Use exponential backoff for cache-stampede polling (R4)

waitForCache, the schedule month-poll loop, and getOrFetchDynamic all
polled Firestore every fixed 500ms (up to ~50 reads) while waiting for a
lock holder to populate the cache. Replace the fixed interval with a
shared backoffDelayMs helper (300ms base, doubling, 5s cap) bounded by the
same ~25s timeout, cutting per-waiter read amplification by roughly 5x.
Timeout/fallback semantics are unchanged.

src/repositories/kboCacheRepository.ts

@@ -110,6 +110,17 @@ async function releaseLock(key: string): Promise<void> {
   await firestore.collection(LOCK_COLLECTION).doc(key).delete().catch(() => undefined);
 }
 
+/**
+ * 캐시 스탬피드 폴링용 지수 백오프 지연(ms)을 계산한다.
+ *
+ * `attempt`(0부터)에 대해 `baseMs * 2^attempt`를 `maxMs`로 클램프한다.
+ * 고정 간격(500ms) 대신 점증 간격을 쓰면 락 보유자가 채울 때까지 대기하는
+ * 동안의 캐시 read 횟수를 크게 줄인다(예: 25초 윈도우에서 ~50회 → ~9회).
+ */
+export function backoffDelayMs(attempt: number, baseMs = 300, maxMs = 5_000): number {
+  return Math.min(maxMs, baseMs * 2 ** attempt);
+}
+
 /**
  * 락이 걸려있는 동안 주기적으로 캐시를 폴링한다.
  *
@@ -122,8 +133,8 @@ async function releaseLock(key: string): Promise<void> {
  */
 async function waitForCache<T>(key: string, ttlMs: number, timeoutMs = 25_000): Promise<T | null> {
   const start = Date.now();
-  while (Date.now() - start < timeoutMs) {
+  for (let attempt = 0; Date.now() - start < timeoutMs; attempt++) {
-    await new Promise((r) => setTimeout(r, 500));
+    await new Promise((r) => setTimeout(r, backoffDelayMs(attempt)));
     const cached = await getCached<T>(key, ttlMs);
     if (cached !== null) return cached;
   }

src/repositories/kboRepository.ts

@@ -24,6 +24,7 @@ import {
   setCached,
   acquireLock,
   releaseLock,
+  backoffDelayMs,
 } from "./kboCacheRepository";
 import { firestore } from "../firebase";
 import { getGameList } from "../services/gameListService";
@@ -394,10 +395,10 @@ async function fetchScheduleMonth(
         await releaseLock(lockKey);
       }
     } else {
-      // 다른 요청이 fetch 중. 짧게 polling.
+      // 다른 요청이 fetch 중. 지수 백오프로 polling(대기 중 read 폭증 완화).
       const start = Date.now();
-      while (Date.now() - start < 25_000) {
+      for (let attempt = 0; Date.now() - start < 25_000; attempt++) {
-        await new Promise((r) => setTimeout(r, 500));
+        await new Promise((r) => setTimeout(r, backoffDelayMs(attempt)));
         cached = await readDayDocs(keys);
         missing = allDays.filter((_, i) => cached.get(keys[i]) === null);
         if (missing.length === 0) break;

src/services/gameDetailService.ts

@@ -9,6 +9,7 @@ import {
   setCached,
   acquireLock,
   releaseLock,
+  backoffDelayMs,
 } from "../repositories/kboCacheRepository";
 
 const SEVEN_DAYS_MS = 7 * 24 * 60 * 60 * 1000;
@@ -115,8 +116,9 @@ async function getOrFetchDynamic<T>(
 
   const locked = await acquireLock(key);
   if (!locked) {
-    for (let i = 0; i < 50; i++) {
+    const start = Date.now();
-      await new Promise((r) => setTimeout(r, 500));
+    for (let attempt = 0; Date.now() - start < 25_000; attempt++) {
+      await new Promise((r) => setTimeout(r, backoffDelayMs(attempt)));
       const c = await getCached<T>(key, Number.MAX_SAFE_INTEGER);
       if (c !== null) return c;
     }