Optimal design of demand adaptive paired-line hybrid transit: Case of radial route structure

This paper studies the design problem of a demand adaptive paired-line hybrid transit system with a radial network structure. Depending on whether the demand adaptive service is operated along circular or radial transit lines, two variants of such systems are considered: a Circular Model (or C-Model) and a Radial Model (or R-Model). A continuous approximation approach is employed to develop the optimal design problem, which is formulated as a mixed integer program. A comprehensive numerical experiment is performed to compare various cost components corresponding to the optimal design of the two systems, and a discrete-event simulation is developed to validate the analysis. Numerical and simulation results suggest that the radial route network outperforms the grid route network, which was analyzed previously in the literature, with a significant margin, while the C-Model and R-Model offer similar performance.