This paper analyzes the impacts of stochastic population changes on the timing of an investment that reduces congestion in an open, monocentric city with fixed boundaries. Congestion pricing cannot be implemented, but a welfare-maximizing planner can buy land and build transportation infrastructure. Under certainty, I derive a rule of thumb to evaluate infrastructure investments that corrects a standard benefit-cost analysis. Under uncertainty, I show that relying on a standard benefit-cost ratio could lead to investing in bad projects, or investing prematurely, or ignoring attractive projects because of population barriers and the impacts of the congestion externality on the land market.