Don’t rely on the thread scheduler for correctness or performance. Instead, ensure that the average number of runnable threads is not significantly greater than the number of processors, i.e. by using the executor framework and an appropriately sized thread pool.
For more information, see Effective Java 3rd Edition §84.
Suppress false positives by adding the suppression annotation @SuppressWarnings("ThreadPriorityCheck") to the enclosing element.