An Analytical Model for Worst-case Reorder Buffer Size of Multi-path Minimal Routing NoCs Gaoming Du 1, Miao Li 1, Zhonghai Lu 2, Minglun Gao 1, Chunhua Wang 1 1 Hefei University of Technology, Anhui Province, China 2 KTH Royal Institute of Technology, Sweden

Outline 1 Motivation 2 Concepts 3 Method 4 Evaluation

Multi-path Routing NoC Prospects –Minimize network congestion and packet delay –Improve the load balance –Reduce power consumption –Fault tolerant routing Problem –Out of order P1 P2 P3 P4

disadvantage The area overhead. Low hardware utilization. With worst-case analysis, it can reduce the reorder buffer size with proper flow splitting configuration effectively. Out of Order [1] S. Murali, D. Atienza, L. Benini, and G. De Micheli, “A method for routing packets across multiple paths in NoCs with In-Order delivery and Fault- Tolerance gaurantees,” VLSI Design, vol. 2007, pp. 1–11, Solution 1: flow control –Prospects Easy to control Less hardware overhead –Side effect More congestion Longer packet delay Out of order packets Packet in need

Out of Order Solution 2: reorder buffer –Prospects Less on chip congestion Less re-arbitration time –Side effect Area overhead [11] M. Daneshtalab, M. Ebrahimi, P. Liljeberg, J. Plosila, and H. Tenhunen, “Memory- efficient on-chip network with adaptive interfaces,” Computer-Aided Design of ntegrated Circuits and Systems, IEEE Transactions on, vol. 31, no. 1, pp. 146–159, Out of order packets Packet in need

Reorder Buffer Size Traditional approaches –By experience –No formal method –Too pessimistic Our target –A general analytical model for worst-case reorder buffer size –A method to diminish the reorder buffer size Traffic splitting proportion

Outline 1 Motivation 2 Concepts 3 Method 4 Evaluation

NoC Architecture Assumption –Non-intersecting sub-flows –Sub-flow number: 2 –Delay bounds for sub-flows already known

Network Calculus Basics Results Assume: Linear arrival curve Latency-Rate (LR) server The delay bound is

Outline 1 Motivation 2 Concepts 3 Method 4 Evaluation

General Analysis S rb Size of reorder buffer D 1 Packet delay in path f 1 D 2 Packet delay in path f 2 △ t Packet injection interval Ideal case –No contention

Worst-case Reorder Buffer Size Definition 1

NC Model for Multi-path Routing Step 1 –Non-intersecting sub-flow identification –Traffic split proportion calculation

NC Model for Multi-path Routing Step 2 –Equivalent Service Curve (ESC) Calculation R: equivalent minimum service rate T: equivalent maximum processing latency [2] G. Du, C. Zhang, Z. Lu, A. Saggio, and M. Gao, “Worst-case performance analysis of 2-d mesh nocs using multi-path minimal routing,” in ISSS+CODES 2012.

NC Model for Multi-path Routing Step 3 –Calculation of Worst-case Reorder Buffer Size.

Algorithm Step 1 Path identification Step 2 ESC calculation Step 3 Worst case reorder buffer size calculation

Outline 1 Motivation 2 Concepts 3 Method 4 Evaluation

Evaluation Experiments targets – △ D ~ ? –↓ ? Experiments methods –Synthetic pattern –Industry pattern

Flow typearrival curveService curve Target flow Contention flows Experiments Setup f(1,16) f(2,12) f(3,8) f(6,11)

Delta Delay VS. Buffer Size The bigger the delay difference, the larger the reorder buffer size To balance the traffic & proper path configuration Maximum reduction: 56.99%

Full Traffic Splitting Target flow: full traffic splitting The more balanced traffic, the smaller the reorder buffer size Average improvement of 57.04%

Simulation Setup –P x =0.1 Results –No packet loss –Fully covered by analytical results

Industry Case Shorter long-path –Max hops: 3 Less number of reorder buffers –Number of reorder buffers: 3

Node 4, 6, and 7 Mapping 1 –Less worst-case reorder buffer size –Shorter path delays Node 4 Node 6 Node 7

Total Size Mapping 2 –Reduction of maximum 36.50% (76 packets) –Average 29.20% (61packets) –Minimum 22.12% (46 packets)

Summary Our analytical model – Reduce worst case reorder buffer size To choose proper sub-flows pairs To alter traffic splitting proportion –Explore mapping effects Reorder buffer size Future work –To extend to more general cases

Conclusion 2 nd priority initiatives Evaluate whether offer DT store more margin is possible Together with other strong brands, communicate “Unilever” company brand more Optimize our promotion pack allocation policy Optimize island display in Northern area, pay more attention to season differences Add more POSMs to more outlets. Using multiple ways to communicate with consumers Thanks for your time