  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. 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 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.
