Traffic initially becomes congested (e.g., queuing occurs) at the end of a link because
link inflow is greater than link outflow (put another way, a congested traffic state arises at the
end of the link under these conditions). According to the basic tenets of traffic flow theory—
upon which dynamic models are based—for a given value of outflow, there is a corresponding
value of density and speed under congested conditions. This is best thought of in the case of a
freeway, where the outflow is roughly constant, as opposed to a signalized road where outflow is
constantly fluctuating. For purposes of this discussion, we assume that the outflow is in fact
constant. The longer this condition (inflow > outflow) persists, the more vehicles accumulate on
the link, and the portion of the link covered by the congested traffic grows in the upstream
direction until it reaches the link entrance. At this point in time, the inflow is reduced. It is, in
fact, equal to the outflow, and the link is in a steady-state condition, meaning that speed, density,
and flow are essentially constant at all positions (in space) along the link. The speed and density
on the link correspond to the flow (inflow and outflow, which are equal) in a well-defined
mathematical way, called the fundamental diagram of traffic flow.
In a dynamic model, each link may be defined by its own fundamental diagram, if
desired. This is sometimes thought of as the dynamic analogy to the static VDF, but this analogy
is loose as the two mathematical relationships actually perform very different functions in the
contexts of their respective models. In a static model, the VDF actually represents the congested
condition, while in a dynamic model, the fundamental diagram describes how congestion at the
exit node (reduced link outflow) is propagated upstream though the link, until it spills back onto
the next upstream links.
This phenomenon brings forth the question of congestion spill-back, which is not
represented in a static model. At the moment that the link inflow becomes equal to the outflow
(as described above), the congestion then continues to spread upstream into whichever upstream
links are feeding traffic into the congested link. The outflows of these links are thus reduced, and
the process repeats as described above. This queue spillback process also describes how a long
queue (congested traffic) can be represented over a sequence of links in a dynamic traffic model.
There is also the question of link FIFO (first-in, first-out). Static models, and even some
dynamic models that are based on fluid mechanics, enforce the link FIFO rule. In a static model,
this means that all vehicles traveling on the link experience the same travel time. In a dynamic
model with FIFO, this means that all vehicles entering the link at a given point in time
experience the same travel time. What this implies is that there is no overtaking between vehicles
and, in particular, this means no overtaking between vehicles that exit the link by different
turning movements. In reality, it is quite obvious that if there are two turning movements for
exiting a link and if one is oversaturated and the other is not, then the vehicles in queue for the
oversaturated movement can be overtaken by the other vehicles (assuming the link has more than
one lane), and that the latter vehicles can have significantly lower travel times than the former.
Models that move individual vehicles on discrete lanes of the roadway can model non-FIFO
conditions realistically, and thus have no need of employing the FIFO assumption. Further, if the
turn bay queue spills back to the through lane, the resulting capacity reduction also needs to be
properly accounted for through appropriate traffic modeling.
Last, it is worth noting that, as there is no explicit representation of individual lanes in
static models, there can be no distinction between the traffic conditions on different lanes of the
same link. There is no way to represent the fact, for example, that the outside lane of a freeway is
at a crawl due to an oversaturated off-ramp, while the other lanes are moving at a higher speed.