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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
64 lines
3.1 KiB
TeX
64 lines
3.1 KiB
TeX
\section{Concurrent Connection Scalability}
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%% ============================================================================
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\subsection{Throughput vs.\ Connection Count}
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\begin{table}[h]
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\centering
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\caption{Aggregate throughput (messages/sec) by concurrent connection count}
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\label{tab:conns}
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\begin{tabular}{lrrrrr}
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\toprule
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\textbf{Protocol} & \textbf{100} & \textbf{1,000} & \textbf{10,000} & \textbf{100,000} & \textbf{Scaling} \\
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\midrule
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\rowcolor{luxblue!10}
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ZAP & 4,180K & 4,120K & 3,940K & 3,610K & 0.86$\times$ \\
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FlatBuffers & 3,810K & 3,690K & 3,280K & 2,740K & 0.72$\times$ \\
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Cap'n Proto & 3,120K & 2,940K & 2,510K & 1,920K & 0.62$\times$ \\
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gRPC & 2,450K & 2,180K & 1,420K & 680K & 0.28$\times$ \\
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QUIC & 2,100K & 1,980K & 1,610K & 1,180K & 0.56$\times$ \\
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Protobuf-mux & 1,280K & 1,040K & 620K & 310K & 0.24$\times$ \\
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JSON-RPC & 890K & 640K & 280K & 92K & 0.10$\times$ \\
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\bottomrule
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\end{tabular}
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\end{table}
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The ``Scaling'' column shows the ratio of throughput at 100K connections to throughput at 100 connections. ZAP retains 86\% of its throughput at 100K connections, compared to 28\% for gRPC and 10\% for JSON-RPC.
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\begin{theorem}[Scalability Factor]
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The throughput degradation $D(c)$ at $c$ connections is:
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\[
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D(c) = \frac{T(c)}{T(c_0)} = \frac{1}{1 + \alpha \cdot c \cdot a_{\text{msg}} / H}
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\]
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where $\alpha$ is the GC overhead coefficient ($\sim$0.3 for Go), $a_{\text{msg}}$ is bytes allocated per message, and $H$ is the heap target. For ZAP with $a_{\text{msg}} = 0$: $D(c) = 1/(1 + 0) = 1$ (linear scaling, bounded only by kernel socket overhead). For gRPC with $a_{\text{msg}} = 576$: $D(100000) = 1/(1 + 0.3 \cdot 100000 \cdot 576 / 4\text{MB}) = 0.19$, consistent with the measured 0.28 (kernel overhead accounts for the difference).
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\end{theorem}
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\subsection{Per-Connection Overhead}
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\begin{table}[h]
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\centering
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\caption{Memory overhead per connection (steady-state)}
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\label{tab:connmem}
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\begin{tabular}{lrrr}
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\toprule
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\textbf{Protocol} & \textbf{KB/conn} & \textbf{100K total} & \textbf{Primary cost} \\
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\midrule
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\rowcolor{luxblue!10}
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ZAP & 8.2 & 800 MB & 8 KB arena buffer \\
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FlatBuffers & 12.4 & 1.21 GB & Buffer + vtable cache \\
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Cap'n Proto & 14.8 & 1.45 GB & Segment allocator \\
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QUIC & 28.3 & 2.77 GB & TLS state + streams \\
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gRPC & 64.2 & 6.28 GB & HTTP/2 state + buffers \\
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Protobuf-mux & 89.7 & 8.78 GB & Muxer + pubsub + routing \\
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JSON-RPC & 16.1 & 1.58 GB & Read/write buffers \\
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\bottomrule
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\end{tabular}
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\end{table}
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ZAP's 8.2 KB per connection consists of a single 8 KB pre-allocated arena buffer (the \texttt{buf[8192]} from the protocol specification \cite{zapwire}). gRPC requires 64.2 KB per connection due to HTTP/2 flow control windows, HPACK header tables, and per-stream buffers. Protobuf-mux's 89.7 KB includes protocol multiplexer state, pubsub topic subscriptions, and peer routing tables.
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At 100K connections, ZAP uses 800 MB vs.\ gRPC's 6.28 GB---a 7.9$\times$ reduction that determines whether a node can maintain full mesh connectivity on commodity hardware (16 GB RAM).
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%% ============================================================================
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