ICT'2003 10th International Conference on Telecommunications - - PowerPoint PPT Presentation

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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,

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SLIDE 1
  • - 10th 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

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

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  • - 10th 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

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

l11 l12 l1 l10 l2 l3 l4 l5 l6 l7 l8 l9

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5 R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

25-transmission request

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

Round-robin schedule

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5 R1 R3 R2 R4 R5 T1 T2 T3 T4 T5 R1 R3 R2 R4 R5 T1 T2 T3 T4 T5 R1 R3 R2 R4 R5 T1 T2 T3 T4 T5 R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

phase 1 phase 2 phase 3.1 phase 3.2 phase 4.1 phase 4.2

Round-robin Throughput

phase 5

Troundrobin 25 7 ⁄ 1Gbps ⋅ 3.57Gbps = =

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

time frame 2 time frame 2 time frame 2 time frame 2 time frame 2 time frame 2

Liquid schedule

Tliquid 25 6 ⁄ 1Gbps ⋅ 4.16Gbps = =

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

The 25 transfer traffic

X =

λ l1 X , ( ) 5 = …λ l12 X , ( ) 6 = , l1 l6 , { } … l1 l12 l9 , , { } … , ,

Transfers:

5

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

5 5 5 5 5 5 5 5 5 6 6

b

  • t

t l e n e c k s

Transfers and Load of Links

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SLIDE 8
  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

l11 l12 l1 l10 l2 l3 l4 l5 l6 l7 l8 l9

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

λ l1 X , ( ) 5 = …λ l10 X , ( ) 5 = , λ l11 X , ( ) 5 = …λ l12 X , ( ) 6 = ,

{l1, l6}, {l1, l7}, {l1, l8}, {l1, l12, l9}, {l1, l12, l10}, {l2, l6}, {l2, l7}, {l2, l8}, {l2, l12, l9}, {l2, l12, l10}, {l3, l6}, {l3, l7}, {l3, l8}, {l3, l12, l9}, {l3, l12, l10}, {l4, l11, l6}, {l4, l11, l7}, {l4, l11, l8}, {l4, l9}, {l4, l10}, {l5, l11, l6}, {l5, l11, l7}, {l5, l11, l8}, {l5, l9}, {l5, l10}

X=

Λ X ( ) 6 =

Duration of Traffic

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

{l1, l6}, {l1, l7}, {l1, l8}, {l1, l12, l9}, {l1, l12, l10}, {l2, l6}, {l2, l7}, {l2, l8}, {l2, l12, l9}, {l2, l12, l10}, {l3, l6}, {l3, l7}, {l3, l8}, {l3, l12, l9}, {l3, l12, l10}, {l4, l11, l6}, {l4, l11, l7}, {l4, l11, l8}, {l4, l9}, {l4, l10}, {l5, l11, l6}, {l5, l11, l7}, {l5, l11, l8}, {l5, l9}, {l5, l10}

X=

traffic’s duration (the load of its bottlenecks) total number of transfers the throughput of a single link

Tliquid # X ( ) Λ X ( )

  • Tlink

⋅ 25 6

  • 1Gbps

⋅ 4.17Gbps = = =

Liquid Throughput

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SLIDE 10
  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

Schedules yielding the liquid throughput

{l1, l6}, {l1, l7}, {l1, l8}, {l1, l12, l9}, {l1, l12, l10}, {l2, l6}, {l2, l7}, {l2, l8}, {l2, l12, l9}, {l2, l12, l10}, {l3, l6}, {l3, l7}, {l3, l8}, {l3, l12, l9}, {l3, l12, l10}, {l4, l11, l6}, {l4, l11, l7}, {l4, l11, l8}, {l4, l9}, {l4, l10}, {l5, l11, l6}, {l5, l11, l7}, {l5, l11, l8}, {l5, l9}, {l5, l10}

X=

  • 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.

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

2 4 5 6 3 7 1 PR63 PR00 P R 2 PR04 P R 6 PR08 PR10 PR12 P R 1 4 PR16 P R 1 8 PR20 P R 2 2 PR24 PR26 PR28 P R 3 PR32 P R 3 4 PR36 P R 3 8 PR40 PR42 PR44 P R 4 6 PR48 P R 5 PR52 P R 5 4 PR56 PR58 PR60 P R 6 2 P R 6 1 PR59 P R 5 7 PR55 PR53 PR51 P R 4 9 PR47 P R 4 5 PR43 P R 4 1 PR39 PR37 PR35 P R 3 3 PR31 P R 2 9 PR27 P R 2 5 PR23 PR21 PR19 P R 1 7 PR15 P R 1 3 PR11 P R 9 PR07 PR05 PR03 P R 1 N00 N 1 N 2 N03 N04 N05 N06 N 7 N08 N09 N 1 N11 N12 N13 N14 N 1 5 N16 N17 N 1 8 N19 N20 N21 N22 N 2 3 N24 N25 N26 N27 N28 N29 N30 N31

Swiss-T1 Cluster

Node Switch Rx Proc Tx Proc Routing Link

N00 PR01 PR00

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

200 400 600 800 1000 1200 1400 1600 1800 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Number of contributing nodes Liquid throughput (MB/s)

363 Test Traffics

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

400 800 1200 1600 2000 2400 2800

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) Aggregate throughput (MB/s)

363 Topology Test-bed

Crossbar throughput Liquid throughput

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

200 400 600 800 1000 1200 1400 1600 1800

6 4 8 8 1 9 1 2 1 1 1 1 4 4 1 2 1 4 4 1 2 1 6 9 1 3 1 9 6 1 4 2 2 5 1 5 2 2 5 1 5 2 5 6 1 6 2 8 9 1 7 3 2 4 1 8 3 6 1 1 9 3 6 1 1 9 4 2 4 4 1 2 1 4 8 4 2 2 5 7 6 2 4 6 7 6 2 6 9 3

Transfers / Contributing nodes Throughput (MB/s) theoretical liquid measured round-robin

Round-robin throughput

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

{l1, l6}, {l1, l7}, {l1, l8}, {l1, l12, l9}, {l1, l12, l10}, {l2, l6}, {l2, l7}, {l2, l8}, {l2, l12, l9}, {l2, l12, l10}, {l3, l6}, {l3, l7}, {l3, l8}, {l3, l12, l9}, {l3, l12, l10}, {l4, l11, l6}, {l4, l11, l7}, {l4, l11, l8}, {l4, l9}, {l4, l10}, {l5, l11, l6}, {l5, l11, l7}, {l5, l11, l8}, {l5, l9}, {l5, l10}

X =

{l1, l7}, {l2, l8}, {l3, l12, l9}, {l5, l11, l6} {l1, l6}, {l2, l12, l10}, {l3, l7}, {l4, l11, l8} {l3, l12, l10}, {l4, l9}, {l5, l11, l8}

} }

}

{ {

{

, ,

{l1, l12, l9}, {l2, l7}, {l3, l8}, {l4, l11, l6}, {l5, l10} {l1, l12, l10}, {l2, l6}, {l4, l11, l7}, {l5, l9} {l1, l8}, {l2, l12, l9}, {l3, l6}, {l4, l10}, {l5, l11, l7}

}

}{

} {

{

, , ,

α =

number of timeframes load of the bottlenecks

A α ∈ ( ) ∀ ⇔ # α ( ) Λ X ( ) = ⇔ ⇔ schedule α is liquid ⇔ A is a team of X

Team: a set of mutually non-congesting transfers using all bottlenecks

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

R= R x= R x=

  • transfer x
  • transfers congesting with x
  • transfers non-congesting with x

{ }

excluder includer depot

{ }

excluder includer depot

{ }

excluder includer depot

ℑ X ( ) all teams of the traffic X ,

  • To cover the full solution space when

constructing a liquid schedule an effi- cient technique obtaining the whole set

  • f possible teams of a traffic is required.
  • We designed an efficient algorithm enu-

merating all teams of a traffic traversing each team once and only once.

  • This algorithm obtains each team by

subsequent partitioning of the set of all teams.

  • We introduced tri-

plets consisting of subsets of the traf- fic, representing one- by-one partitions of the set of all teams.

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

...

X ℘ X ( ) A1 A2 A3…An , , { } = → X1 X A1 – = ℘ X1 ( ) A1 1

,

A1 2

, …

, { } = → X1 1

,

X1 A1 1

,

– = X1 2

,

X1 A1 2

,

– = X2 X A2 – = ℘ X2 ( ) A2 1

,

A2 2

, …

, { } = → X2 1

,

X2 A2 1

,

– = X2 2

,

X2 A2 2

,

– = ℘ Y ( ) A ℑ X ( ) ∈ A Y ⊂ { } =

all teams of X possible steps to the next layer

Liquid schedule search tree

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

A1,1 A1,1,1 X (25 transfers) X1 = X - A1 (20 transfers) X1,1 = X1 - A1,1 (16 transfers) A1 A(X)=6 (X1)=5 A

2 bottlenecks 2 bottlenecks 4 bottlenecks 4 bottlenecks 6 bottlenecks 8 bottlenecks

(X1,...)=3 A (X1,...)=2 A (X1,...)=1 A (X1,1)=4 A A1,... A1,... A1,...

Additional bottlenecks

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

4 bottlenecks

(X1,1)=4 A

16-transfer traffic load is 4 load is 4

A1,1 A1,1,1 X (25 transfers) X1 = X - A1 (20 transfers) X1,1 = X1 - A1,1 (16 transfers) A1 A(X)=6 (X1)=5 A

2 bottlenecks 2 bottlenecks

Prediction of dead-ends

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

...

X ℘ X ( ) A1 A2 A3…An , , { } = → X1 X A1 – = ℘ X1 ( ) A1 1

,

A1 2

, …

, { } = → X1 1

,

X1 A1 1

,

– = X1 2

,

X1 A1 2

,

– = X2 X A2 – = ℘ X2 ( ) A2 1

,

A2 2

, …

, { } = → ℘ Y ( ) A ℑ X ( ) ∈ A Y ⊂ { } = ℘ Y ( ) ℑ Y ( ) = →

decreasing the search space without affecting the solution space

ℑ Y ( ) A ℑ X ( ) ∈ A Y ⊂ { } ⊂

  • riginal traffic’s teams formed

from the reduced traffic teams of the reduced traffic

Liquid schedule search optimization

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

For more than 90% of the test-bed topologies construction of a global liquid schedule is com- pleted in a fraction of a second (less than 0.1s).

additionally decreas- ing the search space without affecting the solution space

Choice ℘ Y ( ) ℑfull Y ( ) = = ℑfull Y ( ) ℑ Y ( ) ⊂

full teams of the reduced traffic

{

Liquid schedules construction

Choice ℘ Y ( ) ℑ Y ( ) = =

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

200 400 600 800 1000 1200 1400 1600 1800 2000 8 10 12 13 14 15 16 17 18 19 21 22 24 27 Number of contributing nodes for the 363 sub-topologies All-to-all throughput (MB/s) liquid throughput carried out according to the liquid schedules

Results

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

x

1 , 1

x

2 , 1

x

3 , 1

x

4 , 1

x

5 , 1

x

1 , 2

x

2 , 2

x

3 , 2

x

4 , 2

x

1 , 3

x

2 , 3

x

3 , 3

x

4 , 3

x

1 , 4

x

2 , 4

x

3 , 4

x

4 , 4

x

5 , 4

x

1 , 5

x

4 , 5

x

5 , 5

The 25 vertices of the graph represent the 25 transfers

  • transfers. The edges repre-

sent congestion relations be- tween transfers, i.e. each edge represents one or more communication links shared by two transfers.

Bold edges represent all conges- tions due to bottleneck links

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

5

R1 R3 R2 R4 R5 T1 T2 T3 T4 T5

5 5 5 5 5 5 5 5 5 6 6

bottlenecks

Congestion Graph

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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

5 10 15 20 1 49 64 81 100 100 121 144 144 144 169 169 196 196 225 225 225 256 256 289 289 324 324 324 361 361 400 400 441 484 484 529 576 576 676 729 961 number of transfers for each of 363 topologies loss in performance (%)

Loss of performance induced by schedules com- puted with a graph colouring heuristic algorithm

  • For 74% of the topologies Dsatur algorithm does not induce a loss of performance.
  • For 18% of topologies, the performance loss is bellow 10%.
  • For 8% of topologies, the loss of performance is between 10% and 20%.
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  • - 10th International Conference on Telecommunications, ICT’2003, February 23 - 28, 2003, Papeete, Tahiti, French Polynesia --

Conclusion

  • Data exchanges relying on the liquid schedules may be carried out several

times faster compared with topology-unaware schedules.

  • Thanks to introduced theoretical model we considerably reduce the liquid

schedule search space without affecting the solution space.

  • Our method may be applied to applications requiring efficiency in concurrent

continuous transmissions, such as video and voice traffic management, high energy physics data acquisition and reassembling.

  • Liquid scheduling is applicable in wormhole, cut-through networks and can

be useful in wavelength assignment problem in WDM optical networks.

Thank You!

Contact: Emin.Gabrielyan@epfl.ch