Using Deficit Function to Determine the Minimum Fleet Size of an Autonomous Modular Public Transit System

Emerging technologies, such as connected and autonomous vehicles, electric vehicles, and information and communication, are surrounding us at an ever-increasing pace, which, together with the concept of shared mobility, have great potential to transform existing public transit (PT) systems into far more user-oriented, system-optimal, smart, and sustainable new PT systems with increased service connectivity, synchronization, and better, more satisfactory user experiences. This work analyses such a new PT system comprised of autonomous modular PT (AMPT) vehicles. In this analysis, one of the most challenging tasks is to accurately estimate the minimum number of vehicle modules, that is, its minimum fleet size (MFS), required to perform a set of scheduled services. The solution of the MFS problem of a single-line AMPT system is based on a graphical method, adapted from the deficit function (DF) theory. The traditional DF model has been extended to accommodate the definitions of an AMPT system. Some numerical examples are provided to illustrate the mathematical formulations. The limitations of traditional continuum approximation models and the equivalence between the extended DF model and an integer programming model are also provided. The extended DF model was applied, as a case study, to a single line of an AMPT system, the dynamic autonomous road transit (DART) system in Singapore. The results show that the extended DF model is effective in solving the MFS problem and has the potential to be applied to solving real-life MFS problems of large-scale, multi-line and multi-terminal AMPT systems.