diff --git a/qa/L0_model_queue/model_queue_test.py b/qa/L0_model_queue/model_queue_test.py
index 14d2349c8c..e7be471f79 100755
--- a/qa/L0_model_queue/model_queue_test.py
+++ b/qa/L0_model_queue/model_queue_test.py
@@ -140,7 +140,7 @@ def test_max_queue_size(self):
         for trial in self.trials_:
             preceding_thread = threading.Thread(
                 target=self.check_response,
-                args=(8, dtype, shapes, 0, 0, (1999, 1000)),
+                args=(8, dtype, shapes, 0, 0, (5999, 1000)),
             )
             threads = []
             for i in range(10):
@@ -160,8 +160,10 @@ def test_max_queue_size(self):
             for t in threads:
                 t.join()
 
-            # Expect at most two exception with exceeding max queue size error
-            for i in range(2):
+            # Expect exactly two exception with exceeding max queue size error
+            expected_exceeded_count = 2
+            exceeded_count = 0
+            for i in range(expected_exceeded_count):
                 try:
                     self.check_deferred_exception()
                 except InferenceServerException as ex:
@@ -171,6 +173,14 @@ def test_max_queue_size(self):
                             ex
                         ),
                     )
+                    exceeded_count = exceeded_count + 1
+            self.assertEqual(
+                exceeded_count,
+                expected_exceeded_count,
+                "expected {} requests to fail with exceeded max queue size error, got {}".format(
+                    expected_exceeded_count, exceeded_count
+                ),
+            )
             try:
                 self.check_deferred_exception()
             except InferenceServerException as ex:
diff --git a/qa/L0_model_queue/test.sh b/qa/L0_model_queue/test.sh
index 667f902db0..577b7b7fc2 100755
--- a/qa/L0_model_queue/test.sh
+++ b/qa/L0_model_queue/test.sh
@@ -82,7 +82,7 @@ rm -fr models && mkdir models && \
         echo "    }" >> config.pbtxt && \
         echo "}" >> config.pbtxt && \
         echo "parameters [" >> config.pbtxt && \
-        echo "{ key: \"execute_delay_ms\"; value: { string_value: \"1000\" }}" >> config.pbtxt && \
+        echo "{ key: \"execute_delay_ms\"; value: { string_value: \"5000\" }}" >> config.pbtxt && \
         echo "]" >> config.pbtxt)
 
 TEST_CASE=test_max_queue_size