Download - Statistical Approach to NoC Design
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Statistical Approach Statistical Approach to NoC Designto NoC Design
Itamar Cohen, Ori Rottenstreich and Isaac Keslassy
Technion (Israel)
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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
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ProblemProblem
The traffic matrix in NoCs is often-changing and unpredictable
makes NoCs hard to design
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Example: Road CapacitiesExample: Road Capacities
We need to design link capacities for Israeli roads
Let’s model the traffic matrices…
Haifa
Tel Aviv
AshdodJerusalem
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Road CapacitiesRoad Capacities
Morning peak: most traffic towards Tel Aviv
Haifa
Tel Aviv
AshdodJerusalem
10
10
10
1
1
1
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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!
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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
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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
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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
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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
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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
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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”
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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
Traffic-load distribution plot (T-plot)
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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
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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?”
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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
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NUCA network – Total capacityNUCA network – Total capacity Total capacity required for various Capacity
Allocation (CA) targets. Gain of statistical approach
48%
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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
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Thank you.Thank you.