Discretised route travel time models based on cumulative flows

摘要

The computation of route travel times is a fundamental work in solving dynamic traffic assignment problems, and hence, it is important to develop accurate and efficient methods. In this paper, both the step function (SF) and linear interpolation (LI) are used to approximate cumulative flows over time and develop formulations of route travel time models. We propose two categories of discretised route travel time models: (i) models based on route cumulative flow curves, and (ii) models based on link cumulative flow curves. We prove that all route travel time models proposed in this paper satisfy some desirable properties such as route first-in-first-out and continuity, and all discretised route travel times converge to the continuous-time route travel times. Finally, numerical methods are developed to evaluate the accuracy and computational efficiency of each type of route travel time models.