## Line Graph: Effective Bandwidth vs. Offloading Ratio ### Overview The graph illustrates the relationship between effective bandwidth (EB) and offloading ratio, distinguishing between memory-bound and compute-bound scenarios. Two regions (Region 1 and Region 2) are highlighted, with distinct trends for memory and compute-bound systems. ### Components/Axes - **Y-Axis (Effective Bandwidth (EB))**: - Labels: `Bg + Bh`, `Bg`, `Bh`, `Bi = Ci / T_comp` - Scale: Linear, with key thresholds marked. - **X-Axis (Offloading Ratio)**: - Labels: `Bh / (Bh + Bg)`, `Bh / Bi` - Scale: Linear, with critical ratios annotated. - **Legend**: - Top-right placement. - Colors: - Blue: Memory-bound - Red: Compute-bound - Red hatch: Region 1 - Green hatch: Region 2 ### Detailed Analysis 1. **Memory-bound Curve (Blue)**: - Starts at `Bg + Bh` (peak) and declines exponentially. - Intersects the `Bg` threshold at `Bh / (Bh + Bg)` offloading ratio. - Crosses `Bi = Ci / T_comp` at `Bh / Bi` offloading ratio. 2. **Compute-bound Curve (Red)**: - Begins at `Bg` and decreases gradually. - Overlaps with the memory-bound curve at `Bh / Bi` offloading ratio. - Flattens near `Bh` threshold. 3. **Regions**: - **Region 1 (Red hatch)**: - Bounded by `Bg` to `Bg + Bh` bandwidth and `0` to `Bh / (Bh + Bg)` offloading ratio. - **Region 2 (Green hatch)**: - Bounded by `Bg` to `Bg + Bh` bandwidth and `Bh / (Bh + Bg)` to `Bh / Bi` offloading ratio. ### Key Observations - The memory-bound system achieves higher bandwidth at low offloading ratios but degrades sharply beyond `Bh / (Bh + Bg)`. - Compute-bound performance remains stable until `Bh / Bi`, after which it declines. - The intersection at `Bh / Bi` suggests a critical transition point between memory and compute bottlenecks. - Region 1 (low offloading) is dominated by memory constraints, while Region 2 (high offloading) shifts to compute limitations. ### Interpretation The graph demonstrates that offloading ratio directly impacts system performance, with memory-bound systems excelling at low offloading and compute-bound systems taking over at higher ratios. The critical thresholds (`Bh / (Bh + Bg)` and `Bh / Bi`) define operational boundaries for optimizing resource allocation. The exponential drop in memory-bound bandwidth highlights diminishing returns beyond a certain offloading point, while the compute-bound curve’s gradual decline suggests scalability limits in computational resources. This analysis is critical for designing hybrid systems that balance memory and compute offloading to maximize effective bandwidth.