Uncertainty and the timing of an urban congestion relief investment.: The no-land case

We analyze the impact of population uncertainty on the socially optimum timing of a congestion-relief project in a linear monocentric city with fixed boundaries, where congestion pricing cannot be implemented. This project requires time to bear fruit but no urban land. Under certainty, we show that utility maximization is roughly equivalent to a standard benefit-cost analysis (BCA). Under uncertainty, we derive an explicit optimal threshold for relieving congestion when the urban population follows a geometric Brownian motion. If the time to implement the project is short, we show analytically that deciding on the timing of congestion relief based on a BCA could lead to acting prematurely; the reverse holds if project implementation is long and uncertainty is large enough.