1. Statistical Approach to NoC Design Itamar Cohen, Ori Rottenstreich and Isaac Keslassy Technion (Israel)

2. NoC  Network-on-Chip (NoC) architecture: replace bus-based spaghetti chips with router-based network Computing module Network router Network link Bus

3. Problem The traffic matrix in NoCs is often-changing and unpredictable  makes NoCs hard to design The traffic matrix in NoCs is often-changing and unpredictable  makes NoCs hard to design

4. Example: Road Capacities  We need to design link capacities for Israeli roads  Let’s model the traffic matrices… Haifa Tel Aviv Ashdod Jerusalem

5. Road Capacities  Morning peak: most traffic towards Tel Aviv Haifa Tel Aviv Ashdod Jerusalem 10 1 1 1

6. Road Capacities  Morning peak: most traffic towards Tel Aviv  Afternoon peak: most traffic leaving Tel Aviv Haifa Tel Aviv Ashdod Jerusalem 1 1 1 10 Good luck after the seminar!

7. Road Capacities  Morning peak: most traffic towards Tel Aviv  Afternoon peak: most traffic leaving Tel Aviv  Night: no traffic Haifa Tel Aviv Ashdod Jerusalem 0 0 0 0 0 0

8. Solution (1): Average-Case  Solution (1): average-case approach  i.e. allocate capacity of ~5 for each link. λ < μλ < μ  Problem: traffic jam during many hours, every day  Traffic matrix keeps changing Haifa Tel Aviv Ashdod Jerusalem 5 5 5 5 5 5

9. Solution (2): Worst-Case  Solution (2): worst-case approach  i.e. allocate capacity of ~10 for each link Haifa Tel Aviv Ashdod Jerusalem 10

10. 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 Ashdod Jerusalem 10 50

11. Back to the NoC world  Similar problems in NoC design process  City  Shared cache  Suburbs  Cores  Many possible traffic matrices: writing, reading, etc. Core Cache Core

12. Statistical Approach to NoC Design Given:  Set of traffic matrices  Topology  Routing  Link capacities Compute congestion guarantee  “99% of traffic matrices will receive enough capacity”

13. T-Plots in NoCs Traffic Matrix Set S 12 2 1 1 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2 21 1 2 1 2 1 2 1 2 21 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. 14 T-Plot (closer view) Gaussian? Worst-case traffic load = 2 99.99% of traffic matrices bring load under 1.6 20% capacity gain Link Load PDF

15. Computing 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?”

16. Example: 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

17. NUCA network – Total capacity  Total capacity required for various Capacity Allocation (CA) targets. Gain of statistical approach 48%

18. Summary  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

19. Thank you.