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.

► Priority parameters are used to model different driver behavior.
► Solution non-uniqueness is found to result from realistic behavioral assumptions.
► A necessary and sufficient condition for solution uniqueness is formulated.
► Approaches solving the non-uniqueness in point-like intersection models are proposed.
► We reveal spatial models to exhibit non-uniqueness and sometimes unrealistic results.