On-Demand Public Transit: A Markovian Continuous Approximation Model

Abstract

With recent advances in mobile technology, public transit agencies around the world have started actively experimenting with new transportation modes, many of which can be characterized as on-demand public transit. Design and efficient operation of such systems can be particularly challenging, because they often need to carefully balance demand volume with resource availability. We propose a family of models for on-demand public transit that combine a continuous approximation methodology with a Markov process. Our goal is to develop a tractable method to evaluate and predict system performance, specifically focusing on obtaining the probability distribution of performance metrics. This information can then be used in capital planning, such as fleet sizing, contracting, and driver scheduling, among other things. We present the analytical solution for a stylized single-vehicle model of first-mile operation. Then, we describe several extensions to the base model, including two approaches for the multivehicle case. We use computational experiments to illustrate the effects of the inputs on the performance metrics and to compare different modes of transit. Finally, we include a case study, using data collected from a real-world pilot on-demand public transit project in a major U.S. metropolitan area, to showcase how the proposed model can be used to predict system performance and support decision making.