A Math Problem

In my city of Victoria, British Columbia, one of the main streets has been gentrified. Not building-wise, but the street itself. It use to be two lanes running through a downtown area with two intersections where the left lane was also a turning lane, which would sometimes lead to having to wait in that lane until a driver ahead had completed their turn. There was parking alongside the right lane.

This was changed. A bicycle lane was put in on the right and now for a 4 block stretch there is a single lane, parking, and the bicycle lane. At the two main left turn intersections, turning lanes have been put it. This changes the dynamics of driving into town along this street.

Previously, it was important to remain in the right lane to avoid getting caught behind cars that were making left turns. Everybody who used the street regularly knew this and acted accordingly. Now, it’s important to stay in the left lane because the right lane coming into the downtown area vanishes so drivers in it will get caught behind parked cars and have to shift into the left lane (a problem because of much traffic). And, in the left lane there is no problem now with cars making left turns — they have their own lane for this. This has created some traffic tie-ups, but presumably as people learn the new layout these will diminish.

So, the math problem.

Assume a fixed population P of size N, plus a fraction of occasional visitors who have no clue. For each member of P there will be two dimensions: a learning curve — how many times to…