The continuous signalized (COS) node model for dynamic traffic assignment

In macroscopic dynamic network loading, the role of the node model is to determine transfer volumes between each in- and outgoing link, while respecting in a consistent way all forward and backward-moving traffic waves (or boundary conditions) and desired turning fractions. In addition, capacity constraints on the node itself need to be respected; they result from priority rules on conflict points, or from traffic signal control. The most common way in literature to implement signalized node models is to track second by second which turns have green or are blocked by red. This imposes a fine – and thus computationally demanding – time discretization step in the numerical solution algorithm of the entire dynamic network loading, often unnecessary or even undesired for the DNL application. As an alternative, this paper proposes a continuous approach that finds the average turn (or transfer) volume over a full cycle under the prevailing link boundary conditions and traffic signal timing. This average ‘continuous’ volume can then be applied to any (fine or coarse) time discretization. To this end, it discusses in depth and proposes mathematical formulations for all boundary and consistency requirements that a traffic signal imposes, and the intricate interactions between stage timing and arrival patterns of vehicles and outflow opportunities (gaps). This COntinuous Signalized or COS node model and its iterative solution algorithm combine all these boundaries and interactions in a theoretically consistent way. In a case study, we show that COS is the only existing, theoretically consistent continuous signalized node model, as alternative models sometimes fail to produce holding-free solutions, and/or violate boundary conditions imposed by the connecting links (especially in more complicated combinations of boundary conditions involving congestion spillback).