Optimal design of demand -responsive feeder transit services

The general public considers Fixed-Route Transit (FRT) to be inconvenient\nwhile Demand-Responsive Transit (DRT) provides much of the desired flexibility with a\ndoor-to-door type of service. However, FRT is typically more cost efficient than DRT to\ndeploy. Therefore, there is an increased interest in flexible transit services including all\ntypes of hybrid services that combine FRT and pure DRT. The demand-responsive\nfeeder transit, also known as Demand-Responsive Connector (DRC), is a flexible transit\nservice because it operates in a demand-responsive fashion within a service area and\nmoves customers to/from a transfer point that connects to a FRT network. In this\nresearch we develop analytical models, validated by simulation, to design the DRC\nsystem.\nFeeder transit services are generally operated with a DRC policy which might be\nconverted to a traditional FRT policy for higher demand. By using continuous\napproximations, we provide an analytical modeling framework to help planners and\noperators in their choice of the two policies. We compare utility functions of the two policies to derive rigorous analytical and approximate closed-form expressions of critical\ndemand densities. They represent the switching conditions, that are functions of the\nparameters of each considered scenario, such as the geometry of the service area, the\nvehicle speed and also the weights assigned to each term contributing to the utility\nfunction: walking time, waiting time and riding time.\nWe address the problem faced by planners in determining the optimal number of\nzones for dividing a service area. We develop analytical models representing the total\ncost functions balancing customer service quality and vehicle operating cost. We obtain\nclose-form expressions for the FRT and approximation formulas for the DRC to\ndetermine the optimal number of zones.\nFinally we develop a real-case application with collected customer demand data\nand road network data of El Cenizo, Texas. With our analytical formulas, we obtain the\noptimal number of zones, and the times for switching FRT and DRC policies during a\nday. Simulation results considering the road network of El Cenizo demonstrate that our\nanalytical formulas provide good estimates for practical use.