Regret Approach in Estimating Traffic Volume for a Congested Road with Unknown Inverse Demand Function

Traditional road supply models assume full knowledge of the inverse demand function, such that the supply-demand equilibrium point can be easily obtained. However, in practice, it is often difficult to completely characterize the inverse demand function, especially for a congested road. In this paper, we study the traffic volume estimating problem for a congested road with partial information about the inverse demand function, i.e., range or total willing to pay for travel. In particular, we first propose a minimax regret model for minimizing the planner's maximum opportunity cost of not acting optimally, and then obtain some analytical solutions by transforming it into a moment problem equivalently with some simplified assumptions. The model and results in this paper are both instructive and can be extended to investigate more realistic scenarios for practical application.