The dynamic system-optimal route choice problem and toll policies

The dynamic system-optimal route choice problem is formulated as a discrete-time link-based model using the variational inequality approach. This model complies with the dynamic system-optimal equilibrium condition in which for each origin-destination pair, the marginal route travel times experienced by travelers are equal and minimal. A nested diagonalization procedure is then proposed for obtaining the solution. Numerical examples are provided for showing equilibrated route travel times, demonstrating Braess's paradox and an approximating static counterpart solution. In addition, a two-stage procedure is used for computing a toll imposition such that a dynamic system-optimal is also a dynamic user-optimal solution.