papers/hanzo-federated-agents/sections/15-bandwidth-analysis.tex

\section{Bandwidth Analysis}

\label{app:bandwidth}

The per-node bandwidth consumption per round is:

\paragraph{Outgoing bandwidth:}
\begin{equation}
    B_{\text{out}} = k_{\text{peers}} \cdot |B_{\text{compressed}}|
    = k_{\text{peers}} \cdot M \cdot \left(\frac{d}{8} + \frac{d}{g} \cdot 4 + 64\right) \; \text{bytes}.
\end{equation}
For $k_{\text{peers}} = 8$, $M = 100$, $d = 768$, $g = 128$:
$B_{\text{out}} = 8 \times 29{,}472 \approx 236\,\text{KB/round}$.

\paragraph{Incoming bandwidth:}
Each node receives batches from $k_{\text{peers}}$ peers, so
$B_{\text{in}} \approx B_{\text{out}}$.

\paragraph{Gossip propagation:}
A single experience reaches all $N$ nodes within
$T_{\text{prop}} = O(\log N / \log k_{\text{peers}})$ rounds~\cite{demers1987epidemic}.
For $N = 100$, $k = 8$: $T_{\text{prop}} \approx 2.2$ rounds.