Shuttle Bus Line Planning in Response to Unexpected Disruption in Urban Rail Transit Networks

Abstract

When metro systems need to be temporarily closed due to an unexpected disruption, the metro operators have to arrange shuttle buses as alternative transport for trains, while passengers have to find new routes to complete their journeys. However, the additional shuttle bus lines might be redundant if the well-known phenomenon of the “Braesss Paradox” exists. To address this issue, this paper proposes a bi-level programming model in which the objective of the upper-level model is to minimize the number of shuttle bus lines, while the lower-level model is a UE (User Equilibrium) model that simulates the route choice of passengers. To solve this bi-level programming model, the Overload Arc-oriented Heuristics (OAH) algorithm is developed to find an initial solution, and then we develop a BS (Bi-direction Search) algorithm to obtain the optimal solution to our model. Numerical cases of the partial Beijing Metro network have proved the efficiency and effectiveness of our method, and the result shows that: (1) compared with the standard bus bridging routes, the additional shuttle bus lines can significantly reduce the number of stranded passengers; (2) the number of stranded passengers at each station can be controlled by two strategies: adjust the departure frequency of each shuttle bus line and control the passenger flow at each station.