diff --git a/cwltool/executors.py b/cwltool/executors.py
index 03fa948e7..e25426c9d 100644
--- a/cwltool/executors.py
+++ b/cwltool/executors.py
@@ -429,7 +429,7 @@ def run_jobs(
         logger: logging.Logger,
         runtime_context: RuntimeContext,
     ) -> None:
-        self.taskqueue: TaskQueue = TaskQueue(threading.Lock(), psutil.cpu_count() or 1)
+        self.taskqueue: TaskQueue = TaskQueue(threading.Lock(), int(math.ceil(self.max_cores)))
         try:
             jobiter = process.job(job_order_object, self.output_callback, runtime_context)