Bus frequency optimization in a large-scale multi-modal transportation system: Integrating 3D-MFD and dynamic traffic assignment

Abstract

A properly designed public transport system is expected to improve traffic efficiency. A high-frequency bus service would decrease the waiting time for passengers, but the interaction between buses and cars might result in more serious congestion. On the other hand, a low-frequency bus service would increase the waiting time for passengers and would not be able to reduce the use of private cars. It is important to strike a balance between high and low frequencies in order to minimize the total delays for all road users. It is critical to formulate the impacts of bus frequency on congestion dynamics and mode choices. However, as far as the authors know, most proposed bus frequency optimization formulations are based on static demand and the Bureau of Public Roads function, and do not properly consider the congestion dynamics and their impacts on mode choices. To fill this gap, this paper proposes a bi-level optimization model. A three-dimensional Macroscopic Fundamental Diagram based modeling approach is developed to capture the bi-modal congestion dynamics. A variational inequality model for the user equilibrium in mode choices is presented and solved using a double projection algorithm. A surrogate model-based algorithm is used to solve the bi-level programming problem.