We have the first example of scheduler deadlock in the willd for MySQL for the new scheduler:

https://github.com/apache/airflow/pull/8550/checks?check_run_id=1258193958#step:6:1439

Would be great to track it down and fix before the prod release:

**NOTE**  For now the issue has been mitigated (according to the documentation of MySQL) by applying restarts (with exponential back-off) in #12046. This should help with beta-testing of Airlfow by the users and to see if the retries on deadlock has some potential negative effects (according to the documentation - they might have if they happen frequently enough). 

Some more analysis might be performed between now and 2.0.0 which might result in deciding that this issue does not need any more fixes than the current mitigation or some actual changes in the code that might result in preventing the deadlocks.


tests/jobs/test_scheduler_job.py
"""
        Utility function that runs a single scheduler loop without actually
        changing/scheduling any dags. This is useful to simulate the other side effects of
        running a scheduler loop, e.g. to see what parse errors there are in the
        dags_folder.
        :param dags_folder: the directory to traverse
        :type dags_folder: str
        """
        scheduler = SchedulerJob(
            executor=self.null_exec,
            num_times_parse_dags=1,
            subdir=os.path.join(dags_folder))
        scheduler.heartrate = 0
        scheduler.run()
    def test_no_orphan_process_will_be_left(self):
        empty_dir = mkdtemp()
        current_process = psutil.Process()
        old_children = current_process.children(recursive=True)
        scheduler = SchedulerJob(subdir=empty_dir,
                                 num_runs=1,
                                 executor=MockExecutor(do_update=False))
        scheduler.run()
        shutil.rmtree(empty_dir)
        
        current_children = set(current_process.children(recursive=True)) - set(
            old_children)
        self.assertFalse(current_children)
    @mock.patch('airflow.jobs.scheduler_job.TaskCallbackRequest')
    @mock.patch('airflow.jobs.scheduler_job.Stats.incr')
    def test_process_executor_events(self, mock_stats_incr, mock_task_callback):