Performance Analysis of 2D and 3D Bufferless NoCs Using Markov Chain Models
Abstract
:1. Introduction
2. Related Work
- It estimates expected latency (number of hops) between individual nodes, as well as the average for a given topology and traffic pattern, more accurately than current state-of-the-art static models.
- It raises the level of abstraction from cycle-accurate simulation, reducing the estimation time by at least four orders of magnitude, from minutes and hours to milliseconds.
3. Proposed Methodology
3.1. Topology Modeling
3.2. Traffic Modeling
- Given a NoC topology, determine node distance classes and therefore the minimum number of Markov Chains.
- Fill each Markov chain transition matrix with the transition probabilities.
- Use Equations (1)–(3) to obtain the expectations for each source–destination node pair.
- Use Equation (4) to obtain the mean expected latency for the entire network based on the traffic pattern.
4. Experimental Results
4.1. Deflection Probability Simulation
4.2. Average Latency Analysis
4.3. Model Accuracy Evaluation
5. Conclusions and Future Work
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
NoC | Network-on-Chip |
URT | Uniform Random Traffic |
BCT | Bit-Complement Traffic |
ADM | Average Distance Model |
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Topology | γ | Absolute Error URT/BCT | Percentage Error (%) URT/BCT | Normalized Error (%) URT/BCT |
---|---|---|---|---|
4 × 4 × 4 | 0.002 | 0.0945/0.0296 | 2.48/0.49 | 2.48/0.49 |
0.01 | 0.0824/0.1005 | 2.11/1.66 | 2.16/1.67 | |
0.04 | 0.0434/0.5588 | 1.04/7.76 | 1.13/9.31 | |
0.06 | 0.1403/1.3748 | 3.34/16.60 | 3.68/23.24 | |
0.08 | 0.127 | 2.83 | 3.33 | |
8 × 4 × 2 | 0.002 | 0.2385/0.0299 | 5.32/0.42 | 5.36/0.43 |
0.01 | 0.2006/0.0695 | 4.36/0.92 | 4.51/0.99 | |
0.04 | 0.208 | 4.42 | 4.68 | |
0.06 | 0.14 | 2.8 | 3.15 | |
0.08 | 0.306 | 5.36 | 6.88 | |
8 × 8 × 1 | 0.002 | 0.29/0.0379 | 5.47/0.47 | 5.54/0.47 |
0.01 | 0.35/0.4073 | 6.46/4.74 | 6.61/5.09 | |
0.04 | 0.49 | 7.65 | 9.26 |
Topology/Traffic Pattern | Average Distance | Topology Regularity (R) | ADM | Proposed | Range ADM | Range Proposed | |
---|---|---|---|---|---|---|---|
4 × 4 × 4/URT | 3.8 | 1 | 0.04 | 0.09 | 0.12 | 33% | 75% |
8 × 4 × 2/URT | 4.44 | 1.1667 | 0.04 | 0.06 | 0.08 | 50% | 75% |
8 × 8 × 1/URT | 5.33 | 1.41667 | 0.015 | 0.02 | 0.06 | 25% | 33% |
4 × 4 × 4/BCT | 6 | 1 | 0.03 | 0.05 | 0.08 | 37.5% | 62.5% |
8 × 4 × 2/BCT | 7 | 1.1667 | 0.015 | 0.018 | 0.04 | 37.5% | 45% |
8 × 8 × 1/BCT | 8 | 1.41667 | 0.009 | 0.011 | 0.025 | 36% | 44% |
Topology/Traffic Pattern | R | |||
---|---|---|---|---|
4 × 4 × 4/URT | 3.8 | 1 | 3.8 | 0.12 |
8 × 4 × 2/URT | 4.44 | 1.1667 | 3.8 | 0.08 |
8 × 8 × 1/URT | 5.33 | 1.41667 | 3.76 | 0.06 |
4 × 4 × 4/BCT | 6 | 1 | 6 | 0.08 |
8 × 4 × 2/BCT | 7 | 1.1667 | 6 | 0.04 |
8 × 8 × 1/BCT | 8 | 1.41667 | 5.65 | 0.025 |
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Tatas, K. Performance Analysis of 2D and 3D Bufferless NoCs Using Markov Chain Models. Technologies 2022, 10, 27. https://doi.org/10.3390/technologies10010027
Tatas K. Performance Analysis of 2D and 3D Bufferless NoCs Using Markov Chain Models. Technologies. 2022; 10(1):27. https://doi.org/10.3390/technologies10010027
Chicago/Turabian StyleTatas, Konstantinos. 2022. "Performance Analysis of 2D and 3D Bufferless NoCs Using Markov Chain Models" Technologies 10, no. 1: 27. https://doi.org/10.3390/technologies10010027