Just in time train schedule?

Thought experiment: if we have the same number of trains we have at the moment and we let them travel as we do at the moment – but without time tables (basically a train is always on time – it is there when it arrives – similar to today). Customers would have real time access to all trains and the system could provide estimates when a certain train is where – perhaps with a confidence interval and probabilities of connections and travel times (obviously with an understandable user interface).

Would this be a better or worse model of public transport?

… and by the way the coach I was in has the IP address 192.168.97.181 and runs DOS ;-)