Continuous Approximation Model for Hybrid Flexible Transit Systems with Low Demand Density

Document Type

Journal Article

Publication Date


Subject Area

economics - benefits, ridership - demand, planning - methods, planning - route design, planning - service rationalisation


Flexible transit, fixed route, hybrid transit, demand, cost


Flexible transit systems are a way to address challenges associated with conventional fixed route and fully demand responsive systems. Existing studies indicate that such systems are often planned and designed without established guidelines, and optimization techniques are rarely implemented on actual flexible systems. This study presents a hybrid transit system where the degree of flexibility can vary from a fixed route service (with no flexibility) to a fully flexible transit system. Such a system is expected to be beneficial in areas where the best transit solution lies between the fixed route and fully flexible systems. Continuous approximation techniques are implemented to model and optimize the stop spacing on a fixed route corridor, as well as the boundaries of the flexible region in a corridor. Both user and agency costs are considered in the optimization process. A numerical analysis compares various service areas and demand densities using input variables with magnitudes similar to those of real-world case studies. Sensitivity analysis is performed for service headway, percent of demand served curb-to-curb, and user and agency cost weights in the optimization process. The analytical models are evaluated through simulations. The hybrid system proposed here achieves estimated user benefits of up to 35% when compared with fixed route systems, under different case scenarios. Flexible systems are particularly beneficial for serving corridors with low or uncertain demand. This provides value for corridors with low demand density as well as communities in which transit ridership has dropped significantly because of the COVID-19 pandemic.


Permission to publish the abstract has been given by SAGE, copyright remains with them.