papers/lux-consensus/sections/08-evaluation.tex

\section{Evaluation}

\label{sec:evaluation}

\subsection{Experimental Setup}

We evaluated Lux Consensus on a global testnet of 1,000 validators distributed across
five regions: North America (300), Europe (250), Asia-Pacific (300),
South America (100), and Africa (50). Validators ran on commodity hardware (16 cores,
32 GB RAM, 1 Gbps network). Mean inter-region latency: 30ms (intra-region)
to 280ms (NA to APAC).

Byzantine behavior was injected in up to 330 validators (33\%) using worst-case strategies.

\subsection{Throughput Results}

\begin{table}[h]
\centering
\caption{Lux Consensus throughput under various conditions}
\label{tab:throughput}
\begin{tabular}{@{}llll@{}}
\toprule
Configuration & TPS & Median Finality & p99 Finality \\
\midrule
1,000 nodes, 0\% Byzantine & 6,200 & 580ms & 920ms \\
1,000 nodes, 10\% Byzantine & 5,800 & 620ms & 980ms \\
1,000 nodes, 33\% Byzantine & 4,500 & 650ms & 1,100ms \\
500 nodes, 33\% Byzantine & 4,100 & 510ms & 850ms \\
100 nodes, 33\% Byzantine & 3,800 & 380ms & 620ms \\
2,000 nodes, 0\% Byzantine & 5,900 & 710ms & 1,150ms \\
2,000 nodes, 33\% Byzantine & 4,200 & 780ms & 1,280ms \\
\bottomrule
\end{tabular}
\end{table}

The DAG structure enables parallelism: non-conflicting transactions are queried simultaneously,
and throughput scales with DAG width rather than being limited by a single chain.

\subsection{Finality Latency Distribution}

Finality latency follows a log-normal distribution, with median 650ms and p99 1,100ms under
33\% Byzantine conditions. The tail arises from cross-region RTT variance.

\subsection{Comparison with Alternative Protocols}

\begin{table}[h]
\centering
\caption{Protocol comparison at 1,000 validators}
\label{tab:comparison}
\begin{tabular}{@{}lllll@{}}
\toprule
Protocol & TPS & Finality & Msg/Decision & Byzantine Limit \\
\midrule
Lux & 4,500 & 650ms & $O(kn)$ & $f < n/3$ \\
HotStuff & 1,200 & 300ms & $O(n)$ & $f < n/3$ \\
Tendermint & 800 & 500ms & $O(n^2)$ & $f < n/3$ \\
Ethereum 2.0 & 350 & 12,000ms & $O(n^2)$ & $f < n/3$ \\
Bitcoin (PoW) & 7 & 3,600,000ms & $O(n)$ & $f < n/2$ \\
Narwhal-Tusk & 130,000$^\dagger$ & 2,000ms & $O(n)$ & $f < n/3$ \\
\bottomrule
\end{tabular}
\smallskip
\newline $^\dagger$Narwhal throughput includes mempool optimization; finality requires additional ordering layer.
\end{table}

Lux achieves the highest throughput among comparable BFT protocols. HotStuff achieves
lower single-decision latency but is limited by its leader-based architecture and
view-change overhead under Byzantine leaders.

\subsection{Impact of Byzantine Strategies}

\begin{itemize}
\item \textbf{Always-minority}: Byzantine nodes respond with the minority color.
Impact: 10--15\% throughput reduction, 20\% latency increase.
\item \textbf{Eclipsing}: Byzantine nodes attempt to route queries to themselves.
Impact: Ineffective due to randomized stake-weighted sampling.
\item \textbf{Preference cycling}: Byzantine nodes cycle preferences each round.
Impact: 25\% throughput reduction, 40\% latency increase at 33\% Byzantine.
\item \textbf{Selective delay}: Byzantine nodes delay responses to maximize timeout rate.
Impact: 15\% throughput reduction; adaptive threshold compensates.
\end{itemize}

\subsection{Scalability}

We measured throughput as a function of validator count from 100 to 5,000 nodes:

\begin{table}[h]
\centering
\caption{Scalability with increasing validator count (0\% Byzantine)}
\label{tab:scalability}
\begin{tabular}{@{}llll@{}}
\toprule
Validators & TPS & Median Finality & Messages/Decision \\
\midrule
100 & 5,200 & 320ms & 2,000 \\
500 & 5,800 & 480ms & 10,000 \\
1,000 & 6,200 & 580ms & 20,000 \\
2,000 & 5,900 & 710ms & 40,000 \\
5,000 & 5,400 & 920ms & 100,000 \\
\bottomrule
\end{tabular}
\end{table}

Throughput remains stable because the sample size $k$ is constant regardless of $n$. Latency
increases logarithmically with $n$ due to convergence time $O(\log n)$.

\subsection{Fault Recovery}

Network partitions of 5--30 seconds were simulated by dropping cross-region messages.
After partition healing, the network recovered within $2\Delta + O(\beta)$ rounds. No safety
violations were observed across 10,000 partition events.

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