f2b: replace top-1/5/10% bars with full CDF; align all docs to replay-trace numbers

The previous f2b_session_skew.png was a 3-bar chart (top 1/5/10%) computed
from the production trace summary (which is not present locally, only its
precomputed JSON). The new figure is a continuous CDF of cumulative
input-token mass vs session rank percentile, generated directly from the
replay trace traces/w600_r0.0015_st30.jsonl so any percentile is readable.

Headline numbers update accordingly:
  replay trace (n=274 sessions): top 1% = 24.3%, top 5% = 61.9%, top 10% = 75.8%
  production trace (n=1.3M):     top 1% = 46.5%, top 5% = 66.5%, top 10% = 74.6%

Both show extreme skew well above the y=x uniform reference; the replay
trace is less extreme at top-1% because n=274 makes that bucket only
~3 sessions. We standardize §2/§3 narrative on the replay-trace numbers
so motivation matches §5 evaluation; production numbers kept as a side
note for context.

- scripts/plot_session_skew_cdf.py: reproducible figure generator
- MEETING.md / PAPER_OUTLINE.md: update narrative + caption

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 | top 1% = 46.5% input mass | ![](figs/f2b_session_skew.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) |
 | 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 1% 的 session 占 46.5% input 量、且 hot session 数量多于 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：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。
 
 ---
 

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**：top 1% session 贡献 **46.5%** input token 量
+- **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%
 
 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 — top 1% = 46.5% input mass](figs/f2b_session_skew.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)
 
 ![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 1% session 占 46.5% input mass，hot session 数量 ≥ 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：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。
 
 **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

@@ -0,0 +1,90 @@
+#!/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
+per-session input_length, sorts sessions descending by total, and plots
+cumulative fraction of input-token mass vs session-rank percentile.
+
+The figure replaces the previous discrete top-1%/5%/10% bars with a
+continuous curve so any percentile can be read off directly.
+"""
+from __future__ import annotations
+
+import argparse
+import json
+from collections import defaultdict
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def load_session_input_tokens(trace_path: Path) -> dict[str, 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)
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--trace",
+        default="traces/w600_r0.0015_st30.jsonl",
+        help="JSONL trace path",
+    )
+    parser.add_argument(
+        "--out",
+        default="figs/f2b_session_skew.png",
+        help="Output figure path",
+    )
+    args = parser.parse_args()
+
+    session_totals = load_session_input_tokens(Path(args.trace))
+    n_sessions = len(session_totals)
+    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]
+    mark_idx = [int(np.ceil(n_sessions * p / 100)) - 1 for p in marks]
+
+    fig, ax = plt.subplots(figsize=(8, 5))
+    ax.plot(rank_pct, cum * 100, color="#2f6fab", lw=2.2,
+            label="cumulative input-token mass")
+    ax.plot([0, 100], [0, 100], color="#999", ls="--", lw=1,
+            label="uniform reference (y = x)")
+
+    for p, i in zip(marks, mark_idx):
+        y = cum[i] * 100
+        ax.scatter([p], [y], color="#c44e52", zorder=5, s=40)
+        ax.annotate(
+            f"top {p}% → {y:.1f}%",
+            xy=(p, y),
+            xytext=(p + 2, y - 5),
+            fontsize=9,
+            color="#333",
+        )
+
+    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(
+        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)
+
+    out_path = Path(args.out)
+    out_path.parent.mkdir(parents=True, exist_ok=True)
+    fig.savefig(out_path, dpi=150, bbox_inches="tight")
+    print(f"wrote {out_path}")
+
+
+if __name__ == "__main__":
+    main()