Statistical Approach Statistical Approach to NoC Designto NoC Design

Itamar Cohen, Ori Rottenstreich and Isaac Keslassy

Technion (Israel)

NoCNoC

Network-on-Chip (NoC) architecture: replace bus-based spaghetti chips with router-based network

Computingmodule

Networkrouter

Networklink

Bus

Module

Module Module

Module Module

Module Module

Module

Module

Module

Module

Module

ProblemProblem

The traffic matrix in NoCs is often-changing and unpredictable

makes NoCs hard to design

Example: Road CapacitiesExample: Road Capacities

We need to design link capacities for Israeli roads

Let’s model the traffic matrices…

Haifa

Tel Aviv

AshdodJerusalem

Road CapacitiesRoad Capacities

Morning peak: most traffic towards Tel Aviv

Haifa

Tel Aviv

AshdodJerusalem

10

10

10

1

1

1

Road CapacitiesRoad Capacities

Morning peak: most traffic towards Tel Aviv

Afternoon peak: most traffic leaving Tel Aviv

Haifa

Tel Aviv

AshdodJerusalem

1

1

1

10

10

10

Good luck after the seminar!

Road CapacitiesRoad Capacities

Morning peak: most traffic towards Tel Aviv

Afternoon peak: most traffic leaving Tel Aviv

Night: no traffic

Haifa

Tel Aviv

AshdodJerusalem

0

0

0

0

0

0

Solution (1): Average-CaseSolution (1): Average-Case Solution (1): average-case

approach i.e. allocate capacity of ~5 for

each link. λ < μ

Problem: traffic jam during many hours, every day Traffic matrix keeps changing

Haifa

Tel Aviv

AshdodJerusalem

5

5

5

5

5

50 10 10 10 0 1 1 1 0 0 0 01 0 0 0 10 0 0 0 0 0 0 01 0 0 0 10 0 0 0 0 0 0 01 0 0 0 10 0 0 0 0 0 0 0

Solution (2): Worst-CaseSolution (2): Worst-Case Solution (2): worst-case

approach i.e. allocate capacity of ~10 for

each link

Haifa

Tel Aviv

AshdodJerusalem

10

10

10

10

10

10

Problem: Sukkot…Problem: Sukkot…

Problem: traffic matrix in Sukkot as a rare event

Solution (3): statistical approach Enough capacity for 99% of

the time Allow for occasional

congestion

Haifa

Tel Aviv

AshdodJerusalem

10

10

10

10

10

10

5050

Back to the NoC worldBack to the NoC world

Similar problems in NoC design process City Shared cache Suburbs Cores Many possible traffic

matrices: writing, reading, etc.

Core

Cache

CoreCore

Statistical Approach to NoC DesignStatistical Approach to NoC Design

Given: Set of traffic matrices Topology Routing Link capacities

Compute congestion guarantee “99% of traffic matrices will receive enough

capacity”

T-Plots in NoCsT-Plots in NoCs

ijT

klT

Traffic Matrix Set S

1 2

2

1

1

2

2

1

2

1

1

2

1 2

2 1

2

1

1

2

2 1

1 2

1

2

1

2

1

2

2 1

1 2

l

T

Given: Link l in 3x4 mesh topology Traffic matrix set S XY routing

Find load distribution on l

Link Load

PDF

Traffic-load distribution plot (T-plot)

14

T-Plot (closer view)T-Plot (closer view)

Gaussian?

Worst-case traffic load = 299.99% of traffic

matrices bring load under 1.6

20%capacity

gain

Link Load

PDF

Computing T-PlotsComputing T-Plots

Theorem: for an arbitrary graph and routing, computing the T-Plot is #P-complete.

#P-complete problems are at least as hard as NP-complete problems. NP: “Is there a solution?” #P: “How many solutions?”

Example: NUCA networkExample: NUCA network NUCA (Non-Uniform Cache Architecture)

Sharing degree 4 Traffic model: each core (cache) may only send/receive traffic

to/from caches (cores) in its sub-network.

Processors

Caches

Processors

NUCA network – Total capacityNUCA network – Total capacity Total capacity required for various Capacity

Allocation (CA) targets. Gain of statistical approach

48%

SummarySummary

Statistical approach Deals with several traffic matrices Can apply to nearly any network

Networks-on-Chip are a new and exciting field Multi-core chips (Intel, AMD) Technion NoC research group:

www.ee.technion.ac.il/matrics

Thank you.Thank you.