Statistical Approach to NoC Design

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

2. NoC Networklink Networkrouter Module Module Module Computingmodule Module Module Module Module Bus Module Module Module Module Module • Network-on-Chip (NoC) architecture: replace bus-based spaghetti chips with router-based network

3. Problem 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 Jerusalem Ashdod

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

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

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

8. Solution (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 5 5 5 5 5 5 Haifa Tel Aviv Jerusalem Ashdod

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

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 10 10 10 10 10 10 Haifa 50 50 Tel Aviv Jerusalem Ashdod

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 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 2 1 1 1 2 2 1 2 2 2 1 2 1 1 1 1 2 1 2 2 2 1 2 1 2 1 2 1 2 1 1 1 2 2 • Given: • Link l in 3x4 mesh topology • Traffic matrix set S • XY routing • Find load distribution on l l Traffic-load distribution plot (T-plot) T PDF Traffic Matrix Set S Link Load

14. T-Plot (closer view) Gaussian? PDF Worst-case traffic load = 2 99.99% of traffic matrices bring load under 1.6 20% capacity gain Link Load

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.