2E just had a casting time, equivalent to "segments", but not actually defined as any particular length of time.
You'd make the initiative roll (d10) and add your weapon speed or casting time, the lower roll would strike first.
As I've never, ever understood the 1E initiative system properly, I preferred the 2E system. (I liked 2.5 even better, and I also like 3E, though it has a different take on it).