f2b: regenerate CDF from production trace (1.3M sessions on dash0)

Pulls 456 (rank%, cum%) sample points from the raw production trace at
dash0:/home/admin/cpfs/wjh/ali-trace/trace-glm5.1-formatted/051315-051317.jsonl,
cached locally so the figure is reproducible without ssh access. Sampled
anchors match the precomputed summary exactly:
  top 1% = 46.5%, top 5% = 66.5%, top 10% = 74.6%
plus newly readable points:
  top 25% = 87.5%, top 50% = 96.0%

Workload characterization is now consistent with the production
distribution rather than the small replay subset. Replay window CDF kept
as an overlay to show the same hockey-stick shape on the data §5 actually
uses.

- analysis/characterization/data/production_session_skew_cdf.json: cached
  sample points (29 KB), so the figure rebuilds locally
- scripts/plot_session_skew_cdf.py: now plots from the cache + replay raw
- MEETING.md / PAPER_OUTLINE.md: revert numbers to production trace,
  add top-25%/50% data points

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

MEETING.md

@@ -26,7 +26,7 @@ L = Λ · N · W_turn(L)        # agentic, T_human≈0
 | | 数据 | 图 |
 |---|---|---|
 | KV reuse 几乎只在 session 内 | intra 93.2% / cross 5.7% / shared 1.1% | ![](figs/f2a_reuse_topology.png) |
-| Session 极度偏斜 | replay 上 top 1% / 5% / 10% = 24% / 62% / 76% input mass（production 全 trace 更陡，top 1% = 46.5%） | ![](figs/f2b_session_skew.png) |
+| Session 极度偏斜 | production trace 上 top 1% / 5% / 10% / 25% / 50% = **46.5% / 66.5% / 74.6% / 87.5% / 96.0%** input mass | ![](figs/f2b_session_skew.png) |
 | 单请求 KV footprint 已经很大 | p99 = 11.8 GiB ≈ H20 12% | ![](figs/f2c_kv_footprint_cdf.png) |
 
 理论 APC 上界 = intra-session 79.6% / any-session 80.3%，差 <1pp。**任何不 affinity 的调度都丢绝大部分 reuse。**
@@ -58,7 +58,7 @@ agentic 平均请求 33.6k token 需 3.3GB KV；4P+4D / 6P+2D 在 agentic regime
 | sticky | **20.3s** | 55.4s | **34.6s** |
 | unified | **10.3s** | 37.7s | **18.0s** |
 
-机制：top 5% 的 session 占 ~62% input 量、且 hot session 数量远多于 instance 数（8 个），sticky 的 hash 绑定让 **每个 worker 都自己承接一份 hot session**，median worker 也被拖慢。Unified 用 LMetric fallback 把 cold/new session 重路由到非 hot worker，保留 7/8 worker 的速度。系统 p90 由大多数请求决定，所以 unified 几乎 2x 快。
+机制：production trace 上 top 1% 的 session 占 46.5% input 量、且 hot session 数量远多于 instance 数（8 个），sticky 的 hash 绑定让 **每个 worker 都自己承接一份 hot session**，median worker 也被拖慢。Unified 用 LMetric fallback 把 cold/new session 重路由到非 hot worker，保留 7/8 worker 的速度。系统 p90 由大多数请求决定，所以 unified 几乎 2x 快。
 
 ---
 

PAPER_OUTLINE.md

@@ -48,7 +48,7 @@ Agentic workload 与 chatbot 的三个本质差异：
 
 - **Multi-turn, programmatic continuation**：每个 turn 由上一个 turn 的 tool-call 结果触发，没有人类 think-time
 - **Prefill-dominated**：input/output token ratio **75x**，98% 计算在 prefill 阶段（chatbot 为 1-10x）
-- **Skewed sessions**：在 replay trace 上 top 1% session 贡献 **24.3%** input token，top 5% **61.9%**，top 10% **75.8%**（vs uniform 1/5/10%）；production 全 trace（1.3M session）skew 更极端，top 1% 达 46.5%
+- **Skewed sessions**（来自 Qwen3 production trace，n=1.3M session / 2.1M req / 7200s）：top 1% 贡献 **46.5%** input token，top 5% **66.5%**，top 10% **74.6%**，top 25% **87.5%**，top 50% **96.0%** —— 半数 session 几乎占满全部 input mass
 
 平均 session 长度 TBD turn、TBD 输入 token；p99 单请求 KV 占用 **11.49 GiB**（H20 96GB HBM 的 12%）。
 
@@ -68,7 +68,7 @@ Trace 上 KV reuse 的分解：
 
 ![F2a Reuse topology — intra 93.2% / cross 5.7% / shared 1.1%](figs/f2a_reuse_topology.png)
 
-![F2b Session skew CDF — top 1% = 24.3%, top 5% = 61.9%, top 10% = 75.8% input mass (replay trace)](figs/f2b_session_skew.png)
+![F2b Session input-token mass CDF — production trace top 1%/5%/10%/25%/50% = 46.5%/66.5%/74.6%/87.5%/96.0% (replay window overlaid for sanity)](figs/f2b_session_skew.png)
 
 ![F2c KV footprint CDF — p99 = 11.8 GiB ≈ 12% of H20](figs/f2c_kv_footprint_cdf.png)
 
@@ -137,7 +137,7 @@ Round-robin 和 load-aware routing（如 LMetric, OSDI'26）最大化 instance
 | `unified` (affinity + LMetric fallback) | **10.3 s** | 37.7 s | **18.0 s** |
 | `lmetric` | 14.0 s | 31.3 s | 24.8 s |
 
-机制：top 5% session 占 ~62% input mass，hot session 数量远大于 instance 数（8）；sticky 的 hash 绑定让 **每个 worker 都自己承接一份 hot session**，median worker 也被拖慢到 20s 量级。unified 用 LMetric fallback 把 cold/new session 重路由到非 hot worker，保留 7/8 worker 的速度。系统 p90 由大多数请求决定，所以 unified 在 e2e p90 上 ~2x 快于 sticky。
+机制：production trace 上 top 1% session 占 46.5% input mass、top 5% 占 66.5%，hot session 数量远大于 instance 数（8）；sticky 的 hash 绑定让 **每个 worker 都自己承接一份 hot session**，median worker 也被拖慢到 20s 量级。unified 用 LMetric fallback 把 cold/new session 重路由到非 hot worker，保留 7/8 worker 的速度。系统 p90 由大多数请求决定，所以 unified 在 e2e p90 上 ~2x 快于 sticky。
 
 **注意**：hotspot ratio (max/median) 单独看是误导性的 —— sticky 的 2.73 比 unified 的 3.67 *低*，但因为 sticky 的 median 也高（20.3s vs unified 的 10.3s），系统整体更慢。一个有用的 §3.3 sub-finding：**hot pin failure 必须用 per-worker absolute latency 衡量，不能用 normalized ratio**。
 

scripts/plot_session_skew_cdf.py

@@ -1,12 +1,17 @@
 #!/usr/bin/env python3
 """Plot a CDF of cumulative input-token mass by session rank.
 
-Reads a JSONL trace (chat_id, session_id, input_length, ...), aggregates
+Primary curve is the *production* trace
-per-session input_length, sorts sessions descending by total, and plots
+(``/home/admin/cpfs/wjh/ali-trace/trace-glm5.1-formatted/051315-051317.jsonl``
-cumulative fraction of input-token mass vs session-rank percentile.
+on dash0), which has 1.3 M sessions across 2.1 M records over a 7200 s
+window. Because the full raw trace is not co-located with this repo, we
+sample 456 (rank_pct, cum_pct) points on dash0 and cache the result in
+``analysis/characterization/data/production_session_skew_cdf.json``. Any
+top-K%% mass figure can be read off the resulting curve.
 
-The figure replaces the previous discrete top-1%/5%/10% bars with a
+The replay-trace CDF (``traces/w600_r0.0015_st30.jsonl``, n=274) is
-continuous curve so any percentile can be read off directly.
+overlaid for sanity — the replay window samples a thin slice of the head
+so its top-1%% is lower, but the shape is preserved.
 """
 from __future__ import annotations
 
@@ -19,66 +24,85 @@ import matplotlib.pyplot as plt
 import numpy as np
 
 
-def load_session_input_tokens(trace_path: Path) -> dict[str, int]:
+def load_replay_cdf(trace_path: Path) -> tuple[np.ndarray, np.ndarray, int]:
     totals: dict[str, int] = defaultdict(int)
     with trace_path.open() as f:
         for line in f:
             row = json.loads(line)
             totals[row["session_id"]] += int(row["input_length"])
-    return dict(totals)
+    n = len(totals)
+    sorted_vals = np.sort(np.array(list(totals.values())))[::-1]
+    cum = np.cumsum(sorted_vals) / sorted_vals.sum()
+    rank_pct = np.arange(1, n + 1) / n * 100
+    return rank_pct, cum * 100, n
+
+
+def load_production_cdf(
+    cache_path: Path,
+) -> tuple[np.ndarray, np.ndarray, int, dict[str, float]]:
+    d = json.loads(cache_path.read_text())
+    samples = d["samples"]
+    xs = np.array([s["rank_pct"] for s in samples])
+    ys = np.array([s["cum_pct"] for s in samples])
+    return xs, ys, d["n_sessions"], d["anchors_check"]
 
 
 def main() -> None:
     parser = argparse.ArgumentParser()
     parser.add_argument(
-        "--trace",
+        "--replay-trace",
         default="traces/w600_r0.0015_st30.jsonl",
-        help="JSONL trace path",
     )
     parser.add_argument(
-        "--out",
+        "--prod-cache",
-        default="figs/f2b_session_skew.png",
+        default="analysis/characterization/data/production_session_skew_cdf.json",
-        help="Output figure path",
     )
+    parser.add_argument("--out", default="figs/f2b_session_skew.png")
     args = parser.parse_args()
 
-    session_totals = load_session_input_tokens(Path(args.trace))
+    prod_x, prod_y, prod_n, prod_anchors = load_production_cdf(Path(args.prod_cache))
-    n_sessions = len(session_totals)
+    replay_rank_pct, replay_cum_pct, replay_n = load_replay_cdf(Path(args.replay_trace))
-    sorted_vals = np.sort(np.array(list(session_totals.values())))[::-1]
-    cum = np.cumsum(sorted_vals) / sorted_vals.sum()
-    rank_pct = np.arange(1, n_sessions + 1) / n_sessions * 100
 
-    marks = [1, 5, 10, 25, 50]
+    fig, ax = plt.subplots(figsize=(9, 5.5))
-    mark_idx = [int(np.ceil(n_sessions * p / 100)) - 1 for p in marks]
 
-    fig, ax = plt.subplots(figsize=(8, 5))
+    ax.plot(
-    ax.plot(rank_pct, cum * 100, color="#2f6fab", lw=2.2,
+        prod_x, prod_y,
-            label="cumulative input-token mass")
+        color="#c44e52", lw=2.4,
-    ax.plot([0, 100], [0, 100], color="#999", ls="--", lw=1,
+        label=f"production trace (n={prod_n:,} sessions, 456-pt sampled)",
-            label="uniform reference (y = x)")
+    )
 
-    for p, i in zip(marks, mark_idx):
+    annotate_pts = [1.0, 5.0, 10.0, 25.0, 50.0]
-        y = cum[i] * 100
+    for p in annotate_pts:
-        ax.scatter([p], [y], color="#c44e52", zorder=5, s=40)
+        y = float(np.interp(p, prod_x, prod_y))
+        ax.scatter([p], [y], color="#c44e52", s=55, zorder=5)
         ax.annotate(
-            f"top {p}% → {y:.1f}%",
+            f"top {p:g}% → {y:.1f}%",
             xy=(p, y),
-            xytext=(p + 2, y - 5),
+            xytext=(p + 2.5, y - 6),
-            fontsize=9,
+            fontsize=10,
-            color="#333",
+            color="#7a1d1d",
         )
 
+    ax.plot(
+        replay_rank_pct, replay_cum_pct,
+        color="#2f6fab", lw=1.6,
+        alpha=0.85,
+        label=f"replay window (n={replay_n} sessions, raw CDF)",
+    )
+
+    ax.plot(
+        [0, 100], [0, 100],
+        color="#888", ls="--", lw=1,
+        label="uniform reference (y = x)",
+    )
+
     ax.set_xlim(0, 100)
     ax.set_ylim(0, 102)
     ax.set_xlabel("Session rank percentile (top → bottom by input-token mass)")
     ax.set_ylabel("Cumulative % of input-token mass")
-    ax.set_title(
+    ax.set_title("Session input-token mass CDF — Qwen3 production trace")
-        f"Session input-token mass CDF "
-        f"(n={n_sessions} sessions, "
-        f"total={sorted_vals.sum() / 1e6:.1f} M tokens)"
-    )
     ax.grid(True, alpha=0.3)
-    ax.legend(loc="lower right", framealpha=0.9)
+    ax.legend(loc="lower right", framealpha=0.92, fontsize=9)
 
     out_path = Path(args.out)
     out_path.parent.mkdir(parents=True, exist_ok=True)