Phased replacement of bus lines by rail in a transit network with passenger flow modeling

Abstract

New urban rail lines are often built gradually, aiming to leverage the revenue from operating on built infrastructure to increase the available budget for further extensions. Each candidate inter-station link competes with the others in funding allocation and offers different benefits in travel time reduction and increased fare revenue. Previous studies have relied on travel paths that are fixed over time for the users of each origin-destination pair, thus failing to capture their actual dependence on network development in redundant networks.A bi-level optimization method is proposed here to solve the Rail Link Building Sequencing Problem with replacement of bus lines. The first level uses a genetic algorithm to optimize the sequence in which new links from multiple rail lines of a network will be built, replacing preexisting bus lines, with the objective of maximizing the present value of the total societal net benefit (?) over a time horizon. As the evolution of the network caused by a building sequence is modeled, the second level of optimization maximizes each year’s undiscounted ? by means of an iterative process to algebraically reoptimize the headways of individual lines for that year, while simultaneously recomputing user travel paths, travel times and flows in response to those headways. Travel time computations are performed on a graph with several edges per link to ease the correct inclusion of waiting times at transfer stations. The algorithm was used to optimize the rail link-building sequence of a proposed urban transit network in San Jose, Costa Rica, under two different user path modeling strategies: 1) dynamic re-computation each year, and 2) adherence of the users of each O-D pair throughout the entire timeframe to the path that will be the fastest upon rail network completion. In both cases, the objective function was found to be maximized by replacing each bus line by rail in a mostly uninterrupted way. As the main finding, the results show how dynamic path modeling yields sequences 3% better in terms of ? and more strongly favors completing radial lines before circular lines.