I've written a few times about the "Selfish Merge" problem. Recently, reading the new book Traffic: Why We Drive the Way We Do by Tom Vanderbilt, I came upon some new research that has changed and refined my thinking.

The selfish merge problem occurs when two lanes reduce to one. Typically, most people try to be "good" and merge early, and that leaves the right lane, which is ending, mostly vacant. So some people zoom ahead of everybody in the right lane, and then merge at the very end. This is selfish in the sense that butting into any line is selfish. Even if overall traffic flow is not reduced (and even if it is increased) the person butting in moves everybody back one slot so they can get ahead by many slots. This angers people and generates more counter-productive behaviour, including road rage, and attempts to straddle the lanes so that the selfish mergers can't move up to the merge point.

In Traffic, Vanderbilt writes of surprising research that changed his mind, which showed that, in simulations, some merging forms provided up to 15% more traffic throughput than proper attempts at a zipper merge. In particular, a non-selfish merge fully using the vanishing lane worked better than the typical butt-in situation described at the top.

In this merge, which I'll call the "slow and fair merge," drivers are told to use both lanes up to the merge-point, and then to fairly "take their turn" at the merge point entering the continuing lane. Nobody is selfish here, in that nobody butts ahead of anybody else, but both lanes are fully utilized up to the merge point.

This problem is complex, I believe, because there is a switch-over point, which I call the "collapse" point. This is the point at which the merge flow becomes high enough that traffic collapses to "stop and go" mode, before and at the merge-point. Before that point, in lighter traffic, there is little doubt (for reasons you will see below) that the "cooperating fast zipper" merge results in the best traffic flow. In particular, there are traffic volumes where you could either have cooperating zipper or "slow and fair" but cooperating zipper would do a fair bit better. There are also traffic volumes where cooperating zipper just isn't possible any more, and we will either have "slow and fair" (which has the best volume) or "selfish merge" which has a worse volume.

Real world experiments show different results from the theoretical. In particular, many drivers, used to the anarchic selfish-merge approach, don't understand fair and slow, even when signs are explicit about it, and so they resist using both lanes and try to merge early. They also try to straddle, devolving to selfish merge. An experiment with digital signs which changed from advising drivers to zipper-merge in light traffic to advising "use both lanes" and "merge here, take your turn" in heavier traffic was disobeyed in fair and slow mode by too many drivers. The experiment ended before people could learn the system.

Each scenario is understood by looking for the "chokepoint," which is the point with the lowest flow capacity. The rest of the system doesn't matter, because the system will only flow vehicles at the rate the chokepoint can handle. That chokepoint is somewhere near the merge point. Just past the merge point, vehicles start accelerating, and as you move downstream, the capacity increases until the cars are back at highway speed, in this case with just one lane.

Traffic lane capacity

A typical lane of traffic at highway speed handles around 2,000 cars per hour -- one car every 1.8 seconds (This is 1.6 seconds for the gap and 0.2 seconds for the car itself.) However, drop down to much slower speeds and this drops. When it devolves to "stop and go" the capacity is as little as 1,000 cars/hour.

In "cooperative fast zipper" the chokepoint is the place in the merge where drivers slow the most in order to do the merge safely, or if they don't slow, it's simply the one-lane segment. The capacity of such a system, working correctly, is close to the 2,000 cars/hour.

In "fair and slow" we will have two lanes of stop and go, each able to handle 1,000 cars/hour -- in other words the same capacity as the single lane going out at highway speed. However, this doesn't matter because at the merge point we have the actual chokepoint. There, after merging, cars are in a single lane but only going a few mph, and ready to accelerate. While going slow we have a small segment of road which has perhaps a 1,200-1,400 cars/hour capacity. As the cars accelerate it quickly turns into a higher capacity lane.

With selfish merge mode, we have one stop-and go lane at 1,000 cars/hour and a mostly empty lane delivering perhaps 100-200 cars/hour. These merge to the acceleration zone with its slightly higher capacity. Thus the chokepoint is the section where the vanishing lane is not being used, because the selfish mergers, due to their need to get in, have reduced the continuing lane (and for a short distance, the vanishing lane) to stop-and-go.

Around the collapse zone we have a tragedy. If everybody cooperated, we would get the best flow and no jam. Once we get to the point where incoming traffic is more than can be zippered, trying to be good and merge early is counter-productive. It is better to try to use both lanes.

Of course, drivers don't know what state we are in, and the threshold points also vary based on the highway conditions and the sort of drivers found on the highway.

To a solution

Engineers found that digital signs didn't work to solve the problem, at least in initial tests. It's well known that unusual signs cause traffic jams, as people slow, then stop, to read and consider them. It may be that solving this problem simply requires that drivers become used to the situation.

However, there is one system that drivers are getting familiar with already, and that's the metering light. This includes the two-lane metering light, where the lights alternate between left and right, so that jackrabbit accelerators are guided into a flawless zipper merge in an on-ramp. We have not yet quite mastered the "2 cars per green" metering light, which is used when high traffic flow is needed. These metering lights often gum up because confused drivers in slot #2 don't have the reflexes to go when the light turns green.

Nonetheless, it seems a good solution on a 2-into-1 merge would be to install metering lights, along with traffic volume sensors. When traffic volume was light, the left light would be green and the right light would be red, and cooperative zipper would be encouraged with other signs well in advance of the light.

As traffic volume got too high for cooperative zipper, we would see a collapse to stop and go. The sensors would detect this, and change the early signs to say "metering lights ahead, use both lanes." The lights would switch to metering mode. Once traffic cleared, the lights and signs would revert to zipper mode.

The problem seems a bit harder when trying to handle 3 into 2 or 4 into 3. Here the right behaviour is to try to move as much traffic as will fit into the left lanes, so that the 2 right lanes can do zipper merge without collapse. However, it is not possible when near collapse to tell the two right lanes to go metered while the left lanes zoom along. So design of solutions for this situation will need more care.

We also need to do more research, perhaps research that is specific to every different merge. That's because these numbers are remarkably close. I haven't found exact figures for the lane capacities of the combined lane where everybody is finally accelerating again. Those figures will have a great deal to say about where the chokepoint is. In addition, the stop-and-go dynamics of the actual lanes vary based on driver attitude, and the stop-and-go merge dynamics are also complex.

It does seem that teaching an ethic of "use both lanes if you see traffic coming to a halt" would make sense. In part, it is the fact that selfish mergers are "getting ahead" in a way that feels unfair that makes people resist this. Lots of people don't want to be the one who is cheating and getting ahead, believe it or not. If everybody did it, bizarrely, it would not longer feel like cheating, and thus be acceptable to all. Of course, some revel in doing it -- "so long, suckahs!" -- and this engenders vigilante blocking. Indeed, until everybody is doing it, they are indeed butting ahead of the others, and are generating the slowest of the three modes.

Summary

1. So long as traffic keeps moving, the ideal situation is a cooperative zipper merge, at speed, over a long distance before the merge point
2. If traffic collapses to stop and go, the best situation is to have both lanes fill with stop-and-go traffic, and do do a well timed merge of those two lanes at the merge point, ideally with left and right metering lights.
3. The worst case, which is what we commonly have now, is to have one lane with stop-and-go, and the vanishing lane almost empty, with cars zooming along to the merge point, and then getting into a merging battle there, with associated aggressive driving, blocking etc.

The paradox is this: So long as the vanishing lane is sparsely used, people who use it are selfish, or perceived as selfish, because they jump ahead in line to the detriment of those who don't. Only once half the drivers become "selfish" -- and thus the action is no longer of individual benefit -- does it become the right thing to do. Right now if you selfish merge you (and the misguided drivers to your left) create a worse merge situation, an angry merge, with people stopping to let you in, some people refusing to, some mergers trying to force their way in by playing chicken, some straddling the lane to stop people from jumping ahead of them. My intuition is that this angry merge becomes the poor-flow chokepoint.

There is an argument that one should do the selfish merge simply to drive up the numbers of people doing it until it no longer becomes individually advantageous and instead benefits all traffic. But until that time it may make things worse. I suspect metering lights are the best means to that.