Symptoms: all threads in BackgroundScheduledPool busy, lot of tasks in replication queue, none of the tasks is executing. 

![Screenshot from 2021-04-16 16-21-44_](https://user-images.githubusercontent.com/1549571/115193796-e767d600-a0ec-11eb-887c-5c9c2412e50c.png)

Related to #16895

Possible workarounds (poor options): increasing the background_schedule_pool_size to huge values, or restart server every time when that happens etc. - 

String value;
        if (!zookeeper->tryGet(fs::path(zookeeper_path) / "replicas" / replica / "min_unprocessed_insert_time", value))
            continue;
        time_t replica_time = value.empty() ? 0 : parse<time_t>(value);
        if (replica_time == 0)
        {
            /** Note
              * The conclusion that the replica does not lag may be incorrect,
              *  because the information about `min_unprocessed_insert_time` is taken
              *  only from that part of the log that has been moved to the queue.
              * If the replica for some reason has stalled `queueUpdatingTask`,
              *  then `min_unprocessed_insert_time` will be incorrect.
              */
            have_replica_with_nothing_unprocessed = true;
            break;
        }
        if (replica_time > max_replicas_unprocessed_insert_time)
            max_replicas_unprocessed_insert_time = replica_time;
    }
    if (have_replica_with_nothing_unprocessed)
        out_relative_delay = out_absolute_delay;
    else
    {
        max_replicas_unprocessed_insert_time = std::min(current_time, max_replicas_unprocessed_insert_time);
        time_t min_replicas_delay = current_time - max_replicas_unprocessed_insert_time;
        if (out_absolute_delay > min_replicas_delay)
            out_relative_delay = out_absolute_delay - min_replicas_delay;
    }
}
void StorageReplicatedMergeTree::fetchPartition(