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

•Unifying steady-state link travel formulations for three perspectives (functional longitudinal, functional cross-sectional, and experienced) and across three modelling paradigms (dynamic, semi-dynamic, static).•All formulations are derived from a state-of-the-art continuous time macroscopic first order network loading model of the Generalised Link Transmission Model (GLTM) family.•Demonstrating functional and experienced perspective formulations yield identical results regardless of their difference in context.•Explicit derivation for a number of existing formulations in the literature, which are to be considered special cases of our more general formulation.•Classification for a large number of existing formulations is provided as well as numerical examples to highlight the use of various perspectives. Travel times are one of the most important outputs of transport planning models, especially in a strategic context. It is therefore paramount that the methods that underpin the construction of travel times are well understood. A plethora of methods exists to extract and/or construct travel times given some underlying network loading procedure, also known as the traffic flow propagation model. However, the relation between these different travel time methods and the consistency between such methods has received relatively little attention in the literature. This might in part be due to the many different traffic flow propagation models in existence, ranging from vehicle based (microscopic), to flow based (macroscopic), and models that explicitly account for the time varying nature of traffic flows (dynamic) to models that do not (static). In this work, we limit ourselves to flow based, i.e. macroscopic, traffic flow models. Within this modelling paradigm we consider dynamic, semi-dynamic, and static traffic flow propagation formulations used to construct link travel times. The semi-dynamic and static approaches are considered as more aggregate versions of the dynamic formulation. Within this context we formulate a unified (link) travel time formulation that is consistent across these three modelling paradigms under the assumption of steady-state flow conditions. The dynamic link travel time formulation is based on a recent state-of-the-art continuous time macroscopic dynamic network loading model. In the dynamic model we assume steady-state conditions to remain consistent with steady-state semi-dynamic and static approaches. This allows us to derive semi-dy