Lane changing

All lane changing rules, no matter if for CA or other models, follow a similar scheme (e.g. 110): In order to change lanes, drivers need an incentive, and the lane change needs to be safe. An incentive can be that the other lane is faster, or that the driver eventually needs to make a turn. Safety implies that one needs enough space on the target lane. Thus, a simple lane changing condition can read as (101) (Fig. 17.2):

(I)

Incentive: $min[v+1,v_{max},gap_{other}] > \min[v+1,v_{max},gap]$, i.e. the gap on the other lane is larger than the gap on the current lane, allowing a higher speed on the other lane.

Bounding the comparison at $\min[v+1,v_{max}]$ makes sure that only gaps sizes which are relevant for the car's current speed are considered.

(S)

Safety: $gap_{other,back} > v_{back}$, i.e. the backwards gap on the other lane is large enough that a vehicle approaching with $v_{back}$ does not have to slow down immediately.

Lane changing includes an additional sub-timestep, which is best exectued before the car following step. The full sequence is:

Go through whole system and tag vehicles for lane change.

Go through whole system and execute lane changes for tagged vehicles (sideways movement of vehicles).

Go through whole system and compute new velocities.

Go through whole system and execute forward movement of vehicles.

The separation of the lane change into a tagging and a movement step is useful to maintain the parallel update: Because of reaction delays, driver decisions should be based on ``old'' information.

The above lane changing rules may have vehicles from both sides compete for the same cell in a middle lane. This can be overcome by making lane changes to the right only in even and lane changes to the left only in odd time steps. Another possible artifact are long rows of vehicles synchronously oscillating between left and right lane. This can be suppressed by executing the above lane changes with a probability smaller than one, for example 0.99.

All this together is essentially the lane changing criterion currently used in the Transims micro-simulation, and it seems to work reasonably well for U.S. traffic (88).

Figure 17.2: Lane changing. A smalle ``gap'' will give an incentive to change lanes. The lane change is actually executed if both ``forward gap'' and ``backward gap'' are large enough.

The above lane changing criterion is symmetric, since changing to the left happens according to the same criterion as changing to the right. One result of this is that people stay in the left lane until some incentive pushes them out of it, again not totally unrealistic for traffic in the United States. For European (and other) countries, one has the constraint that passing on the right is not allowed, at least not when traffic is not congested. There are many ways to implement this. A fairly straightforward version is to change to the left when either on the same lane or on the left lane a slower vehicle is present:

(I'.a)

Incentive to go to left: ``$v \ge v_r$ .OR. $v \ge v_l$'' , where $v_r$ refers to the vehicle in front on the same lane, and $v_l$ refers to the vehicle in front one lane to the left.

Since the lane changing is no longer symmetric, many plausible rules are possible to trigger lane changes to the right. A good construction criterion for rules is to make lane changes to the right based on the logical negation of lane changes to the left. This results in

(I'.b)

Incentive to go to right: ``$v < v_r$ .AND. $v < v_l$''. Note that now $v_l$ now refers to the same lane, and $v_r$ refers to the lane to the right.

This leaves as a free parameter the distance $d$ how far vehicles look forward for vehicles in the same and in the other lane. Larger $d$ results in a stronger incentive to go to the left.

An important observation is that microscopic lane changing rules need not be realistic in order to generate plausible macroscopic traffic. For example, all lane changes according to the above rules happen in one simulation time step, which is usually one second, whereas in reality this takes longer (3-5 seconds). Also, the above rules result in too many lane changes when traffic on both lanes is similar - an effect that is annoying in animations (see, for example, one of the Transims videos), but macroscopic relations such as fundamental diagrams still come out correct (101,90).

As noted above, the incentive to change lanes could also come from an intended turn movement at the end of the link, and one can partially over-ride the safety criterion with increasing urgency of the incentive criterion.