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O1TURN : Near-Optimal Worst-Case Throughput Routing for 2D-Mesh Networks
DaeHo Seo, Akif Ali, WonTaek LimNauman Rafique, Mithuna Thottethodi
School of Electrical and Computer EngineeringPurdue University
June 08 2005 Purdue University 2
Motivation
• New routing algorithm for 2D Mesh networks : O1TURN
• Why 2D Mesh networks?– Important class of interconnection
network– Natural topology for on-chip
network– Many Applications
• “yet another routing algorithm”?
June 08 2005 Purdue University 3
Routing Algorithms: Objectives
• Maximize throughput and minimize latency
• O1TURN satisfies all design goals
IDEAL DOR ROMM VALIANT MIN-ADAPTIVE
Average case throughput X X X
Worst case Throughput X X ?
Minimal # of network hops X X X X
Low complexity router X X X
June 08 2005 Purdue University 4
Challenges
• Intuition: Path flexibility, Load Balancing, Throughput correlated
• Prior results – Throughput : Increasing path flexibility [SPAA 2002]
• May not improve worst case throughput, even decrease• Likely to improve average case throughput
– Latency : Increasing path flexibility may increase router complexity
IDEAL DOR ROMM VALIANT MIN-ADAPTIVE
Average case throughput X X X
Worst case Throughput X X ?
Minimal # of network hops X X X X
Low complexity router X X X
# of Paths ? 1 Θ(K’2) Θ(K2) Θ(2K’)
June 08 2005 Purdue University 5
Contributions
• Develop new routing algorithm : O1TURN• Throughput
– Better than DOR / ROMM for worst-case throughput• Near optimal worst-case throughput for 2D Mesh
– Captures most of the “opportunity” with limited path flexibility for average case throughput
• O1TURN (with 2 paths) as good as ROMM (with Θ(K’2) paths)
• Latency– Router Implementation for O1TURN
• Comparable complexity as simple DOR router
• Key Point :– Partition the delay-critical circuitry
• O1TURN is minimal : One goal trivially satisfied
June 08 2005 Purdue University 6
Outline
• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and Q&A
June 08 2005 Purdue University 7
Outline
• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and Q&A
June 08 2005 Purdue University 8
Background
• Packet Switched, 2D mesh network– Each packet independently routed
• Terminology– Network Radix = k in kxk network (NOT Degree)
• Simplifying assumptions for this talk – One packet crosses a link in one cycle– Square mesh networks (K x K)– K is even (K = 2p)
• Analytical method for throughput analysis– TD Method [Towles and Dally, SPAA 2002]– Worst-case throughput = (Maximum channel load)-1
– Given permutation and (oblivious) routing algorithm• Find maximum channel load
– Given only (oblivious) routing algorithm• Find permutation that causes maximum channel load
June 08 2005 Purdue University 9
TD-Method Example
A B
C D
Traffic :Src -> DstA -> DD -> A
A -> B -> D A -> B -> DA -> C -> D
A B
C D
1
11
1
D -> C -> A
A B
C D
0.5
0.5
0.5 0.5
0.5
0.5
0.50.5
D -> B -> AD -> C -> A
• Max Channel Load = 1• Worst-case Throughput = (1 / 1) = 1
• Max Channel Load = 0.5• Worst-case Throughput = (1 / 0.5) = 2
Unit of worst-case throughput = packets / node / cycle
June 08 2005 Purdue University 10
Outline
• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and Q&A
June 08 2005 Purdue University 11
O1TURN routing algorithm
• Orthogonal 1 TURN routing– There is no U-TURN => Orthogonal– At most 1 turn => 1TURN
• Use 2 routes– At most 2 minimal, 1-turn routes in
2D MESH (XY, YX)– Two routing algorithms (XY routing,
YX routing)– With same probability
S
D1
2
June 08 2005 Purdue University 12
O1TURN routing algorithm
• Claim: Maximum channel load of O1TURN is K / 2• Proof: Two sources of load contributions
– # of nodes of left side of channel by XY routing– # of nodes of right side of channel by YX routing
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C
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CN * 0.5 (K - N) * 0.5
XY routing YX routing
June 08 2005 Purdue University 13
Optimal Worst Case Throughput
• Maximum channel load = K / 2– Worst-case Throughput = 2 / K by TD
Method
• Consider a permutation where 100% packets cross bisection– Throughput (X) bounded when bisection links
saturated– X * (K2 / 2) = K – X = 2 / K packets / node / cycle
• When K is odd, O1TURN is within (1 / K2) of optimal worst-case throughput
K x K mesh
June 08 2005 Purdue University 14
0
0.2
0.4
0.6
0.8
1
2 4 6 8 10 12 14 16
Network Radix (k)
No
rma
lize
d T
hro
ug
hp
ut
OPTIMAL
DOR
ROMM
O1TURN
Worst-case Throughput Trends
• Worst-case channel load as network size changes– Normalized to Optimal worst-case throughput– Worst case throughput of DOR, ROMM degrades with K
RecallEven Radix : Opt * 1Odd Radix : Opt * (1 - 1 / K2)
June 08 2005 Purdue University 15
Average Case Analysis
• Extension of TD method [B.Towles et.al., SPAA 2003] – Examine randomly chosen permutations– Harmonic means of worst-case throughput of various
permutations– 1 M random permutations
• O1TURN shows the better or the same average case throughput
4 x 4 2D MESH
DOR ROMM O1TURN
Average case throughput 1 1.113 1.136
8 x 8 2D MESH
Average case throughput 1 1.180 1.188
June 08 2005 Purdue University 16
O1TURN Summary
• Near optimal worst-case Throughput– By TD method– Optimal for even K – Approaches Optimal for large, odd K
• Average case throughput– Better than DOR and comparable to ROMM
• Minimal # of network hops
– O1TURN is minimal routing
June 08 2005 Purdue University 17
Outline
• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and Q&A
June 08 2005 Purdue University 18
Base Router Implementation
• Base Router : Pipelined Virtual Channel Router– 4 Stages : Routing, Virtual Channel allocation, Switch allocation,
Crossbar & Physical Channel transfer– One control block controls all virtual channels– Critical Stage : Virtual Channel allocation stage
VC ID
INJECT
X+
X-
Y+
Y-
EJECT
5 X 5CROSSBAR
Routing AlgorithmVC Allocation
Switch Allocation
CREDITS OUT (ALL PCs and VCs) CREDITS IN (ALL PCs and VCs)
June 08 2005 Purdue University 19
O1TURN Router Implementation
• O1TURN Router– Separate Virtual Channels into two virtual networks (VN)– One VN for XY routing, the other for YX routing– Deadlock prevention in each independent VN due to DOR
VC ID
INJECT
X+
X-
Y+
Y-
EJECT
5 X 5CROSSBAR
Routing (YX)VC Allocation
CREDITS OUT (ALL PCs and YX VCs)CREDITS IN
(ALL PCs and YX VCs)
Routing (XY)VC Allocation
Switch Allocation
CREDITS IN (ALL PCs and XY VCs)
CREDITS OUT (ALL PCs and XY VCs)
June 08 2005 Purdue University 20
• Existing router delay models for pipelined routers – Peh and Dally [HPCA 2001]
• Based on the logical effort method – [I.Sutherland, B. Sproull, 1999]– FO4 unit
– Comparable complexity as DOR router
Delay Analysis
VCs / PC DOR O1TURN
VC allocation SW allocation VC allocation SW allocation
4 17 14 14 14
8 20 16 17 16
June 08 2005 Purdue University 21
O1TURN Summary
• Near Optimal Worst case Throughput
• Good average case Throughput• Minimal Network Hops
• Low Complexity Router Implementation– Comparable complexity as
DOR router
IDEAL O1TURN
Average case throughput X X
Worst case Throughput X X
Minimal # of network hops X X
Low complexity router X X
June 08 2005 Purdue University 22
Outline
• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and Q&A
June 08 2005 Purdue University 23
Evaluation Method
• Modified Popnet network Simulator [L. Shang, 2003]• 4x4 2D MESH (8x8 in paper)• Full-duplex, bidirectional links• 8 VCs per PC• 5 Flits per packet• 500 K cycles• Synthetic Traffic: Uniform Random, BC, MT, HOT SPOT• Compared with existing routing algorithms
– Oblivious routing algorithms (DOR, ROMM)– Adaptive routing algorithm (DUATO)
June 08 2005 Purdue University 24
Simulation Results
• 4 x 4 2D MESH – Uniform Random Traffic Pattern
0
50
100
150
200
0 0.2 0.4 0.6 0.8 1
Throughput (flits / node / cycle)
Av
era
ge
La
ten
cy
(c
yc
le)
DOR
ROMM
O1TURN
DUATO
June 08 2005 Purdue University 25
Simulation Results
• 4 x 4 2D MESH – Matrix Transpose Traffic Pattern– One of the worst-case traffic pattern for DOR
0
50
100
150
200
0 0.2 0.4 0.6 0.8 1
Throughput (flits / node / cycle)
Ave
rag
e L
aten
cy (c
ycle
) DOR
ROMM
O1TURN
DUATO
June 08 2005 Purdue University 26
Simulation Results
• 4 x 4 2D MESH – Bit Complement Traffic Pattern– Already balanced traffic pattern
0
50
100
150
200
0 0.2 0.4 0.6 0.8 1
Throughput (flits / node / cycle)
Ave
rag
e L
aten
cy (c
ycle
) DOR
ROMM
O1TURN
DUATO
June 08 2005 Purdue University 27
Simulation Results
• 4 x 4 2D MESH – HOT SPOT Traffic Pattern– 2 nodes have 20% of traffic
0
50
100
150
200
0 0.2 0.4 0.6 0.8 1
Throughput (flits / node / cycle)
Av
era
ge
La
ten
cy
(c
yc
le)
DOR
ROMM
O1TURN
DUATO
June 08 2005 Purdue University 28
0
500
1000
1500
2000
0 0.2 0.4 0.6 0.8 1
Throughput (flits / node / cycle)
Av
era
ge
La
ten
cy
(F
O4
)
DOR
ROMM
O1TURN
DUATO
Simulation Results
• Delay penalty of adaptive routing– How the complexity of router implementation affects on latency– Hot Spot Traffic Pattern
June 08 2005 Purdue University 29
Outline
• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and Q&A
June 08 2005 Purdue University 30
Related Work
• Routing algorithms– Valiant [L.G.Valiant et.al, ACM 1981]– ROMM [T.Nesson et.al, ACM 1995]– DUATO [J.Duato et.al, 1993]
• Partitioned router implementation– Mad Postman [Jesshope et.al, ISCA 1989]– PFNF [Upadhyay et.al, 1997]
• Analysis methods– Worst-case [B.Towles et.al, 2002]– Throughput centric [B.Towles et.al, 2003]– Delay model [L.S.Peh et.al, HPCA 2001]
June 08 2005 Purdue University 31
Conclusion
• Goals– Good average case throughput– Good or Optimal worst case throughput– Minimal # of network hops– Low complexity router implementation
• O1TURN – Provide near optimal worst case throughput– Provide the better or the same average case throughput
compared with existing routing algorithms– Minimal # of network hops– Simple router implementation : comparable with DOR router– Satisfy all performance aspects