Hierarchical bus transit network design in coordination with an existing metro system

The construction of a well-coordinated metro-bus bimodal system may benefit not only passengers performing bimodal trips but also passengers using each individual transit mode. With this aim, this paper focuses on jointly designing a bus network and determining the frequency of bus lines to ensure coordinated operation with an existing metro system. In particular, rather than implementing a single regular line type, a hierarchical bus network structure consisting of different types of bus lines is proposed with the objective of reaching better intermodal coordination. Each line type is characterized by a specific stopping pattern, commercial speed level, and terminal stations. A novel inter-stop distance-based model is proposed to determine the number and the itinerary of the different types of lines and the appropriate bus frequencies so that the total passenger travel time in the bimodal network is minimized under capacity limitations. Meanwhile, a multinomial logit model is incorporated to explicitly capture the endogenous multimodal passenger assignment regarding service level and ticket price. To efficiently solve the hierarchical network design problem, the concept of an improved hierarchical virtual road network is defined. Based on it, a bi-level heuristic decomposition method that breaks down the integrated problem into two simpler subproblems and then solves them iteratively is presented. In addition, the passenger demand information is used internally by the solving procedure in several specialized operators to accelerate the convergence of the algorithm and improve the quality of the solutions. The results of a small-scale case and a real-world network design instance considering three types of lines show that by making a trade-off between lines with different running speeds resulting from different average inter-stop distances, the hierarchical bus network can incentivize commuters into route choices that improve the overall system performance of the integrated metro-bus bimodal network.