The usual way to represent the behavior of a CA is with a space-time diagram, where space is represented on the horizontal axis, and time on the vertical axis, with time proceeding downward. A typical space-time diagrams for this model is shown in figure 2.
Figure 3 is the same as figure 2, except that on the right half of the figure neither lane can pass, while on the left half of the figure, both lanes can pass. This figure illustrates that passing can dramatically fluidify traffic. The start-stop waves seen in the right half of the figure disappear in the left half. At these densities jams may still occur in the passing zone, but these are of a different character; they are caused by failed or partially failed passes. Note that while "regular" jams move retrograde [1], jams caused by passing may move in the forward direction.
In these two figures, the densities have been chosen to maximize
the effects caused by interactions between two lanes in opposite directions.
We have explored the entire range of densities on the two lanes,
as shown in figure 4. Here the difference between
the flow on the home lane in
two-lane model with passing on both lanes is compared to the flow
in a one-lane model. When the density on either or both lanes
is large then there is little difference between the two-lane and
one-lane models (chartreuse). When the density on the opposite lane
is small ( 
), then the flow on the home
lane can be much greater than in a one-lane model (shades of green and
blue). Maximum improvement occurs near 0 density on the opposite
lane, and density 0.2 on the home lane. If density on the home
lane is small ( 
) then the flow may be lower than
in the corresponding one-lane model since when oncoming cars pass
other oncoming cars they can impede traffic on the home lane. This
region of parameter space, indicated by shades of yellow and red,
covers a narrow band on the left of the figure. In an asymmetric
model in which only vehicles on the home lane can pass, this slowing
effect disappears.
Our bi-directional model allows us to treat a host of new phenomena. For instance, the multi-speed variant (figure 5) can produce a complicated knot of interactions resulting from a slow car leading a group of others through a no-passing zone. While in the no-passing zone the faster cars bunch up behind the slow car, forming a platoon. When the platoon reaches the end of the no-passing zone the platoon disperses.