0 (0) 20 (8) 40 (10) 60 (11) 80 (12) 100 (13) 120 (14) 140 (15) 160 (15) 180 (16) 200 (17) 220 (18) 240 (19) 260 (20) 280 (21) 300 (22) 320 (24) 340 (25) 360 (30) Topology (contributing nodes) -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Round-robin throughput theoretical liquid measured round-robin 1800 Throughput (MB/s) 1600 1400 1200 1000 800 600 400 200 0 121 11 144 12 144 12 169 13 196 14 225 15 225 15 256 16 289 17 324 18 361 19 361 19 400 20 441 21 484 22 576 24 676 26 900 30 0 00 64 08 81 09 Transfers / Contributing nodes -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --

Team : a set of mutually non-congesting transfers using all bottlenecks schedule α is liquid ⇔ {l 1 , l 6 }, {l 1 , l 7 }, {l 1 , l 8 }, {l 1 , l 12 , l 9 }, {l 1 , l 12 , l 10 }, {l 2 , l 6 }, {l 2 , l 7 }, {l 2 , l 8 }, {l 2 , l 12 , l 9 }, {l 2 , l 12 , l 10 }, {l 3 , l 6 }, {l 3 , l 7 }, {l 3 , l 8 }, {l 3 , l 12 , l 9 }, {l 3 , l 12 , l 10 }, X = {l 4 , l 11 , l 6 }, {l 4 , l 11 , l 7 }, {l 4 , l 11 , l 8 }, {l 4 , l 9 }, {l 4 , l 10 }, {l 5 , l 11 , l 6 }, {l 5 , l 11 , l 7 }, {l 5 , l 11 , l 8 }, {l 5 , l 9 }, {l 5 , l 10 } load of the bottlenecks number of timeframes } { {l 1 , l 8 }, {l 1 , l 12 , l 9 }, } { { } {l 2 , l 12 , l 9 }, {l 1 , l 12 , l 10 }, {l 2 , l 7 }, { l 3 , l 6 }, ⇔ # α ( ) Λ X ( ) ⇔ {l 2 , l 6 }, {l 3 , l 8 }, = {l 4 , l 10 }, {l 4 , l 11 , l 6 }, {l 4 , l 11 , l 7 }, , , , {l 5 , l 11 , l 7 } {l 5 , l 10 } {l 5 , l 9 } α = } { { } {l 1 , l 7 }, {l 1 , l 6 }, ⇔ ∀ ( ∈ α ) { { l 3 , l 12 , l 10 }, } {l 2 , l 8 }, {l 2 , l 12 , l 10 }, A { l 4 , l 9 }, { l 3 , l 12 , l 9 }, { l 3 , l 7 }, , , A is a team of X { l 5 , l 11 , l 8 } {l 5 , l 11 , l 6 } { l 4 , l 11 , l 8 } -- ICON 2004, IEEE International Conference On Networks, November 16-19, 2004, Singapore, Hilton -- -- EFFICIENT LIQUID SCHEDULE SEARCH STRATEGIES FOR COLLECTIVE COMMUNICATIONS --