diff --git a/src/__tests__/model-busy-retry.test.ts b/src/__tests__/model-busy-retry.test.ts
index 483e6e7..e99b7c0 100644
--- a/src/__tests__/model-busy-retry.test.ts
+++ b/src/__tests__/model-busy-retry.test.ts
@@ -198,6 +198,18 @@ describe("parseModelBusyRejection", () => {
     });
   });
 
+  it.each([1e300, Number.MAX_VALUE, Number.MAX_SAFE_INTEGER])(
+    "uses retryAfterSeconds when queue waitTime=%s exceeds safe milliseconds",
+    (waitTime) => {
+      expect(parseModelBusyRejection(busyBody({ isQueued: true, waitTime, retryAfterSeconds: 30 }))).toEqual({
+        kind: "queued",
+        waitMs: 30000,
+        queueCount: 0,
+        queueType: "p4",
+      });
+    },
+  );
+
   it("rejects a queued snapshot without the service flags", () => {
     expect(parseModelBusyRejection(busyBody({ isQueued: true, serviceAvailable: undefined }))).toBeUndefined();
   });
diff --git a/src/protocol/stream.ts b/src/protocol/stream.ts
index d1c4455..f51a2c9 100644
--- a/src/protocol/stream.ts
+++ b/src/protocol/stream.ts
@@ -105,8 +105,11 @@ export function parseModelBusyRejection(body: unknown): ModelBusyQueueSnapshot |
   const queue = parseJsonObject(busy.message);
   if (!queue) return undefined;
   if (queue.serviceAvailable !== true) return undefined;
-  const seconds = (value: unknown): number =>
-    typeof value === "number" && Number.isFinite(value) && value > 0 ? Math.round(value * 1000) : 0;
+  const seconds = (value: unknown): number => {
+    if (typeof value !== "number" || !Number.isFinite(value) || value <= 0) return 0;
+    const milliseconds = Math.round(value * 1000);
+    return Number.isSafeInteger(milliseconds) && milliseconds > 0 ? milliseconds : 0;
+  };
   if (queue.isQueued === false) {
     return { kind: "ready", retryAfterMs: seconds(queue.retryAfterSeconds) };
   }