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NoC Routing Algorithms

Fernando Moraes 9/abril/2014

Roteamento: Classificações

Estático

DinâmicoCritérioMomento da realização doroteamento Multicast

UnicastCritérioNúmero de destinatários

Fonte

Centralizado

Distribuído

CritérioLocal onde as decisões deroteamento são tomadas Máquina de estado

TabelaCritérioImplementação baseada em

DeterminísticoCritérioAdaptatividade

Regressivo

Progressivo

Não mínimo

Mínimo

Parcial

Completo

CritérioProgressividade

CritérioMinimalidade

CritérioNúmero de caminhos

Adaptativo

Técnicas de roteamento Livelock e Deadlock

•  Livelock –  Quando uma mensagem trafega permanentemente pela rede

sem chegar ao seu destino

•  Deadlock –  Ocorre quando existe uma dependência cíclica de recursos na

rede e as mensagens são paralisadas

Cab

2

A

3

B C

4Cbc

D

1

Ccd

Cda

X

1 3

4

2

(a) (b) (c)

Roteamento: Exemplo de deadlock Núcleo Núcleo Núcleo

Núcleo Núcleo Núcleo











Roteamento: Evitando o deadlock

•  Deve-se evitar o surgimento de ciclos na rede

Ciclos na malha 2-D




Roteamento: Evitando o deadlock •  Soluções •  Roteamento XY

–  Proíbe qualquer curva do tipo Y-para-X

–  É determinístico

•  Roteamento West-first –  Proibe apenas as voltas em

direção ao oeste –  É parcialmente adaptativo

10

The Turn Model •  Turn-based model to avoid deadlock

•  Possible turns = {NW, NE, SW, SE, WN, WS, EN, ES}

•  Disallow >= 2 turns

•  XY routing only allows turns from X to Y {EN, ES, WN, WS}

•  West-first routing prohibits turns to west {NW, SW} –  Offers full adaptiveness to paths that route east –  Not fair to all paths

Roteamento: Algoritmo XY

(0,0)

(7,7)

1 2

3

4

•  Deterministic •  All messages from Src to Dest will traverse the same path •  Common example: Dimension Order Routing (DOR)

–  Message traverses network dimension by dimension –  Aka XY routing

•  Cons: –  Eliminates any path diversity provided by topology –  Poor load balancing

•  Pros: –  Simple and inexpensive to implement –  Deadlock free

West-first routing algorithm •  The prohibited turns are the two to the West

–  if XT ≤ XS, packets are routed deterministically, as in the XY algorithm, (paths 1 and 2)

–  if XT > XS packets can be routed adaptively in East, North or South directions (paths 3 and 4)

1 2

3

4

(0,0)

(7,7)

(3) e (4) – caminhos adapta5vos (1) e (2) – caminhos determinís5cos

obstáculos

13

West First não mínimo •  Route a packet first west if necessary, and then adaptively south , east, and

north. •  Both minimal and non-minimal paths are shown. •  [Dally and Seitz] proof show that a routing algorithm is deadlock free if the

channels in the interconnection network can be numbered so that the algorithm routes every packet along channels with strictly decreasing numbers.

North-Last routing algorithm •  The prohibited turns are the two when traveling

North –  - if YT ≤ YS packets are routed deterministically (paths 2 and 3) –  - if YT > YS packets can be routed adaptively in West, East, or

South directions (paths 1 and 4)

1 2

3

4

(0,0)

(7,7)


obstáculos

Negative-First routing algorithm •  packets are routed first in negative directions,

i.e., to the North or to the West directions –  if (XT≤XS and YT≥YS) or (XT≥XS and YT≤YS) packets are

deterministically routed - paths 1 /3 –  all other conditions allow some form of adaptive routing - paths

4 / 2

1 2

3

4

(0,0)

(7,7)


obstáculos

Odd-Even Wormhole Routing

•  In the previous methods, at least half of S/D pairs are restricted to having one minimal path, while full adaptiveness is provided to the others

–  Unfair! •  Odd-even turn routing offers solution:

–  Even column: no EN or ES turn –  Odd column: no NW or SW turn

Odd-Even Routing

Relative destination

Possible turns

NE SE, WN

NW SW, EN

SE NE, WS

SW NW, ES

even col

odd col

S

D

even odd even

D

S

even odd even when routing east and dest is in even col…

(don’t go into dest. col unless row matches)

(don’t go N/S in odd col)

D

S

even odd even

S

D

even odd even

when routing west…

On average, 2 routing options once for every 5 routes

(1.2 opt/route)

Valiant’s Routing Algorithm

•  To route from s to d, randomly choose intermediate node d’ –  Route from s to d’ and

from d’ to d. •  Randomizes any traffic

pattern –  All patterns appear to be

uniform random –  Balances network load

•  Non-minimal

d’

d

s

Minimal Oblivious

•  Valiant’s: Load balancing comes at expense of significant hop count increase –  Destroys locality

•  Minimal Oblivious: achieve some load balancing, but use shortest paths –  d’ must lie within minimum

quadrant –  6 options for d’ –  Only 3 different paths

d

s

Rotamento Hamiltoniano

•  Algoritmo de roteamento Hamiltoniano –  Livre de deadlock –  Simples de se obter uma versão determinística a partir da

versão adaptativa –  Suporte a algoritmos multicast

•  Caminho Hamiltoniano –  Caminho acíclico no qual é possível atingir todos os nodos de

um grafo passando apenas uma vez em cada nodo –  Roteadores rotulados de 0 a N-1 –  Caminho segue a ordem crescente ou decrescente dos

rótulos

Serviço de comunicação com roteamento diferenciado

•  Versão não-mínima parcialmente adaptativa

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

Serviço de comunicação com roteamento diferenciado

•  Versão mínima determinística

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

Collective communication service

•  Dual-path multicast algorithm –  Originally proposed for Multicomputers (1994) –  2D mesh topology –  Hamiltonian routing algorithm

•  Multicast messages –  Parallel search algorithms –  Blocked matrix multiplication –  Cache coherence protocol –  Control messages

Collective communication service

•  Dual-path multicast algorithm –  Targets set divided in 2 sub-sets –  A message copy sent to each sub-set

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

7 8 11 12

3 1 0

> 5

Ascending

< 5

Descending

27

Routing Adaptivity in Function of Traffic ■  Congestion Signaling

–  Single bit (congested/not congested) –  Bus (free slots, congestion levels)

Leste

Oeste

Norte

Sul

cong

cong

cong

cong

Fully Adaptive Routing with VCs •  Can achieve fully adaptive routing with VCs

–  Problem: minimize required number of VCs –  Use of symetrical routing algorithms

c

VIRTUAL CHANNEL

c

c

c

PHYSICAL CHANNEL

CROSSBAR 9x9EAST

OUTPUT CHANNELS

INPUT CHANNELS

WEST

NORTH

SOUTH

LOCAL

EAST WEST NORTH SOUTH LOCAL

29

Replicated Channels x Virtual Channels

Switch Control

Crossbar 10x10North

North

South

East

West

Local

Input buffers

Router

South

East

West

Local

Switch Control

Crossbar 10x10

North2

North1

South2

South1

East2

East1

West2

West1

Local2

Local1

North2

North1

South2

South1

East2

East1

West2

West1

Local2

Local1

Input buffers

Router

X

2 physical channels 2 virtual channels

•  Smaller area: same crossbar, mux/demux suppressed

30


•  Latency/throughput evaluation –  Mesh 4x4 –  XY –  Packet switching –  Virtual channel router: 16-flit deep buffer/virtual channel –  Replicated channel router: 16-flit deep buffer/physical

channel

00 10 20 30

01 11 21 31

02 12 22 32

03 13 23 33

•  Each source transmits 500 packets/257-flits size

•  Packets are injected in the NoC at the channel rate

31


•  Average latency/throughput packet

•  Replicated channels when compared to virtual channels –  reduce 47.3% the average latency –  doubles the average throughput

•  Expected result, since the internal NoC bandwidth doubles

32


•  FPGA area consumption

•  12% area reduction for a single 5 ports router •  15% area reduction for a 4x4 mesh NoC

33


•  ASIC area consumption

■  Replicated channels –  Alternative to virtual channels –  Smaller logic area and increased performance –  Power dissipation due to the switching activity in wires:

future work

■  4% area reduction for a single 5 ports router ■  6.4% area reduction for a 4x4 mesh NoC

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