Declining transportation funding and need for analytical solutions: dynamics and control of VMT tax

There is a growing concern among policy makers and analysts regarding the mismatch between demand and supply of the revenue for improving and maintaining highway infrastructure. One possible solution is to link actual vehicle miles traveled (VMT) to the fee structure. The main objective of this paper is to model VMT dynamics and establish a methodology for designing an optimal VMT tax rate. The paper proposes a novel model for VMT dynamics and estimates the model parameters using historical data. An optimal control problem is then formulated by designing a cost function which aims to maximize the generated revenue while keeping the tax rate at a reasonable rate. Using optimal control theory, a solution is provided to this problem. Steady-state analysis of this model is provided and simulations are performed for the 50-year period showing the projected VMT, generated revenue, and the optimal tax rate. The model provides a parameter in the cost function which can be adjusted for achieving a certain amount of revenue in a given time frame.