On node models for high-dimensional road networks

- We identify an issue in the “first-in-first-out” (FIFO) assumption in modern node models for dynamic traffic assignment.
- This issue can lead to a trade-off between model complexity (e.g., large numbers of links) and realism.
- A “relaxed” FIFO construction is proposed, which allows for partial spillback, easily understood in terms of lane overlap.
- Node flows in this construction can be found algorithmically, and can be illustrated with a simple geometric interpretation.
- All proposed models are given for multicommodity traffic, with solution algorithms readily implementable in simulation software.

Macroscopic traffic models are necessary for simulation and study of traffic's complex macro-scale dynamics, and are often used by practitioners for road network planning, integrated corridor management, and other applications. These models have two parts: a link model, which describes traffic flow behavior on individual roads, and a node model, which describes behavior at road junctions. As the road networks under study become larger and more complex - nowadays often including arterial networks - the node model becomes more important. Despite their great importance to macroscopic models, however, only recently have node models had similar levels of attention as link models in the literature. This paper focuses on the first order node model and has two main contributions. First, we formalize the multi-commodity flow distribution at a junction as an optimization problem with all the necessary constraints. Most interesting here is the formalization of input flow priorities. Then, we discuss a very common “conservation of turning fractions” or “first-in-first-out” (FIFO) constraint, and how it often produces unrealistic spillback. This spillback occurs when, at a diverge, a queue develops for a movement that only a few lanes service, but FIFO requires that all lanes experience spillback from this queue. As we show, avoiding this unrealistic spillback while retaining FIFO in the node model requires complicated network topologies. Our second contribution is a “partial FIFO” mechanism that avoids this unrealistic spillback, and a (first-order) node model and solution algorithm that incorporates this mechanism. The partial FIFO mechanism is parameterized through intervals that describe how individual movements influence each other, can be intuitively described from physical lane geometry and turning movement rules, and allows tuning to describe a link as having anything between full FIFO and no FIFO. Excepting the FIFO constraint, the present node model also fits within the well-established “general class of first-order node models” for multi-commodity flows. Several illustrative examples are presented.