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This paper discusses the use of a statistical approach to design a Network-on-Chip (NoC) architecture, which replaces traditional bus-based designs with router-based networks. It addresses the challenge of designing NoCs with unpredictable and ever-changing traffic matrices. The approach is demonstrated through examples and T-Plots analysis. The paper also highlights the application of this approach to the design of road link capacities, showcasing its versatility. The Statistical Approach to NoC Design is a valuable resource for researchers and engineers in the field. (476 characters)
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Statistical Approach to NoC Design Itamar Cohen, Ori Rottenstreich andIsaac Keslassy Technion (Israel)
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
Problem The traffic matrix in NoCs is often-changing and unpredictable makes NoCs hard to design
Example: Road Capacities We need to design link capacities for Israeli roads Let’s model the traffic matrices… Haifa Tel Aviv Jerusalem Ashdod
Road Capacities Morning peak: most traffic towards Tel Aviv 1 10 1 10 1 10 Haifa Tel Aviv Jerusalem Ashdod
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
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
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
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
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
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
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”
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
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
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?”
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
NUCA network – Total capacity • Total capacity required for various Capacity Allocation (CA) targets. Gain of statistical approach 48%
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
