## Description

Fixes the throughput metrics script and introduces new visibility into backlog bottlenecks and priority distribution.

### Changes
- **Throughput Fixes**: Resolved a `ReferenceError` where `isMaintainer` was not correctly scoped, fixed a malformed license header, and added a new metric for `issue_arrival_rate_per_day` to enable growth-vs-closure analysis.
- **Backlog Bottlenecks**: Introduced `bottlenecks.ts` to identify "Zombie" issues (no activity > 30 days) and "Hot" issues (high activity).
- **Priority Distribution**: Introduced `priority_distribution.ts` to track the count of open issues by priority level (P0-P3).

### Impact
These metrics will provide the necessary data to confirm if the repository is experiencing systemic backlog growth (Arrival Rate > Throughput) and help identify which segments of the backlog require urgent triage.

tools/gemini-cli-bot/metrics/scripts/throughput.ts

@@ -2,13 +2,33 @@
  * @license
  * Copyright 2026 Google LLC
  * SPDX-License-Identifier: Apache-2.0
- *
- * @license
  */
 
 import { GITHUB_OWNER, GITHUB_REPO } from '../types.js';
 import { execSync } from 'node:child_process';
 
+/**
+ * Checks if the author association belongs to a maintainer.
+ */
+const isMaintainer = (assoc: string) =>
+  ['MEMBER', 'OWNER', 'COLLABORATOR'].includes(assoc);
+
+interface Item {
+  association: string;
+  date: number;
+}
+
+/**
+ * Calculates items per day over the sample period.
+ */
+const calculateThroughput = (items: Item[]) => {
+  if (items.length < 2) return 0;
+  const first = items[0].date;
+  const last = items[items.length - 1].date;
+  const days = (last - first) / (1000 * 60 * 60 * 24);
+  return days > 0 ? items.length / days : items.length;
+};
+
 try {
   const query = `
   query($owner: String!, $repo: String!) {
@@ -25,68 +45,64 @@ try {
           closedAt
         }
       }
+      arrival: issues(last: 100) {
+        nodes {
+          createdAt
+        }
+      }
     }
   }
   `;
   const output = execSync(
     `gh api graphql -F owner=${GITHUB_OWNER} -F repo=${GITHUB_REPO} -f query='${query}'`,
-    { encoding: 'utf-8' },
-  );
+    { encoding: 'utf-8', stdio: ['ignore', 'pipe', 'ignore'] },
+  ).trim();
   const data = JSON.parse(output).data.repository;
 
-  const prs = data.pullRequests.nodes
+  const prs: Item[] = data.pullRequests.nodes
     .map((p: { authorAssociation: string; mergedAt: string }) => ({
       association: p.authorAssociation,
       date: new Date(p.mergedAt).getTime(),
     }))
-    .sort((a: { date: number }, b: { date: number }) => a.date - b.date);
+    .sort((a: Item, b: Item) => a.date - b.date);
 
-  const issues = data.issues.nodes
+  const issues: Item[] = data.issues.nodes
     .map((i: { authorAssociation: string; closedAt: string }) => ({
       association: i.authorAssociation,
       date: new Date(i.closedAt).getTime(),
     }))
-    .sort((a: { date: number }, b: { date: number }) => a.date - b.date);
+    .sort((a: Item, b: Item) => a.date - b.date);
 
-  const isMaintainer = (assoc: string) =>
-    ['MEMBER', 'OWNER', 'COLLABORATOR'].includes(assoc);
+  const arrivalDates = data.arrival.nodes
+    .map((i: { createdAt: string }) => new Date(i.createdAt).getTime())
+    .sort((a: number, b: number) => a - b);
 
-  const calculateThroughput = (
-    items: { association: string; date: number }[],
-  ) => {
-    if (items.length < 2) return 0;
-    const first = items[0].date;
-    const last = items[items.length - 1].date;
+  const calculateArrivalRate = (dates: number[]) => {
+    if (dates.length < 2) return 0;
+    const first = dates[0];
+    const last = dates[dates.length - 1];
     const days = (last - first) / (1000 * 60 * 60 * 24);
-    return days > 0 ? items.length / days : items.length; // items per day
+    return days > 0 ? dates.length / days : dates.length;
   };
 
   const prOverall = calculateThroughput(prs);
   const prMaintainers = calculateThroughput(
-    prs.filter((i: { association: string; date: number }) =>
-      isMaintainer(i.association),
-    ),
+    prs.filter((i) => isMaintainer(i.association)),
   );
   const prCommunity = calculateThroughput(
-    prs.filter(
-      (i: { association: string; date: number }) =>
-        !isMaintainer(i.association),
-    ),
+    prs.filter((i) => !isMaintainer(i.association)),
   );
 
   const issueOverall = calculateThroughput(issues);
   const issueMaintainers = calculateThroughput(
-    issues.filter((i: { association: string; date: number }) =>
-      isMaintainer(i.association),
-    ),
+    issues.filter((i) => isMaintainer(i.association)),
   );
   const issueCommunity = calculateThroughput(
-    issues.filter(
-      (i: { association: string; date: number }) =>
-        !isMaintainer(i.association),
-    ),
+    issues.filter((i) => !isMaintainer(i.association)),
   );
 
+  const arrivalRate = calculateArrivalRate(arrivalDates);
+
   process.stdout.write(
     `throughput_pr_overall_per_day,${Math.round(prOverall * 100) / 100}\n`,
   );
@@ -105,6 +121,9 @@ try {
   process.stdout.write(
     `throughput_issue_community_per_day,${Math.round(issueCommunity * 100) / 100}\n`,
   );
+  process.stdout.write(
+    `throughput_issue_arrival_rate_per_day,${Math.round(arrivalRate * 100) / 100}\n`,
+  );
   process.stdout.write(
     `throughput_issue_overall_days_per_issue,${issueOverall > 0 ? Math.round((1 / issueOverall) * 100) / 100 : 0}\n`,
   );