O1TURN : Near-Optimal Worst-Case Throughput Routing for 2D-Mesh Networks

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O1TURN Near-Optimal Worst-Case Throughput
Routing for 2D-Mesh Networks

• DaeHo Seo, Akif Ali, WonTaek Lim
• Nauman Rafique, Mithuna Thottethodi
• School of Electrical and Computer Engineering
• 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?

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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
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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 T(K2) T(K2) T(2K)
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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
  T(K2) 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

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Outline

• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and QA

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Outline

• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and QA

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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

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TD-Method Example
Unit of worst-case throughput packets / node /
cycle

• Max Channel Load 0.5
• Worst-case Throughput (1 / 0.5) 2

• Max Channel Load 1
• Worst-case Throughput (1 / 1) 1

A -gt B -gt D A -gt C -gt D
Traffic Src -gt Dst A -gt D D -gt A
A -gt B -gt D
D -gt C -gt A
D -gt B -gt A D -gt C -gt A
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Outline

• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and QA

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O1TURN routing algorithm

• Orthogonal 1 TURN routing
• There is no U-TURN gt Orthogonal
• At most 1 turn gt 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

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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

N 0.5
(K - N) 0.5
XY routing
YX routing
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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
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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

Recall Even Radix Opt 1 Odd Radix Opt (1
- 1 / K2)
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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 4 x 4 2D MESH 4 x 4 2D MESH 4 x 4 2D MESH
DOR ROMM O1TURN
Average case throughput 1 1.113 1.136
8 x 8 2D MESH 8 x 8 2D MESH 8 x 8 2D MESH 8 x 8 2D MESH
Average case throughput 1 1.180 1.188
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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

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Outline

• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and QA

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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

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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

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Delay Analysis

• 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

VCs / PC DOR DOR O1TURN O1TURN
VCs / PC VC allocation SW allocation VC allocation SW allocation
4 17 14 14 14
8 20 16 17 16
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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
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Outline

• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and QA

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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)

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Simulation Results

• 4 x 4 2D MESH Uniform Random Traffic Pattern

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Simulation Results

• 4 x 4 2D MESH Matrix Transpose Traffic Pattern
• One of the worst-case traffic pattern for DOR

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Simulation Results

• 4 x 4 2D MESH Bit Complement Traffic Pattern
• Already balanced traffic pattern

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Simulation Results

• 4 x 4 2D MESH HOT SPOT Traffic Pattern
• 2 nodes have 20 of traffic

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Simulation Results

• Delay penalty of adaptive routing
• How the complexity of router implementation
  affects on latency
• Hot Spot Traffic Pattern

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Outline

• Background of interconnection network
• O1TURN routing algorithm
• O1TURN router implementation
• Simulation Results
• Conclusion and QA

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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

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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

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Q A