Continuous Approximation of Deficit Functions for Fleet Size Calculation

Abstract

It is a fundamental and important task to determine the minimum fleet size required for a public transit (PT) system because the fleet cost is a major operating expense experienced by PT agencies. More importantly, the fleet size information has been incorporated into various PT operations planning activities. Therefore, effective, efficient, and practical methods as well as tools are required to calculate the minimum fleet size required for a PT system. This work first presents the limitations of a traditional fleet size model that is widely used in the literature. Second, the traditional deficit function (DF)-based fleet size model, which can overcome these limitations, is introduced. However, one restriction of the traditional DF-based fleet size model is that a DF has been proven to be not differentiable at its significant points. To overcome this restriction, this work proposes the idea of using continuous approximation (CA) instead of the step-function feature of the DF model. A numerical example is provided to illustrate the CA of the DFs technique followed by some theoretical results. The effectiveness of the CA of the DFs technique in calculating the fleet size required is demonstrated in a case study of an autonomous modular PT system that is currently being developed in Singapore. Finally, some further extensions and potential applications of the CA of the DFs technique are discussed in connection with a possible design of future urban mobility systems, such as on-demand transit systems, autonomous modular transit systems, and shared autonomous vehicle systems.