How is CPU time divided between partitions?

The thread scheduler is a fair-share scheduler. This means that it guarantees that partitions receive a defined minimum amount of CPU time (their budget) whenever they demand it. The thread scheduler is also a realtime scheduler. That means it's a preemptive, priority-based scheduler. These two requirements appear to conflict, but the thread scheduler satisfies both of these requirements by scheduling through priority at all times so that it doesn't need to limit a partition in order to guarantee some other partition its budget.

For every scheduling operation, the thread scheduler examines every partition before it chooses a thread to run. This happens for every timer interrupt (typically, every millisecond), every message/pulse send, receive or reply, every signal, every mutex operation, and on every stack fault, and including many times for process manager operations (creation/destruction of processes or threads and open() operations on elements of the path namespace).

If a partition is over budget (meaning that the consumption of CPU time over the last 100 milliseconds exceeds the partition's size, and other partitions are also demanding time) and a thread wants to run, the thread scheduler doesn't run the thread; it runs some other thread. Only when enough time has elapsed so that the average CPU time use of that partition (over the last 100 milliseconds) falls below the partition's size, will the scheduler run the thread. However, the thread is guaranteed to eventually run.