Exploring trade-offs in frequency allocation in a transit network using bus route patterns: Methodology and application to large-scale urban systems

• Coupling of pattern frequencies with perceived frequencies at the route level.
• Bus loading constraints for every stop, route and time combination.
• Temporal and spatial heterogeneity of ridership elasticity viz. headway.
• Bridging gap between user and operator perspectives.
• Win–win solutions exist; optimization tools are required to find them.

Transit agencies seek to allocate their limited operational budget and fleet optimally to service routes in order to maximize user benefits. The Transit Network Frequency Setting Problem formulation developed in this study effectively captures the coupling between the routes and their prevailing patterns, which may have different subsets of stops visited at different times of the day. The number of riders is elastic to the prevailing number of bus trips at a given stop, which is the combination of different pattern dispatch frequencies. As a result, the study bridges the gap between the operator’s perspective where the decision unit is the pattern schedule, and the user’s perspective, which perceives frequencies at the route level. Two main formulations are introduced. The first one maximizes the number of riders and the total waiting time savings under budget, fleet, policy headway and bus loading constraints; the second minimizes the net cost under fleet, policy headway, bus loading, minimum ridership and minimum waiting time savings constraints. In both formulations, pattern headways are the decision variables. Spatial and temporal heterogeneity of ridership elasticity with respect to headway is captured. The formulations are applied to a large-scale test network for the Chicago area. The results show that a win–win solution is possible where both ridership and waiting time savings are increased, while the net cost is decreased.