diff --git a/services/director-v2/tests/unit/with_dbs/comp_scheduler/test_worker.py b/services/director-v2/tests/unit/with_dbs/comp_scheduler/test_worker.py
index c52b842516dc..e4c56b3b88a2 100644
--- a/services/director-v2/tests/unit/with_dbs/comp_scheduler/test_worker.py
+++ b/services/director-v2/tests/unit/with_dbs/comp_scheduler/test_worker.py
@@ -7,6 +7,8 @@
 # pylint:disable=no-name-in-module
 # pylint: disable=too-many-statements
 
+import asyncio
+from typing import Awaitable, Callable
 from unittest import mock
 
 import pytest
@@ -47,7 +49,7 @@ def mocked_get_scheduler_worker(
     )
 
 
-async def test_worker_properly_calls_scheduler_api(
+async def test_worker_properly_autocalls_scheduler_api(
     with_disabled_auto_scheduling: mock.Mock,
     initialized_app: FastAPI,
     mocked_get_scheduler_worker: mock.Mock,
@@ -69,3 +71,34 @@ async def test_worker_properly_calls_scheduler_api(
         project_id=published_project.project.uuid,
         iteration=1,
     )
+
+
+@pytest.fixture
+async def mocked_scheduler_api(mocker: MockerFixture) -> mock.Mock:
+    return mocker.patch(
+        "simcore_service_director_v2.modules.comp_scheduler._scheduler_base.BaseCompScheduler.schedule_pipeline"
+    )
+
+
+async def test_worker_scheduling_parallelism(
+    with_disabled_auto_scheduling: mock.Mock,
+    mocked_scheduler_api: mock.Mock,
+    initialized_app: FastAPI,
+    publish_project: Callable[[], Awaitable[PublishedProject]],
+    run_metadata: RunMetadataDict,
+):
+    with_disabled_auto_scheduling.assert_called_once()
+
+    mocked_scheduler_api.side_effect = asyncio.sleep(10)
+
+    published_project = await publish_project()
+    assert published_project.project.prj_owner
+    await run_new_pipeline(
+        initialized_app,
+        user_id=published_project.project.prj_owner,
+        project_id=published_project.project.uuid,
+        cluster_id=DEFAULT_CLUSTER_ID,
+        run_metadata=run_metadata,
+        use_on_demand_clusters=False,
+    )
+    mocked_scheduler_api.assert_called_once()