diff --git a/swh/scheduler/tests/test_simulator.py b/swh/scheduler/tests/test_simulator.py
index 7c7aaca..b614cfd 100644
--- a/swh/scheduler/tests/test_simulator.py
+++ b/swh/scheduler/tests/test_simulator.py
@@ -1,53 +1,60 @@
 # Copyright (C) 2021  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import pytest
 
 from swh.core.api.classes import stream_results
 import swh.scheduler.simulator as simulator
 from swh.scheduler.tests.common import TASK_TYPES
 
 NUM_ORIGINS = 42
 TEST_RUNTIME = 1000
 
 
 def test_fill_test_data(swh_scheduler):
     for task_type in TASK_TYPES.values():
         swh_scheduler.create_task_type(task_type)
 
     simulator.fill_test_data(swh_scheduler, num_origins=NUM_ORIGINS)
 
     origins = list(stream_results(swh_scheduler.get_listed_origins))
     assert len(origins) == NUM_ORIGINS
 
     res = swh_scheduler.search_tasks()
     assert len(res) == NUM_ORIGINS
 
 
-@pytest.mark.parametrize("policy", ("oldest_scheduled_first",))
+@pytest.mark.parametrize(
+    "policy",
+    (
+        "oldest_scheduled_first",
+        "never_visited_oldest_update_first",
+        "already_visited_order_by_lag",
+    ),
+)
 def test_run_origin_scheduler(swh_scheduler, policy):
     for task_type in TASK_TYPES.values():
         swh_scheduler.create_task_type(task_type)
 
     simulator.fill_test_data(swh_scheduler, num_origins=NUM_ORIGINS)
     simulator.run(
         swh_scheduler,
         scheduler_type="origin_scheduler",
         policy=policy,
         runtime=TEST_RUNTIME,
     )
 
 
 def test_run_task_scheduler(swh_scheduler):
     for task_type in TASK_TYPES.values():
         swh_scheduler.create_task_type(task_type)
 
     simulator.fill_test_data(swh_scheduler, num_origins=NUM_ORIGINS)
     simulator.run(
         swh_scheduler,
         scheduler_type="task_scheduler",
         policy=None,
         runtime=TEST_RUNTIME,
     )