Non‐unique flows in macroscopic first‐order intersection models

Currently, most intersection models embedded in macroscopic Dynamic Network Loading (DNL) models are not well suited for urban and regional applications. This is so because so‐called internal supply constraints, bounding flows due to crossing and merging conflicts inherent to the intersection itself, are missing. This paper discusses the problems that arise upon introducing such constraints. A general framework for the distribution of (internal) supply is adopted, which is based on the definition of priority parameters that describe the strength of each flow in the competition for a particular supply. Using this representation, it is shown that intersection models – with realistic behavioral assumptions, and in simple configurations – can produce non‐unique flow patterns under identical boundary conditions. This solution non‐uniqueness is thoroughly discussed and approaches on how it can be dealt with are provided. Also, it is revealed that the undesirable model properties are not solved – but rather enhanced – when diverting from a point‐like to a spatial modeling approach.