I think it is a mistake to combine the two cases of "either merging or taking a turn".
If there is an upcoming turn and you can only turn from the inside lane and that lane backs up because, say, there is a light after the turn, then I think late merging can be anti-social and end up slower for everyone. A person who continues on in the through-lane eventually reaches the turn since no slots can open up while cars are stopped waiting for the light to change. He does not want to go past his turn so he stops to wait for a slot to open when the light turns. Now through traffic in the outside lane starts backing up so that not only are people who do not plan to take the turn unduely delayed, so are even the people who are going to take the turn since they are now stuck behind the non-turmers. The net result is that the traffic light now becomes a bottleneck for everyone. When people merge early, the bandwidth of the turn is used efficiently and reaches an equilibrium of some stable queue length before the turn, but when even a small number of people wait too long to merge then fewer people are able to make it through the light on each cycle and so the delay is longer for all groups (early mergers, late mergers, and especially through-drivers). This is a common case in NYC, and famously happens at the turnoff from the FDR drive to the Brooklyn Bridge.
Driving in California, it’s a common occurrence where one slow driver in the bottlenecked lane is holding everyone up. One of the major benefits of late merging is it just means getting ahead of those people, who are going to be stuck two traffic lights behind anyway when others could’ve gone ahead and made the turn already.
Yeah, I really don't buy the argument that early merging is "evil communist logic that makes the collective worse off". Even modelling the scenario without any other turns, the flow rate, and therefore time in traffic, is bounded solely by the bottleneck. It is at worst exactly the same. On the other hand, the further the left lane backs up, the more signal that other drivers have that "hey the left lane is backed up, you should turn early if possible"
Really, the inverse argument could be made that it's "this is better for me personally, therefore it must be better for the collective (despite being clearly at the expense of others)" backwards rationalization. Evil, uh, let's say libertarian, logic.
If you're driving in much of the South, including where I live now, people will routinely and predictably leave big gaps that might still make a late merge into a left-turn lane pro-social in this scenario. Someone who should be able to make it through the green arrow is asleep at the wheel and fails to move, you cut in front of her and zero time is lost, and this happens approximately 100% of the time in a backed-up left turn lane.
To be fair, this is the sort of maneuver I'll only do in my own town, which I know well and it basically never goes wrong.
When I used to live in a big Yankee city, I'd estimate literally 2x as many cars could make it through a left-turn light and leaving one of these gaps would instantly ignite a storm of car honks. Though it might also be that smartphone distraction was less a factor in those days, a decade or so ago.
Is this a simple case of bottlenecking through inefficiency of man (CPG Grey's complaint on human lag), thus reducing effectiveness (traffic jams)? Also what would be a more well-articulated alternative to either forms?
A proper Übermensch does not obey (and cite) bureaucrats in midwestern departments of transportation. The Übermensch takes option 3: the otherwise closed lane lesser mortals fear to tread upon. Otherwise, why not go ahead and put on an N95 mask in the car?
The social cohesion and trust of said ethnically-similar states may allow for zippering but...lol I can't keep this up. Great article, your blog is the best
For me the answer is that I want to make sure there’s room in the overhead bin for my carry-on luggage. The overman can’t be bothered to have his luggage get checked in and then wait for the pickup carousel to deliver it.
i always board dead last but not sure if it's because the confucian gentlemen always lets the crowd through first or because the neitzschean ubermensch prefers to spend as little time as possible sealed inside a steel tube with a herd of flatulent untermenschen.
i am an early merger in new york (bc I trust that everyone ahead of me is alert and engaged), and a late merger in cali (bc everyone out here is an airhead glued to their phones). culture matters!
If I see an opening when there is lots of traffic I will merge earlier. I perceive it as safer than continuing to travel at a high speed in hopes someone will let me in. If I trusted other drivers to obey the rules of the road, I would late merge. But many other drivers are incompetent, negligent, or both. Waiting 10 extra seconds in traffic is worth even a minuscule reduction in the probability of an accident. Getting in an accident is orders of magnitude worse than waiting an extra 10 seconds in traffic; the EV calculation is just not there to late merge if it increases your odds of a crash by even .001%. To expose oneself to risk that does not have a proportional reward is not courageous; it is reckless.
Asymmetric downsides (accidents + bottlenecks) vs weak upsides (time gains by late merging)? If so how can one evaluate when to do early merge vs late merge, in relation to traffic density or lane count?
I use my judgment as to when the safest time to merge is based on the flow of traffic. Usually, this means merging earlier. The asymmetries between safety and time-saving are so great that time-saving doesn't even enter my calculus.
(1) I am a Professor that studies fluid flow (and traffic flow). The flow in the single lane goes the speed it goes. Anything that happens before that single lane makes *absolutely* no difference to the number of cars exiting a merger per minute. Zipper is not better for the collective. Nor is it better for me, so please pipe down and leave my open lane - open.
(2) The only way to improve the merge is for the people in the single lane to drive twice as fast (or at least somewhat faster). If they do that, then one lane can carry two lanes worth of cars. This is what molecules do and why if you force a merge at the end of a hose the water comes out faster. Of course, human drivers do the opposite of what they should do, so they are objectively and provably dumber than water.
Question: doesn't early merging effectively make the single lane longer? Whereas zipper merge makes it shorter? If there is any benefit to zipper merging, I would think that would be the source of it.
Zipper merging only makes a difference when the 2 lanes are at half of max capacity (or less).
This is why it is encouraged in a few rural states - where that situation is often true.
Then the zipper causes less "people being stupid" because it can do the same number of merges while doing them slower (and smother, and safer) because there are many of them happening all at the same time.
Zipper is useless in city rush-hour merges. It will reduce the length of the backup section slightly - but not the total number of cars in the backup section.
> Then the zipper causes less "people being stupid" because it can do the same number of merges while doing them slower (and smother, and safer) because there are many of them happening all at the same time.
You appear to be confusing the picture that Hanania linked into his article with the definition of zipper merging given in the article he took it from.
Zipper merging does not allow for multiple cars to merge in parallel. The picture labeled "zipper merge" is not actually depicting one.
Clearly, early merging does make the single lane longer.
But I don't think the length of the single lane matters. As Optional notes, there are two relevant variables: inflow to the single lane, and outflow from the single lane. You have a traffic jam when inflow exceeds outflow.
Neither inflow to the lane nor outflow from it is affected by the length of the single lane. Inflow is determined by the carrying capacity of all sources of traffic to the merge point. Outflow is determined by the carrying capacity of the single lane. If you triple the length of the single lane, the cars in it will move just as fast as they did in the shorter single lane, and outflow will be unchanged. There will be *more cars* in the longer lane -- you have the same number of cars per second, but it takes more seconds to traverse the single lane, meaning more cars in transit at any given time -- but who cares?
Question, slower requires less distance to the next car, isn't there a range where a slower speed could actually increase the flow? Seems to subtly depend on what people deem safe distance at speed?
It is a good observation, and the effect you cite is partly active - but only a very small amount.
You are correct that if the traffic in the single lane (post merge) drove with the same speed as normal (say 60 mph) but with half the car separation (that people normally desire at 60 mph), then the single lane will carry two lanes worth of traffic. But unfortunately, humans don't do that.
We can observe that human psychology requires the car separation to roughly linearly increase with car speed. This is probably because physically the distance required to make an adjustment in a fixed time (say one second) is exactly linearly proportional to speed. And people intuit that physics.
Interesting result 1 (due to the linearity relation): If a road is at maximum human-tolerable packing then it outputs roughly the same number of cars per second - no matter what speed the cars are going. You either have a few far-spaced cars going quickly, or many close-spaced cars going slowly. A road has a "maximum carrying capacity".
Result 2: Trying to force the carrying capacity of 2 (already fully packed) lanes into 1 lane - never works. The road doesn't care. A single lane can only output a maximum number of cars per second. If more cars per second arrive at the beginning of that lane (due to a merge) than that lane can output - it doesn't give a hoot. It does not adapt. Those extra incoming cars just have to wait. From a helicopter you will see the merge backup (slow car section) growing ever larger and traveling backwards up the road.
Result 3: When the cars on the 2-lane highway (way before they hit the backup) deplete to being so few that they can be carried entirely by a single lane at max packing, then the backup does NOT go away. But the existing backup section no longer gets any larger. When the cars coming into to backup are lower than the maximum carrying capacity of a single lane only then does the backup begin to get smaller and eventually get removed (after probably hours).
Results 4: Police on the side of the highway at rush hour (max packing) cause the same basic problem as the merge. Traffic slows down, cars get closer, the road carries the same number of cars as before, but everybody gets home slower. The slow section gets larger with time, moving backwards up the road. The cop leaves. And hours later that slow section the cop created is getting slowly smaller - but is STILL there.
> Results 4: Police on the side of the highway at rush hour (max packing) cause the same basic problem as the merge. Traffic slows down, cars get closer, the road carries the same number of cars as before, but everybody gets home slower. The slow section gets larger with time, moving backwards up the road.
I don't understand the comparison. When a lane is blocked, the carrying capacity of the road should go down. That's what causes the jam before the block.
But a cop on the side of the road isn't closing a lane. The carrying capacity of the road in that case should stay the same... right? Everyone slows down, they pack closer together, and the same number of cars per second make it past the point where the cop is.
But from the inflow/outflow perspective... we've already stated that, as an empiric law, the outflow from the area of the highway governed by the cop does not change. People may be going faster or they may be going slower, but the same number of cars per second make their way past the cop.
And the inflow to the cop's area isn't changing either. The same number of cars per second will also be arriving in the area where the cop is. It's not like people learn there's a cop watching a particular area and then adjust their plans to go drive by the cop -- if they adjust at all, it will be to stay away from the cop.
So, since outflow doesn't change and inflow doesn't change... how can a jam form and creep backwards up the road? All inflow to the jam is constantly being cleared from the other end of the jam. It has no way to grow beyond whatever its current size is.
The lane closure isn't like that; it reduces outflow. The mismatch between (unchanged) inflow and (reduced) outflow is what causes the traffic jam to grow over time. Why would the same happen in the case of the cop?
Result 4 is similar to Result 3 in that once a backup is established, it remains present even when the road is quite capable of carry the incoming number of cars - without that backup present.
You are correct that the cars/second is the same in the cop case at all times.
(This is also true in result 3, as well, where incoming = outgoing).
But this is not the metric of optimality for society. If everybody has a 15 minute longer drive home, and everybody had to throw on their brakes and waste gas driving at low speeds, then everybody has lost. Even though they didn't need to. The road could have carried them all at higher speeds if the cop hadn't fuct it up and then left.
Optimality is the highest safe speed for everybody (time is what is valuable) not the throughput (cars/second).
And the key lesson from Result 4 is that roads do not naturally or quickly obtain the optimal state. When put in a sub-optimal state (traffic jam for a long-gone cop) that state is also fairly stable and just sits there (annoying everybody).
Yes, even the cop causes an expanding backup section.
In the fully packed situation, if any cars are going 30 mph, then all cars behind them go that same speed. The cars approaching the 30 mph section will definitely slow down. And that "shock wave" will propagate backwards. When the cop leaves, the back-up unclogs from the front of the backup, and then that "front" of the backup moves backwards (unclogging as it goes backwards, from the front).
This is all very similar to high-speed (near Mach number) flow of gases (which are compressible, and can take up variable space - like cars).
I am historically a late merger myself because it always seemed right to me, but I know most people find it very rude. As I get older, I am more wearied by the negative interactions that sometimes occur with people when I am trying to merge late and I sometimes consider merging early simply to avoid these. Also, the extra twisting and turning required isn’t as easy for me as it used to be. So, one day soon, I might find myself to be an early merger as well. So, enjoy merging late while it lasts for you. One day you might wake up and find yourself to be one of those people.
Would someone rather lose 2 min by merging early, and sit back and not having to stress anymore … or gain the 2 min, and now have to worry about someone letting them in, and executing without bumping someone?
Obviously this is going to depend a lot on things like whether you’re running late, risk-aversion, and driving competence.
But most people seem to prefer slower and chiller. It’s totally rational.
It is true that using the second lane until the end increases flow to the entry point of the single lane. However, this is unrelated to the overall throughput since throughput is limited by the single lane flow. Your action can never increase the overall flow, your gain is therefore the loss of the early mergers: your jumping the queue for your own gain. Not polite.
In addition, a late merge will inevitably create hazards. Even if you're a perfect driver, which is not very likely, you have to interact with people like me that might be pissed off you jumped the queue, people that have very little skill driving a car, people that get nervous from this aggressive maneuvers, or just not paying attention. Not only can this disruption cause a gap in the front that cannot be (legally) made up, breaking in a queue can get amplified and cause accidents behind you.
So I think your strategy to jump the queue reduces the average flow for everybody and increases the hazards. So I tend to graciously allow people to merge in front of me early on but at the end I take advantage that my car is really old.
Your third category is motivated by shame or stigma - hence why they're conformist not cowardly. But you posit they all could - and believe they could - merge later if they were willing to stand out.
That's well and good but misses an important group - the genuinely cowardly. You're obviously a skilled driver, or believe so, including when confronting or relying on other drivers to execute a maneuver. That's not an uncommon sentiment.
But it's also not universal, at all! In my experience at least, lots of folks do not know what they're doing to merge on a highway. Or, they are afraid they don't know, or it won't work or something will go wrong in this instance.
Plus, it can be genuinely terrifying, or at least unnerving, to watch the end of a lane approaching as you travel a high speed, and see no ready way to merge. The prospect terrifies many people - at worst they crash head on to their demise, at best they broadside the car next to them and chaos and sorry follow.
This group, the cowardly, prefer to avoid that possibility (if not casualties, at least the hassle of having to squeeze in and not screw up after their first plan fails). They're real and not scarce in number, and your taxonomy is incomplete, and its explanatory power diluted, by your omission.
This is exactly right. There are many drivers who correctly realize they do not have the skill to merge late, and so don't. Merging late requires skill and alertness, which not everyone possesses. Ironically, this strategy only works because of those drivers, because aggressive drivers won't let you merge at the front of the line. I'm a guy who, when the light turns green, gets halfway across the intersection before anyone else has even moved, and if you think you're merging ahead of me in a crowded exit lane, you've got another think coming.
Another reason is that there can be risk in waiting too long, getting frozen out of the merge.
For example. I have an north exit nearby, followed in a 1/4 mile by a south exit which generally has a longer backup. If you wait too long to get to the right for the north exit, you can get stuck on the wrong side of the backup of cars waiting for the south exit.
Generally speaking, I completely agree with the point of your post. Similar reasoning holds for following cars pretty closely. This actually speeds up overall traffic quite a lot.
Care to elaborate what "deadweight loss" is? I can only find information on "price ceilings" or loss efficiency due to taxes and regulations. Does that mean there are exceptions where not doing late merging is more effective?
I was talking about perceptions and from a naïve POV a late merge does look like a making a lot of people wait a bit longer so that the late merger can save the time of not just queuing (aggregate loss of time, deadweight loss). Most people normally think queueing is optimal. Now I HAVE read the studies that zippering is most efficient way of binging two in principle equal lines of traffic into one line, but that does not mean that those who have not are just foolish..
I'm confused as to how any behavior *before* the bottleneck can change the speed with which cars pass *through* the bottleneck. If the single lane can admit 0.5 cars per second and the highway is transporting 2 cars per second, traffic is going to back up regardless of where people merge.
I do see how having that backed-up traffic occupy more road space is beneficial, since that means it won't extend back as far and won't interfere with as much cross traffic. But unless zipper merging somehow increases the speed at which cars drive once they're in the single lane (which is very plausible, I just don't get exactly why it would happen), it can't speed up the average travel time of people in the jam to zipper merge.
What am I missing here?
Also, I tend to merge early because I'm very safety-conscious and it's dangerous to try to force myself into another lane of traffic that doesn't want to let me in at the last minute. The earlier I start trying to merge, the more likely it is that I'll find someone who lets me in before I have to slow down to avoid running into the traffic cones.
I think it is a mistake to combine the two cases of "either merging or taking a turn".
If there is an upcoming turn and you can only turn from the inside lane and that lane backs up because, say, there is a light after the turn, then I think late merging can be anti-social and end up slower for everyone. A person who continues on in the through-lane eventually reaches the turn since no slots can open up while cars are stopped waiting for the light to change. He does not want to go past his turn so he stops to wait for a slot to open when the light turns. Now through traffic in the outside lane starts backing up so that not only are people who do not plan to take the turn unduely delayed, so are even the people who are going to take the turn since they are now stuck behind the non-turmers. The net result is that the traffic light now becomes a bottleneck for everyone. When people merge early, the bandwidth of the turn is used efficiently and reaches an equilibrium of some stable queue length before the turn, but when even a small number of people wait too long to merge then fewer people are able to make it through the light on each cycle and so the delay is longer for all groups (early mergers, late mergers, and especially through-drivers). This is a common case in NYC, and famously happens at the turnoff from the FDR drive to the Brooklyn Bridge.
Driving in California, it’s a common occurrence where one slow driver in the bottlenecked lane is holding everyone up. One of the major benefits of late merging is it just means getting ahead of those people, who are going to be stuck two traffic lights behind anyway when others could’ve gone ahead and made the turn already.
exactly right. totally different from lane - ending merges.
Yeah, I really don't buy the argument that early merging is "evil communist logic that makes the collective worse off". Even modelling the scenario without any other turns, the flow rate, and therefore time in traffic, is bounded solely by the bottleneck. It is at worst exactly the same. On the other hand, the further the left lane backs up, the more signal that other drivers have that "hey the left lane is backed up, you should turn early if possible"
Really, the inverse argument could be made that it's "this is better for me personally, therefore it must be better for the collective (despite being clearly at the expense of others)" backwards rationalization. Evil, uh, let's say libertarian, logic.
If you're driving in much of the South, including where I live now, people will routinely and predictably leave big gaps that might still make a late merge into a left-turn lane pro-social in this scenario. Someone who should be able to make it through the green arrow is asleep at the wheel and fails to move, you cut in front of her and zero time is lost, and this happens approximately 100% of the time in a backed-up left turn lane.
To be fair, this is the sort of maneuver I'll only do in my own town, which I know well and it basically never goes wrong.
When I used to live in a big Yankee city, I'd estimate literally 2x as many cars could make it through a left-turn light and leaving one of these gaps would instantly ignite a storm of car honks. Though it might also be that smartphone distraction was less a factor in those days, a decade or so ago.
Is this a simple case of bottlenecking through inefficiency of man (CPG Grey's complaint on human lag), thus reducing effectiveness (traffic jams)? Also what would be a more well-articulated alternative to either forms?
A proper Übermensch does not obey (and cite) bureaucrats in midwestern departments of transportation. The Übermensch takes option 3: the otherwise closed lane lesser mortals fear to tread upon. Otherwise, why not go ahead and put on an N95 mask in the car?
The social cohesion and trust of said ethnically-similar states may allow for zippering but...lol I can't keep this up. Great article, your blog is the best
it's like those people who line up to board the plane when it starts boarding. Why?
the overman stays seated and waits for the line to clear
the overman boards last
For me the answer is that I want to make sure there’s room in the overhead bin for my carry-on luggage. The overman can’t be bothered to have his luggage get checked in and then wait for the pickup carousel to deliver it.
The overman brings a backpack that fits under the seat in front of him.
And a liverworst sandwich to assert his dominance.
Real overman don't mess with overhead, and use included checked luggage (if it is a long trip).
i always board dead last but not sure if it's because the confucian gentlemen always lets the crowd through first or because the neitzschean ubermensch prefers to spend as little time as possible sealed inside a steel tube with a herd of flatulent untermenschen.
guess it depends upon my mood.
Tao-Neitzschean synthesis: I am too tired to deal with people, so getting on when you are not late is good enough for the airline.
Funny how the selfishly practical aligns with the seemingly courteous--good tactic either way, then!
late mergers are ASSHOLES!!!!
i am an early merger in new york (bc I trust that everyone ahead of me is alert and engaged), and a late merger in cali (bc everyone out here is an airhead glued to their phones). culture matters!
Also being from NY, I assume that late merging runs me a slight risk of aggressive retaliation from other drivers.
The fact that you wrote "cali" seems to suggest you aren't from california.
or perhaps i was typing on my phone and am very lazy
Time preference, personality/temperment differences, "nice" vs "kind"? Sorry I don't know enough about the US other than reading news, blogs, and TV.
Probably. But is that actually worse than being stupid?
Agreed! Sometimes I'm one myself.
If I see an opening when there is lots of traffic I will merge earlier. I perceive it as safer than continuing to travel at a high speed in hopes someone will let me in. If I trusted other drivers to obey the rules of the road, I would late merge. But many other drivers are incompetent, negligent, or both. Waiting 10 extra seconds in traffic is worth even a minuscule reduction in the probability of an accident. Getting in an accident is orders of magnitude worse than waiting an extra 10 seconds in traffic; the EV calculation is just not there to late merge if it increases your odds of a crash by even .001%. To expose oneself to risk that does not have a proportional reward is not courageous; it is reckless.
Asymmetric downsides (accidents + bottlenecks) vs weak upsides (time gains by late merging)? If so how can one evaluate when to do early merge vs late merge, in relation to traffic density or lane count?
I use my judgment as to when the safest time to merge is based on the flow of traffic. Usually, this means merging earlier. The asymmetries between safety and time-saving are so great that time-saving doesn't even enter my calculus.
I love this blog
(1) I am a Professor that studies fluid flow (and traffic flow). The flow in the single lane goes the speed it goes. Anything that happens before that single lane makes *absolutely* no difference to the number of cars exiting a merger per minute. Zipper is not better for the collective. Nor is it better for me, so please pipe down and leave my open lane - open.
(2) The only way to improve the merge is for the people in the single lane to drive twice as fast (or at least somewhat faster). If they do that, then one lane can carry two lanes worth of cars. This is what molecules do and why if you force a merge at the end of a hose the water comes out faster. Of course, human drivers do the opposite of what they should do, so they are objectively and provably dumber than water.
Question: doesn't early merging effectively make the single lane longer? Whereas zipper merge makes it shorter? If there is any benefit to zipper merging, I would think that would be the source of it.
Zipper merging only makes a difference when the 2 lanes are at half of max capacity (or less).
This is why it is encouraged in a few rural states - where that situation is often true.
Then the zipper causes less "people being stupid" because it can do the same number of merges while doing them slower (and smother, and safer) because there are many of them happening all at the same time.
Zipper is useless in city rush-hour merges. It will reduce the length of the backup section slightly - but not the total number of cars in the backup section.
> Then the zipper causes less "people being stupid" because it can do the same number of merges while doing them slower (and smother, and safer) because there are many of them happening all at the same time.
You appear to be confusing the picture that Hanania linked into his article with the definition of zipper merging given in the article he took it from.
Zipper merging does not allow for multiple cars to merge in parallel. The picture labeled "zipper merge" is not actually depicting one.
Clearly, early merging does make the single lane longer.
But I don't think the length of the single lane matters. As Optional notes, there are two relevant variables: inflow to the single lane, and outflow from the single lane. You have a traffic jam when inflow exceeds outflow.
Neither inflow to the lane nor outflow from it is affected by the length of the single lane. Inflow is determined by the carrying capacity of all sources of traffic to the merge point. Outflow is determined by the carrying capacity of the single lane. If you triple the length of the single lane, the cars in it will move just as fast as they did in the shorter single lane, and outflow will be unchanged. There will be *more cars* in the longer lane -- you have the same number of cars per second, but it takes more seconds to traverse the single lane, meaning more cars in transit at any given time -- but who cares?
Question, slower requires less distance to the next car, isn't there a range where a slower speed could actually increase the flow? Seems to subtly depend on what people deem safe distance at speed?
It is a good observation, and the effect you cite is partly active - but only a very small amount.
You are correct that if the traffic in the single lane (post merge) drove with the same speed as normal (say 60 mph) but with half the car separation (that people normally desire at 60 mph), then the single lane will carry two lanes worth of traffic. But unfortunately, humans don't do that.
We can observe that human psychology requires the car separation to roughly linearly increase with car speed. This is probably because physically the distance required to make an adjustment in a fixed time (say one second) is exactly linearly proportional to speed. And people intuit that physics.
Interesting result 1 (due to the linearity relation): If a road is at maximum human-tolerable packing then it outputs roughly the same number of cars per second - no matter what speed the cars are going. You either have a few far-spaced cars going quickly, or many close-spaced cars going slowly. A road has a "maximum carrying capacity".
Result 2: Trying to force the carrying capacity of 2 (already fully packed) lanes into 1 lane - never works. The road doesn't care. A single lane can only output a maximum number of cars per second. If more cars per second arrive at the beginning of that lane (due to a merge) than that lane can output - it doesn't give a hoot. It does not adapt. Those extra incoming cars just have to wait. From a helicopter you will see the merge backup (slow car section) growing ever larger and traveling backwards up the road.
Result 3: When the cars on the 2-lane highway (way before they hit the backup) deplete to being so few that they can be carried entirely by a single lane at max packing, then the backup does NOT go away. But the existing backup section no longer gets any larger. When the cars coming into to backup are lower than the maximum carrying capacity of a single lane only then does the backup begin to get smaller and eventually get removed (after probably hours).
Results 4: Police on the side of the highway at rush hour (max packing) cause the same basic problem as the merge. Traffic slows down, cars get closer, the road carries the same number of cars as before, but everybody gets home slower. The slow section gets larger with time, moving backwards up the road. The cop leaves. And hours later that slow section the cop created is getting slowly smaller - but is STILL there.
> Results 4: Police on the side of the highway at rush hour (max packing) cause the same basic problem as the merge. Traffic slows down, cars get closer, the road carries the same number of cars as before, but everybody gets home slower. The slow section gets larger with time, moving backwards up the road.
I don't understand the comparison. When a lane is blocked, the carrying capacity of the road should go down. That's what causes the jam before the block.
But a cop on the side of the road isn't closing a lane. The carrying capacity of the road in that case should stay the same... right? Everyone slows down, they pack closer together, and the same number of cars per second make it past the point where the cop is.
But from the inflow/outflow perspective... we've already stated that, as an empiric law, the outflow from the area of the highway governed by the cop does not change. People may be going faster or they may be going slower, but the same number of cars per second make their way past the cop.
And the inflow to the cop's area isn't changing either. The same number of cars per second will also be arriving in the area where the cop is. It's not like people learn there's a cop watching a particular area and then adjust their plans to go drive by the cop -- if they adjust at all, it will be to stay away from the cop.
So, since outflow doesn't change and inflow doesn't change... how can a jam form and creep backwards up the road? All inflow to the jam is constantly being cleared from the other end of the jam. It has no way to grow beyond whatever its current size is.
The lane closure isn't like that; it reduces outflow. The mismatch between (unchanged) inflow and (reduced) outflow is what causes the traffic jam to grow over time. Why would the same happen in the case of the cop?
Result 4 is similar to Result 3 in that once a backup is established, it remains present even when the road is quite capable of carry the incoming number of cars - without that backup present.
You are correct that the cars/second is the same in the cop case at all times.
(This is also true in result 3, as well, where incoming = outgoing).
But this is not the metric of optimality for society. If everybody has a 15 minute longer drive home, and everybody had to throw on their brakes and waste gas driving at low speeds, then everybody has lost. Even though they didn't need to. The road could have carried them all at higher speeds if the cop hadn't fuct it up and then left.
Optimality is the highest safe speed for everybody (time is what is valuable) not the throughput (cars/second).
And the key lesson from Result 4 is that roads do not naturally or quickly obtain the optimal state. When put in a sub-optimal state (traffic jam for a long-gone cop) that state is also fairly stable and just sits there (annoying everybody).
Yes, I understand that in this model the cop can cause an area of the road to be permanently slower for no real reason.
But you said this:
> The slow section gets larger with time, moving backwards up the road.
And I don't think your model allows for that to happen?
Yes, even the cop causes an expanding backup section.
In the fully packed situation, if any cars are going 30 mph, then all cars behind them go that same speed. The cars approaching the 30 mph section will definitely slow down. And that "shock wave" will propagate backwards. When the cop leaves, the back-up unclogs from the front of the backup, and then that "front" of the backup moves backwards (unclogging as it goes backwards, from the front).
This is all very similar to high-speed (near Mach number) flow of gases (which are compressible, and can take up variable space - like cars).
Also it's funny that you think misanthropy *doesn't* drive many forms of leftism.
Yes. The Leftist elites want to remake the masses in their image.
No, they don’t; they want to keep them at arms length, while lording it over them.
I am historically a late merger myself because it always seemed right to me, but I know most people find it very rude. As I get older, I am more wearied by the negative interactions that sometimes occur with people when I am trying to merge late and I sometimes consider merging early simply to avoid these. Also, the extra twisting and turning required isn’t as easy for me as it used to be. So, one day soon, I might find myself to be an early merger as well. So, enjoy merging late while it lasts for you. One day you might wake up and find yourself to be one of those people.
You missed the main reason: safety and stress.
Would someone rather lose 2 min by merging early, and sit back and not having to stress anymore … or gain the 2 min, and now have to worry about someone letting them in, and executing without bumping someone?
Obviously this is going to depend a lot on things like whether you’re running late, risk-aversion, and driving competence.
But most people seem to prefer slower and chiller. It’s totally rational.
I am not sure the logic is in any way sound.
It is true that using the second lane until the end increases flow to the entry point of the single lane. However, this is unrelated to the overall throughput since throughput is limited by the single lane flow. Your action can never increase the overall flow, your gain is therefore the loss of the early mergers: your jumping the queue for your own gain. Not polite.
In addition, a late merge will inevitably create hazards. Even if you're a perfect driver, which is not very likely, you have to interact with people like me that might be pissed off you jumped the queue, people that have very little skill driving a car, people that get nervous from this aggressive maneuvers, or just not paying attention. Not only can this disruption cause a gap in the front that cannot be (legally) made up, breaking in a queue can get amplified and cause accidents behind you.
So I think your strategy to jump the queue reduces the average flow for everybody and increases the hazards. So I tend to graciously allow people to merge in front of me early on but at the end I take advantage that my car is really old.
You miss a category, no?
Your third category is motivated by shame or stigma - hence why they're conformist not cowardly. But you posit they all could - and believe they could - merge later if they were willing to stand out.
That's well and good but misses an important group - the genuinely cowardly. You're obviously a skilled driver, or believe so, including when confronting or relying on other drivers to execute a maneuver. That's not an uncommon sentiment.
But it's also not universal, at all! In my experience at least, lots of folks do not know what they're doing to merge on a highway. Or, they are afraid they don't know, or it won't work or something will go wrong in this instance.
Plus, it can be genuinely terrifying, or at least unnerving, to watch the end of a lane approaching as you travel a high speed, and see no ready way to merge. The prospect terrifies many people - at worst they crash head on to their demise, at best they broadside the car next to them and chaos and sorry follow.
This group, the cowardly, prefer to avoid that possibility (if not casualties, at least the hassle of having to squeeze in and not screw up after their first plan fails). They're real and not scarce in number, and your taxonomy is incomplete, and its explanatory power diluted, by your omission.
This is exactly right. There are many drivers who correctly realize they do not have the skill to merge late, and so don't. Merging late requires skill and alertness, which not everyone possesses. Ironically, this strategy only works because of those drivers, because aggressive drivers won't let you merge at the front of the line. I'm a guy who, when the light turns green, gets halfway across the intersection before anyone else has even moved, and if you think you're merging ahead of me in a crowded exit lane, you've got another think coming.
Another reason is that there can be risk in waiting too long, getting frozen out of the merge.
For example. I have an north exit nearby, followed in a 1/4 mile by a south exit which generally has a longer backup. If you wait too long to get to the right for the north exit, you can get stuck on the wrong side of the backup of cars waiting for the south exit.
Generally speaking, I completely agree with the point of your post. Similar reasoning holds for following cars pretty closely. This actually speeds up overall traffic quite a lot.
This is a slippery slope to full on emergency-lane shoulder-cutting through traffic, and it will be a cold day in hell before I let anyone do that.
Many people (I until not long ago) think that last minute merging IS anti social (deadweight loss).
Probably most do. But does that mean it actually is anti-social?
Shouldn't bravery be rewarded by society, and cowardice/incompetence not?
Care to elaborate what "deadweight loss" is? I can only find information on "price ceilings" or loss efficiency due to taxes and regulations. Does that mean there are exceptions where not doing late merging is more effective?
I was talking about perceptions and from a naïve POV a late merge does look like a making a lot of people wait a bit longer so that the late merger can save the time of not just queuing (aggregate loss of time, deadweight loss). Most people normally think queueing is optimal. Now I HAVE read the studies that zippering is most efficient way of binging two in principle equal lines of traffic into one line, but that does not mean that those who have not are just foolish..
I'm confused as to how any behavior *before* the bottleneck can change the speed with which cars pass *through* the bottleneck. If the single lane can admit 0.5 cars per second and the highway is transporting 2 cars per second, traffic is going to back up regardless of where people merge.
I do see how having that backed-up traffic occupy more road space is beneficial, since that means it won't extend back as far and won't interfere with as much cross traffic. But unless zipper merging somehow increases the speed at which cars drive once they're in the single lane (which is very plausible, I just don't get exactly why it would happen), it can't speed up the average travel time of people in the jam to zipper merge.
What am I missing here?
Also, I tend to merge early because I'm very safety-conscious and it's dangerous to try to force myself into another lane of traffic that doesn't want to let me in at the last minute. The earlier I start trying to merge, the more likely it is that I'll find someone who lets me in before I have to slow down to avoid running into the traffic cones.
You are missing that you are not an Overman