| There is a move by many North American transit agencies to attract more riders by offering higher frequencies on some lines. But there are currently no available operations research tools for choosing line frequencies across a transit network. The line frequency setting problem is complex with impacts on both system users and the system operator. A conceptual model of a transit agency as a passenger maximizing, budget balancing firm operating in a competitive marketplace is developed. This conceptual model is then translated into a bi-level mathematical model (program) for the determination of optimal line frequencies in a network. A solution algorithm for the continuous relaxation of the bi-level program using cutting-planes is developed. A fast algorithm using traffic assignment by paired alternative segments (TAPAS) is adapted and developed to allow fast, precise solutions of the combined user equilibrium mode split and assignment user model. Test results on the Sioux-Falls network show good convergence properties for the cutting planes method, while results from a network of Anaheim, CA, show the possibility of the methodology having significant impacts on improving ridership. The assignment and combined equilibrium models using TAPAS show a significant improvement over the dominant Frank-Wolfe and Evans algorithms, respectively. Formulations for a multi-time period model and branch-and-bound algorithm are also briefly presented. |
