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Demand adaptive paired-line hybrid transit systems that integrate fixed- and flex-route transit have emerged in the last decade and attracted increasing attention because of their potential to improve accessibility for passengers. To facilitate the operation of such a hybrid transit system, this study develops a model to determine the optimal fare and headways associated with fixed- and flex-route transit along a rectangular corridor. Compared with existing literature, the novelty of this study lies in designing the fare structure while simultaneously considering demand elasticity and passenger behaviour. A continuous approximation modelling approach is employed to derive the agency’s and travellers’ cost components. Using these, a nonlinear programming optimisation model is formulated to minimise the total user cost subject to the agency’s nonnegative revenue constraints and passengers’ route choice behaviour, which is characterised as a path-size logit model. Numerical experiments are performed using a stylised network to examine the properties of the model, in which the solution is obtained by combining a brute force method that enumerates headway and fare combinations and an iterative method that determines equilibrated passenger choices. The results show that as potential demand density increases, fare and headway fluctuate and drop, while the percentage of passengers choosing to ride on flex-route transit increases. In addition, there may be an optimal maximum offset distance, which is defined as the width of the corridor to be covered by the transit system, when the potential demand density is low, leading to minimum user cost and maximum travel demand within the service area.
Guo et al. (Mon,) studied this question.