diff --git a/python/sglang/srt/managers/scheduler.py b/python/sglang/srt/managers/scheduler.py
index 21de52244..10df1914a 100644
--- a/python/sglang/srt/managers/scheduler.py
+++ b/python/sglang/srt/managers/scheduler.py
@@ -1865,13 +1865,24 @@ class Scheduler(
             self.external_corpus_manager.check_pending_load()
 
     def init_req_max_new_tokens(self, req):
-        req.sampling_params.max_new_tokens = min(
-            (
-                req.sampling_params.max_new_tokens
-                if req.sampling_params.max_new_tokens is not None
-                else 1 << 30
+        input_len = len(req.origin_input_ids)
+        # Keep this bound consistent with PrefillAdder's admission budget:
+        # ceil_page(input_len) + max_new_tokens + page_size must be strictly
+        # smaller than max_total_num_tokens. Otherwise a request can be accepted
+        # into the waiting queue but can never be scheduled, blocking the queue
+        # and eventually making health checks fail.
+        paged_input_len = -(-input_len // self.page_size) * self.page_size
+        req.sampling_params.max_new_tokens = max(
+            0,
+            min(
+                (
+                    req.sampling_params.max_new_tokens
+                    if req.sampling_params.max_new_tokens is not None
+                    else 1 << 30
+                ),
+                self.max_req_len - input_len - 1,
+                self.max_total_num_tokens - paged_input_len - self.page_size - 1,
             ),
-            self.max_req_len - len(req.origin_input_ids) - 1,
         )
 
     def _process_and_broadcast_mm_inputs(