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
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
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.