> O(millions)

Big-O doesn't include constant factors for a reason (never mind just being a constant entirely), but maybe I am misunderstanding what you are trying to say?

It's not Big-O complexity notation. It means "a few millions". It's sort of how the word "sanction" can mean one thing or a different thing. The textual glyph sequence means a different thing based on context in English. Pretty normal.

I like to call it Big-O Magnitude Notation.

"Order of millions of GPUs being scheduled on" - which is to say when a workload is submitted to the scheduler, it makes a scheduling decision and the individual compute nodes are being programmed within milliseconds.

This means that if say a job requesting GPUs is submitted with a given topology constraint, we would already computed the physical nodes that satisfy the topology requirement, and begun preemption / begun spinning up processes on the target machines within a few milliseconds of the job being submitted. If there were no preemptions required (which means we need to first wait for graceful termination), the job is fully scheduled in the blink of an eye, whether it's on tens or hundreds of thousands of GPUs.

It means ~millions