ICT'2003 10th International Conference on Telecommunications February 23 - March 1, 2003, Tahiti Sofitel Coralia Maeva Beach Hotel Papeete, French Polynesia Network Topology Aware Scheduling of Collective Communications Emin Gabrielyan, Roger D. Hersch Swiss Federal Institute of Technology Lausanne -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
ICT'2003, 10th International Conference on Telecommunications February 23 - March 1, 2003, Tahiti Network Topology Aware Scheduling of Collective Communications Emin Gabrielyan, Roger D. Hersch Swiss Federal Institute of Technology Lausanne -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
25-transmission request T2 T3 T4 T5 T1 T4 T5 T1 T2 T3 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 R5 R2 R1 R3 R4 R5 R2 -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Round-robin schedule T4 T5 T4 T5 T1 T2 T3 T1 T2 T3 R1 R3 R4 R5 R1 R3 R4 R5 R2 R2 T1 T2 T3 T4 T5 T1 T2 T3 T4 T5 T1 T2 T3 T4 T5 R1 R2 R3 R4 R5 R1 R1 R3 R4 R5 R2 R3 R4 R5 R2 -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Round-robin Throughput phase 4.1 phase 1 phase 3.1 phase 5 phase 3.2 phase 2 phase 4.2 ⁄ ⋅ T roundrobin = 25 7 1 Gbps = 3.57 Gbps -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Liquid schedule time frame 2 time frame 2 time frame 2 time frame 2 time frame 2 time frame 2 ⁄ ⋅ T liquid = 25 6 1 Gbps = 4.16 Gbps -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Transfers and Load of Links T4 T5 T1 T2 T3 T4 T5 T1 T2 T3 5 5 5 5 5 6 s k c e X = n e l t t o 6 b 5 5 5 5 5 R1 R3 R4 R5 R1 R3 R4 R5 R2 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: -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Duration of Traffic T1 T2 T3 T4 T5 λ l 1 X ( , ) , …λ l 10 X ( , ) = 5 = 5 l 2 l 3 l 4 l 5 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 R3 R4 R5 R2 {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 } -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
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) -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
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. -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Swiss-T1 Cluster 7 N08 0 N N06 N09 PR15 PR16 N05 P P N P P 1 PR12 R R PR19 0 R R PR11 1 PR20 1 1 1 N04 4 N11 7 PR10 PR21 3 8 P P R R PR08 PR23 0 2 N03 9 N12 2 PR07 PR24 P P R 2 1 R 0 2 6 2 N13 PR05 5 PR26 0 N PR04 PR27 PR03 1 N14 PR28 0 N P 3 R 0 P 0 R 2 2 9 N00 Node P R P 0 R 1 3 0 N00 N 1 PR00 PR31 5 PR63 PR32 Switch 0 N31 N16 2 6 3 R 3 P R P 1 4 6 3 R 4 R P P 7 PR60 N17 N30 PR35 Rx Proc PR01 PR59 PR36 PR58 PR37 N29 N 7 8 1 5 3 Tx Proc 6 8 R R PR00 5 P P PR56 PR39 PR55 PR40 N19 N28 4 1 5 4 R PR53 PR42 R Routing P PR52 P PR43 N20 N27 PR51 PR44 5 0 6 9 5 PR47 4 PR48 4 4 R R N21 N26 R R P P P P N22 N25 Link N N24 2 3 -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
363 Test Traffics 1800 Liquid throughput (MB/s) 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 -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
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) -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Round-robin throughput theoretical liquid measured round-robin 1800 1600 Throughput (MB/s) 1400 1200 1000 800 600 400 200 0 8 9 1 2 2 3 4 5 5 6 7 8 9 9 0 1 2 4 6 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 0 4 1 1 4 4 9 6 5 5 6 9 4 1 1 0 1 4 6 6 0 0 6 8 2 4 4 6 9 2 2 5 8 2 6 6 0 4 8 7 7 0 1 1 1 1 1 2 2 2 2 3 3 3 4 4 4 5 6 9 Transfers / Contributing nodes -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Team : a set of mutually non-congesting transfers using all bottlenecks {l 1 , l 6 }, {l 1 , l 7 }, {l 1 , l 8 }, {l 1 , l 12 , l 9 }, {l 1 , l 12 , l 10 }, schedule α is liquid ⇔ {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 } 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 }, ⇔ # α ( ) Λ X ( ) ⇔ = { l 3 , l 6 }, {l 2 , l 6 }, {l 3 , l 8 }, {l 4 , l 11 , l 7 }, {l 4 , l 10 }, {l 4 , l 11 , l 6 }, , , , {l 5 , l 11 , l 7 } {l 5 , l 9 } {l 5 , l 10 } α = } { { } {l 1 , l 7 }, {l 1 , l 6 }, { } ⇔ ∀ ( ∈ α ) A { l 3 , l 12 , l 10 }, {l 2 , l 8 }, {l 2 , l 12 , l 10 }, { 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 } -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
ℑ X ( ) all teams of the traffic X , • To cover the full solution space when - transfer x constructing a liquid schedule an effi- - transfers congesting with x cient technique obtaining the whole set - transfers non-congesting with x of possible teams of a traffic is required. { } • We designed an efficient algorithm enu- depot merating all teams of a traffic traversing R= each team once and only once. • This algorithm obtains each team by excluder includer subsequent partitioning of the set of all teams. • We introduced tri- plets consisting of { } { } depot depot subsets of the traf- fic, representing one- R x = R x = by-one partitions of the set of all teams. excluder includer excluder includer -- 10 th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --
Recommend
More recommend
