As AsyncTasks can share a single thread I would try decoupling them by calling:
my_task.executeOnExecutor(AsyncTask.THREAD_POOL_EXECUTOR, (Void[])null);
in place of my_task.execute((Void[])null)
as described in this answer: Android SDK AsyncTask doInBackground not running (subclass)
Another way would be to use Executor framework and ThreadPoolExecutor.