Bus transit network design with uncertainties on the basis of a metro network: A two-step model framework

The metro systems of some megacities are facing serious oversaturation problem due to the heavy passenger flow during high peak hours. We consider the bus transit network design problem based on an existing metro network that can balance the modal split between metro and bus transit systems. The challenges facing this problem lie in that passengers have a different preference between metro and bus services, and the bus travel time and passenger demand may exhibit significant variations. This paper develops a two-step model framework to determine a bus transit network and departure frequency with consideration of travel time and passenger demand uncertainties. Firstly, we develop a column generation method to identify the candidate set of bus transit lines and passenger paths. Then a stochastic linear programming model is developed to optimize the bus line frequency and passenger path flow under demand and bus travel time uncertainty. To solve this model, a primal-dual online algorithm based on the online convex optimization theory is built to obtain the optimal solution with a theoretical performance guarantee. Finally, we implement the developed framework into an illustrative network and a real-world Beijing Second Ring public transit network to demonstrate its applicability and promising effects. The computational results show that the method can provide significant benefits for public transit systems.