I think you're referring to flow control ("2-phase") and arbitration ("4-phase")?
I'm not sure at all when they were first developed, but flow control has to be very old. Digital teleprinters came in the late 1800s or early 1900s as an outgrowth of the telegraph. In telegraphy, there were conventional ways of letting the other party talk ("Over" or "Go Ahead" were abbreviated with special morse codes). In a two-way teleprinter circuit, that kind of convention could be used to switch access to a shared circuit. Later on with modems flow control was accessed using RTS (ready to send) and CTS (clear to send) signals.
Arbitration is needed for multi-master access to shared media, which includes computer buses and also things like Ethernet. Again I don't know the order of discovery, but the IBM 360 definitely had a form of arbitration for its channel architecture and most other large computers of the 1960s had similar features.