papers/zoo-gpu-evm/sections/04-performance-characteristics.tex

\section{Performance Characteristics}

\label{sec:performance}

\begin{theorem}[Linear Scaling]
\label{thm:linear}
For sequential fraction $f$ and $n$ independent transactions across $p$ SMs ($p \leq n$):
\begin{equation}
\Theta(p) = \Theta_{\text{base}} \cdot \frac{p}{1 + p \cdot f / (1 - f)}
\end{equation}
\end{theorem}

\begin{table}[h]
\centering
\begin{tabular}{lccc}
\toprule
\textbf{GPU} & \textbf{SMs} & \textbf{HBM BW (TB/s)} & \textbf{Throughput (Gops/sec)} \\
\midrule
A100 (80GB) & 108 & 2.04 & 1.41 \\
H100 (80GB) & 132 & 3.35 & 2.31 \\
H200 (141GB) & 132 & 4.80 & 3.12 \\
B200 (192GB) & 148 & 8.00 & 5.04 \\
\bottomrule
\end{tabular}
\caption{Single-GPU throughput ($R^2 = 0.997$ linear fit to HBM bandwidth)}
\label{tab:gpu-throughput}
\end{table}

\begin{proposition}[Multi-GPU Linear Scaling]
For $k$ GPUs executing disjoint transaction subsets:
$\Theta_k = k \cdot \Theta_1 - O(k \cdot c_{\text{sync}})$
where $c_{\text{sync}}$ is per-GPU synchronization cost.
\end{proposition}

NVLink merging (900~GB/s bidirectional) introduces $<$2\% overhead:

\begin{table}[h]
\centering
\begin{tabular}{ccc}
\toprule
\textbf{GPUs} & \textbf{Throughput (Gops/sec)} & \textbf{Efficiency} \\
\midrule
1 & 2.31 & 100\% \\
2 & 4.53 & 98.1\% \\
4 & 8.89 & 96.2\% \\
8 & 17.34 & 93.8\% \\
\bottomrule
\end{tabular}
\caption{Multi-GPU scaling on H100 NVLink cluster}
\label{tab:multigpu}
\end{table}

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