What if a low-priority process and a high-priority process send a message to a server at the same time?
If two processes send a message simultaneously, the entire message from the higher-priority process is delivered to the server first.
If both processes are at the same priority, then the messages will be delivered in time order (since there's no such thing as absolutely simultaneous on a single-processor machine—even on an SMP box there will be some ordering as the CPUs arbitrate kernel access among themselves).
We'll come back to some of the other subtleties introduced by this question when we look at priority inversions later in this chapter.