In a corporate environment there would be a team of people who would have a meeting. Whatever is decided would be put in writing and then sent off to the operations (design) team. The written instruction would then be acted upon. The decision making process itself wont take more than a few hours (though this does depend greatly on how important the decision is).
However, when you are on the pit wall, you don't have time to have a 1 hour meeting. Then consult a computer. Then have a meeting to discuss the computer's decision. etc. Then issue the instruction. You have to make the decision "off the cuff". You have seconds. Button made a critical pit stop decision which led to his first race win for McLaren. He made the decision in seconds. The McLaren machine would never have been able to make a decision like that, so quickly and so risky.
maybe there will actually something other than pit times and tyre choices.
