Efficient and fair system states in dynamic transportation networks

- Formulate the problem of dynamic system optimum and user equilibrium.
- Account for dynamic departure time and route choice in a multi-OD network.
- Propose a linear programming relaxation formulation.
- Propose an efficient algorithm with the number of iterations bounded.
- Various tests have been conducted to verify the formulation's properties.

This paper sets out to model an efficient and fair transportation system accounting for both departure time choice and route choice of a general multi-OD network within a dynamic traffic assignment environment. Firstly, a bi-level optimization formulation is introduced based on the link-based traffic flow model. The upper level of the formulation minimizes the total system travel time, whereas the lower level captures traffic flow propagation and the user equilibrium constraints. Then the bi-level formulation is relaxed to a linear programming formulation that produces a lower bound of an efficient and fair system state. An efficient iterative algorithm is proposed to obtain the exact solution. It only requires solving one linear program in one iteration. Further, it is shown that the number of iterations is bounded, and the output traffic flow pattern is efficient and fair. Finally, two numerical cases (including a single OD network and a multi-OD network) are conducted to demonstrate the performance of the algorithm. The results consistently show that the departure rate pattern generated from the algorithm leads to an efficient and fair system state, and the algorithm converges within two iterations across all test scenarios.