Another assumption that does not accord with reality is the zero travel time for the AB segment. Also, in most cases, there already exist numerous routes similar to AB, as people exit on freeway and cut across to another.

Of course, the system becomes much more complex as the number of possible routes increases. As we have learned to our great cost in the financial debacles of late, complex mathematical models which do not fully account for all potential situations, and which are not fully understood by the ultimate decision makers (think Investment Bank Executive Boards, or in this case City Councils/State Highway Authorities), but are instead viewed as “magic boxes” which give infallible answers, will lead to tragic results.

I see the sort of practical results stemming from this approach as being more in the decision of what type of new road to build (i.e. a cutoff as in AB, or an entirely new routs, as in start-C-end, or even in simply improving existing routes), rather than in decisions on whether or not to take action.

As for the specific freeway/back roads distinction, I think the analogy can go either way. The bigger point is that local incentives can result in global inefficiencies–termed “the price of anarchy.”

So what is one to do in practice? I think commuters would tend to minimize risk. That is, they don’t just take the path of expected risk, but one that has a reasonable travel time with low variance. Just my guess

As for the problem in its beginning form… I like to think of it this way. The “T/25″ roads are freeways, which are faster and often times more direct, while the “50″ roads are “back roads” ie, slower, but due to speed restrictions, they are safer and congestion has a negligible effect on drive times. It’s just a different way of looking at it, but it gives the same result–if a new freeway is built which bypasses back roads, then pretty much everybody will use it (especially in winter here in Michigan), and drive times will slow for everyone.