plot: extend batch-scaling curves with saturated-throughput ceiling

Beyond a mapping's SIP capacity (16/C) the throughput plateaus: extra
users run in waves at the saturated rate, they are not un-runnable. Draw
a dashed horizontal extension at the ceiling so 1-kv-per-cube (cap 2)
reads as saturating, not stopping, at B=2. Caption updated.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

docs/report/1H-codesign-paper/sections/05-gqa.tex

@@ -271,10 +271,13 @@ long-context batch sweep is 2H work (\S\ref{sec:future}).
 \si{\micro\second}) versus the number of concurrent decode users on one SIP,
 each user on a disjoint CUBE group. Each mapping scales almost linearly with
 $B$ up to its SIP capacity $16/C$---\textsf{1-kv-per-cube} saturates at two
-users, \textsf{8-kv-per-cube} at sixteen. The dense mapping reaches the
-highest throughput; the spread mapping is latency-optimal but
-capacity-limited. Concurrent users overlap to within
-\SI{3}{}--\SI{5}{\percent} of the single-user latency.}
+users, \textsf{8-kv-per-cube} at sixteen. Solid segments are measured
+concurrent runs; the dashed extensions are the saturated-throughput ceiling
+beyond capacity, where further users run in waves at that sustained rate
+(so the SIP is full, not idle). The dense mapping reaches the highest
+ceiling; the spread mapping is latency-optimal but capacity-limited.
+Concurrent users overlap to within \SI{3}{}--\SI{5}{\percent} of the
+single-user latency.}
 \label{fig:gqa-batch}
 \end{figure}
 

docs/sweeps/plot_scripts/plot_batch_scaling.py

@@ -29,6 +29,7 @@ def main():
     contexts = sorted({int(r["S_kv"]) for r in rows})
     fig, axes = plt.subplots(1, len(contexts), figsize=(6.5 * len(contexts), 4.5),
                              squeeze=False)
+    xmax = max(int(r["B"]) for r in rows)  # largest SIP capacity (= 16)
     for col, S in enumerate(contexts):
         ax = axes[0][col]
         for m in MODES:
@@ -40,8 +41,15 @@ def main():
             if not pts:
                 continue
             xs, ys = zip(*pts)
+            # Measured: concurrent users up to the SIP capacity 16/C.
             ax.plot(xs, ys, marker="o", color=MODE_COLOR[m],
                     label=MODE_LABEL[m])
+            # Beyond capacity the SIP is full: extra users run in waves at
+            # the saturated rate, so throughput plateaus. Draw that ceiling
+            # as a dashed extension (projected, not concurrently measured).
+            if xs[-1] < xmax:
+                ax.plot([xs[-1], xmax], [ys[-1], ys[-1]],
+                        linestyle="--", color=MODE_COLOR[m], alpha=0.55)
             ax.annotate(f"{ys[-1]:.2f}", (xs[-1], ys[-1]),
                         textcoords="offset points", xytext=(4, 4), fontsize=8)
         ax.set_title(f"S_kv = {S // 1024}K")