An Analytical Model for Worst-case Reorder BufferSize of Multi-path Minimal Routing NoCs

Gaoming Du1, Miao Li 1, Zhonghai Lu2, Minglun Gao1, Chunhua Wang1

1 Hefei University of Technology, Anhui Province, China

2 KTH Royal Institute of Technology, Sweden

2014.09.17

Outline

1Motivation2 Concepts 3Method 4Evaluation

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Multi-path Routing NoC

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1 2 3

4 5 6

7 8 9

R

R f 1

f2

• Prospects– Minimize network congestion

and packet delay– Improve the load balance– Reduce power consumption – Fault tolerant routing

• Problem– Out of order

P1P1P2P2P3P3P4P4

disadvantage

The area overhead.Low hardware utilization.

With worst-case analysis, it can reduce the reorder buffer size with proper flow splitting configuration effectively.

Out of Order

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[1] S. Murali, D. Atienza, L. Benini, and G. De Micheli, “A method for routing packets across multiple paths in NoCs with In-Order delivery and Fault- Tolerance gaurantees,” VLSI Design, vol. 2007, pp. 1–11, 2007.

• Solution 1: flow control– Prospects

• Easy to control• Less hardware overhead

– Side effect• More congestion• Longer packet delay

Out of order packets

Packet in need

P4 P3

NI

RB

(b)

...

R1

R4

B

LUTR2

R3

P1P2

...

...

Out of Order

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• Solution 2: reorder buffer– Prospects

• Less on chip congestion• Less re-arbitration time

– Side effect • Area overhead

[11] M. Daneshtalab, M. Ebrahimi, P. Liljeberg, J. Plosila, and H. Tenhunen, “Memory-efficient on-chip network with adaptive interfaces,” Computer-Aided Design of ntegrated Circuits and Systems, IEEE Transactions on, vol. 31, no. 1, pp. 146–159, 2012.

Out of order packets

Packet in need

Reorder Buffer Size

• Traditional approaches– By experience– No formal method– Too pessimistic

• Our target– A general analytical model for worst-case reorder

buffer size– A method to diminish the reorder buffer size

• Traffic splitting proportion

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Outline

1Motivation2 Concepts 3Method 4Evaluation

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NoC Architecture

• Assumption– Non-intersecting sub-flows– Sub-flow number: 2– Delay bounds for sub-flows already known

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1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

PEReorder Buffer

NI

Counter

Packet IDLook-up

Table

110

0Packet In

Packet Out

Network Calculus Basics Results

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Assume: Linear arrival curve

Latency-Rate (LR) server

)()( TtRt

)()( trbt

Rb

TD

V

t

)(t)(t

b

r

R

T

βF : α F*: α*

input outputB

D

The delay bound is

Outline

1Motivation2 Concepts 3Method 4Evaluation

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General Analysis

• Srb Size of reorder buffer• D1 Packet delay in path f1

• D2 Packet delay in path f2

• △ t Packet injection interval

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1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

• Ideal case– No contention

Worst-case Reorder Buffer Size

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Definition 1

1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

NC Model for Multi-path Routing

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tR*1 tR1

1S

tR*2 tR2

2S

t1 t*1

t1

t2 t*2

t2

Taffic Splitting Traffic

Convergence

Tag Flow

1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

• Step 1– Non-intersecting sub-flow identification

– Traffic split proportion calculation

NC Model for Multi-path Routing

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tR*1 tR1

1S

tR*2 tR2

2S

t1 t*1

t1

t2 t*2

t2

Taffic Splitting Traffic

Convergence

Tag Flow

1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

• Step 2

– Equivalent Service Curve (ESC) Calculation

• R: equivalent minimum service rate

• T: equivalent maximum processing latency [2] G. Du, C. Zhang, Z. Lu, A. Saggio, and M. Gao, “Worst-case performance analysis of

2-d mesh nocs using multi-path minimal routing,” in ISSS+CODES 2012.

NC Model for Multi-path Routing

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tR*1 tR1

1S

tR*2 tR2

2S

t1 t*1

t1

t2 t*2

t2

Taffic Splitting Traffic

Convergence

Tag Flow

1 2 3

5 6 7

9 10 11

4

8

12

13 14 15 16

f (1,16)

f2 f1

• Step 3

– Calculation of Worst-case Reorder Buffer Size.

Algorithm

Step 1

Path identification

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Step 2

ESC calculation

Step 3

Worst case reorder buffer size calculation

Outline

1Motivation2 Concepts 3Method 4Evaluation

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Evaluation

• Experiments targets– △ D ~ ?– ↓ ?

• Experiments methods– Synthetic pattern– Industry pattern

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Flow type arrival curve Service curve

Target flow

Contention flows

Experiments Setup

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1 2 3 4

65

14 15 16

1211109

87

13

f(1,16) f(2,12) f(3,8)

f(6,11)65

14 15 16

1211109

87

13

f1

f2 f4f3

1 2 3 4f1

f4f3 f2

1 2 1612843

f2

f1

1 5 161514139

f(1,16)

f(2,12) f(3,8) f(6,11)

Delta Delay VS. Buffer Size

• The bigger the delay difference, the larger the reorder buffer size

• To balance the traffic & proper path configuration

• Maximum reduction: 56.99%2014-09-17

Full Traffic Splitting

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• Target flow: full traffic splitting

• The more balanced traffic, the smaller the reorder buffer size

• Average improvement of 57.04%

Simulation

• Setup– Px =0.1

• Results– No packet loss

– Fully covered by analytical results

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Industry Case

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• Shorter long-path– Max hops: 3

• Less number of reorder buffers– Number of reorder buffers: 3

Node 4, 6, and 7

• Mapping 1– Less worst-case reorder buffer size– Shorter path delays

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Node 4 Node 6 Node 7

Total Size

• Mapping 2– Reduction of maximum 36.50% (76 packets)

– Average 29.20% (61packets)

– Minimum 22.12% (46 packets)2014-09-17

Summary

• Our analytical model– Reduce worst case reorder buffer size

• To choose proper sub-flows pairs• To alter traffic splitting proportion

– Explore mapping effects• Reorder buffer size

• Future work– To extend to more general cases

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Conclusion

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Thanks for your time

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