Steady-state link travel time methods: formulation, derivation, and classification

Abstract

Travel times are one of the most important outputs of transport planning models and this is unlikely to change in the future. It is therefore paramount that the methods that underpin the construction of travel times are well understood. However, while there exist many different travel time formulations to date, their relation to each other is not well researched, especially in the context of the three main types of macroscopic modelling paradigms: dynamic, semi-dynamic, and static traffic assignment. In this work, we provide consistent and general link travel time formulations across these three modelling paradigms, assuming steady state flow rates and by directly deriving them from a recent state-of-the-art continuous time macroscopic dynamic network loading model. We do so from two different perspectives; an experienced perspective, which actively tracks the tail of a physical queue, and a functional perspective, which does not. Based on the existing literature and our generalised link travel time formulations, a classification framework is proposed allowing one to compare existing (and future) methods in the literature in an objective fashion. We provide a number of explicit derivations of existing model formulations that can be considered special cases of our unified approach. In addition a number of representative existing methods in the literature has been classified based on the above mentioned framework for the reader’s convenience.