Transportation network design for maximizing flow-based accessibility

One of the significant aims of transportation network design and management is to improve the service level of the network and the accessibility of individual trips in a certain period. By adopting a well-defined accessibility measure, this paper studies a new discrete network design problem for metropolitan areas, in which some concepts, including the accessible flow, travel time budget function and principles of user equilibrium and system optimization with travel time budgets, are proposed. Then, two deterministic bi-level programming models are firstly formulated to maximize the network accessible flow. The upper level focuses on choosing the potential links in the pre-specified candidate set, and the lower level assigns all the flows to the super network with principles of user equilibrium or system optimization with travel time budgets. Moreover, to handle uncertain potential demands in reality, the problem of interest is further formulated as two-stage stochastic programming models. To solve these proposed models, efficient heuristic algorithms are designed on the basis of probability search algorithm, Frank–Wolfe algorithm and Monte Carlo simulation method. Finally, two sets of numerical experiments in the Sioux Falls network and San Diego freeway network, are executed to test and analyze the rationality and efficiency of the proposed approaches.