Solving Selfish Merge, again

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.

Local and Express Lanes

Did the book discuss highways that have dedicated local and express lanes? I have driven on roads where there are one or two lanes on the right dedicated to cars entering or exiting the highway, then four "express" lanes that carry them for the rest of the trip. This is enforced by a physical barrier between the two roads. The intent is to keep the stop and go of the merging traffic from affecting the traffic moving at speed in the left lanes. The merging/local traffic has more of an opportunity to reach full speed before merging with the express traffic. This could help solve the "3 into 2 or 4 into 3" problem you mentioned above.

It's a different problem to some extent

As we’re usually talking about construction merges here. Indeed, for permanent merges highways do tend to have collector lanes and express lanes for just that reason.

Highway design tends to avoid having permanent lane reductions too many places. A usual way to do this is to have one lane simply become an exit lane. People seem to know that when a lane is “must exit” that they want out of it soon, and there is, rather than a merge point, a split point. Of course they will still, in some circumstances, go all the way to that split point but to stop and wait there is super-selfish because it blocks exiting traffic and is much more dangerous. People don’t have the same instinct to let in (or block out) somebody who does it.

It seems that it might also make sense for construction crews, when closing right lanes, to find a way to make them forced exit instead. Except that it would just be cones enforcing that, which people would ignore, at risk to crews.

Re: Solving Selfish Merge, again

So when confronted with an empty merge lane, should *I* be selfish hoping that others will follow to fill the lane thereby increasing the total throughput?

Or do I have it upside down and backward?

Always ready to sacrifice,
Randy.

What to do?

No, there is no solution for drivers right now.

If you use an empty merge lane, you will jump ahead of the queue, create road range and trigger lane straddlers. You will cause consternation at the merge point as people try to not let you in on one hand, and in the event the continuing lane starts getting back up to speed, you will cause it to collapse again by trying to get in.

The only answer seems to be educating drivers on the right behaviour, and using modern traffic sensors to tell them which of the two behaviours they should enter, including having metering lights that turn on after collapse to stop-and-go.

oh boy...

There you go again.

The obvious merge point is at the end of the lane (usually
the right-hand one) that is terminating. The cues include
the end of the dotted line separating the two merging lanes,
the solid outside line curving to become the boundry of the
remaining lane, and, OH YEAH, THE END OF THE MERGING LANE!

Sure, if traffic is light and one can safely do so, then
merge before the merge point. But if traffic is heavy and
slow, then a zipper merge at the end of the merging lane
is the correct response, fully utilizing both lanes.

The idea that merging early in this situation is somehow
"good", that people who wait until the merge point are
"selfish", and putting one over on others is bullshit,
pure and simple. The people who merge at the merge point
are driving correctly, and people who merge earlier are
not more virtuous.

Your tortured rationalization in an attempt to support your
misguided behavior is a clear indication that, in this case,
you are wrong.

I think you have misread what I wrote

Because I’m saying approximately the same thing you’re saying. To reiterate:

  • When traffic is not stop and go, the cooperative zipper over a long distance is best by a long shot
  • When traffic is stop and go, using both lanes fully (ie. both are stop and go) and merging in turns at the merge point is best
  • What is not best is having one lane be stop and go, and one lane be mosty empty, with people zooming up to the merge point in the mostly empty lane, and then having road rage battles at the merge point.

Unfortunately we mostly get the last choice in collapse conditions, when we want the middle one. Selfish mergers do nothing, possibly even make it worse, until there are so many of them that they are half the traffic, and it is no longer selfish (ie. confers an advantage to the detriment of the others.)

I love how this essentially validates my driving style ;)

I enjoyed this post - the thought of Anon@01:05 seems like a defensive-reflex reaction in anticipation of people taking out anger on h/er with regards to the so-called "selfish" merge.

I like to think of this as an economics problem and solution - since it essentially is: you take the profit-maximizing outcome.

People who claim what you're doing is unfair (i.e., the people Anon@01:05 addresses) are simply bad at economics, rather than driving (or, to belabour the idea even further - you need to be a good economist to be a good driver). ;)

Alas it may not

My supposition, which needs more research, is that it doesn’t validate anybody’s driving style. Right now using that empty lane is selfish and does make the situation worse, because of the poor behaviour it triggers at the merge point — some people stopping to let you in, some refusing to let you in, some people trying to force their way in, making others stop, some people playing chicken, some people straddling lanes to stop you from cutting ahead of everybody — and I suspect this poor behaviour causes the bottleneck which blocks everybody, and also slows down the “uncollapse” of the road back to flowing traffic.

So nobody’s behaviour is vindicated — not the early mergers, not the selfish mergers. The behaviour that is vindicated is two full lanes and a fair and even take-turns merge at the end, and nobody does that.

Education...

Other than your technological solutions, it sounds like what's really needed is education. People early merge because we're taught that jumping lines is wrong. It needs to be made clear that merging at the merge point is not jumping lines. Then more people will use the empty lane then there will not be a line to jump.

3-into-2 merge

An interesting thing you might want to look at is the multi-player train games over at openttdcoop.org (Yes, I know you're talking about cars in a special situation here, but bear with me).

Those guys usually build a loop of 2-or-more train tracks (lanes), with interchanges. That's the mainline, corresponding to a freeway. The "on-ramps" are quite elaborate. One method is what they call a shift main line (SML), where cars... er, trains... in lane 2 are moved into lane 3 (if it's empty enough), and cars in lane 1 are then (closer to the merge point) moved into lane 2. The on-ramp can then merge into lane 1.

Here, this explains it better, with pictures: http://www.openttdcoop.org/blog/2008/03/23/main-line-mergers/ (number 3 is the SML). That example is complicated by the "priority tracks" (which are sensors for the signals) and the doubled bridges. Moreover, that example has the B line merging into the A line. Both lines are double-tracked.

Here's a simpler example: http://www.openttdcoop.org/wiki/Unbalancers

Again, I'm well aware that cars are not trains, let alone comphttp://www.openttdcoop.org/wiki/Unbalancersuter-controlled train simulations (which are perfect at following the rules). But, this might help a robocar with merges :)

Bad pastage. That last

Bad pastage. That last paragraph should read:

Again, I'm well aware that cars are not trains, let alone computer-controlled train simulations (which are perfect at following the rules). But, this might help a robocar with merges :)

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