This doesn't mention the most economically sound and complete solution to traffic: dynamic congestion pricing on roads.
Due to the effects described in the article, entering a road that's close to congested imposes negative externalities due to the delay on everyone behind you, even higher if you are pushing the road below optimal throughput. Push that externality into the price, and suddenly drivers will change their behavior in the desired fashion:
1. People will move their travel to less expensive times. Even if no other change occurs than people waiting for prices to fall, the roads operate at much higher throughput due to never getting into the region of diminishing throughput.
2. People will carpool/vanpool/mass transit- no need for any special treatment for transit, a bus with 50+ people can simply outbid most cars on the road for space, even accounting for the difference in road space taken by the bus. With the economic incentive in place, you'd even expect private buses/etc to pop up spontaneously. Right now, its rarely worth it to pool/bus- it adds extra time for you, but the benefit to the road you never see. With proper pricing, its still faster to take a car, but a lot more expensive- and the carpool/bus/etc is still probably faster than driving would be with congested roads.
3. Similarly, the high prices will incentivize alternatives such as biking, subways, etc, and give very good information on exactly what routes are in high demand when, estimates of how much an improvement would be worth, etc.
Naw, the most economic solution is to make bigger bumpers and let cars push each other forward.
Think about a hose. If you have it at a certain flow and then increase the flow the water doesn't go out faster because it wants it. It flows faster because it's being pushed.
Same thing with cars, as more cars get onto the highway you want them to go at a higher speed so that the throughput matches the on ramp. We just need to cut down the number of 4 lane highways so that we have space to put exit ramps on both sides of a 2 lane highway but the increased speed will make up for it.
How do you propose people find out the cost of traveling if the pricing is dynamic? People won’t check beforehand, and they’ll already be in their cars when they find out the cost
Navigation/maps providers like Google/Apple maps, etc, will incorporate price estimates as well as time estimates- they can even show multiple options if there are price-time tradeoffs available.
At high demand times, you have to be very rich indeed to outbid a full bus without even thinking about it. There aren't enough people who can do that.
But say this does happen a lot-this means rich people pay enormous road use fees, which can then be used for road maintenance, construction, and improvement, as well as other transit infrastructure!
So, the rich willingly subsidize infrastructure for everyone? Seems like a win-win!
That's a nice pipe dream, but what would happen in reality is that all of the congestion fees would go to the rich (perhaps in the form of tax cuts), who would use it to buy more stock, bribe some politicians to ban buses, and then triple the congestion charge because fuck you.
The congestion fees would go to the government responsible for the roads. Of course, they could be captured by the rich, but most governments spend most of their money not on the rich.
You'd set the congestion charge, by law (at least on public roads), to the minimum required for efficient road use- not the revenue maximizing price, which would likely be much higher due to monopoly.
Why do people insist on this tired unimaginative trope. We have the past and present to look at. We know how these things work.
The rules will be crafted, the commas in the laws placed, the contracts handed out, to support those who supported the endeavor. If the plumber's trade group agrees to support it their vans will be exempt. If Palantir supports it, the RFP will be written to make it nigh on impossible to not buy their stuff. No matter how flagrant the badness of the system, if the tech industry makes even a cent, the comment section full of techies will engage in olympic level mental gymnastics and not just do bending over backwards but doing full on backflips to justify the goodness of the system. If the bus drivers have such a comment section they'll do it too.
This is how things were. This is how they are. This is how they will be. Well, right up until the point where the rest of society gets sick of our shit and leaves us in a big communal hole or gives us a free shower or whatever happens to the fashionable way to do that thing is at that point in the future...
But I suppose maybe you're right and they'll throw a few pennies of tax cuts at it if they just need a little upper middle class support to drag it across the finish line.
And also in essentially any relevant private market for goods and services where capacity is limited, especially when there are more and less desirable times.
This blog post has a lot of good ways to think about traffic.
There is on particular phenomenon I ponder about my commute to work on 45 MPH "stroads" involves the interplay between speeders, slugs and the many stop lights.
I strictly keep to the speed limit during day light and good weather (slower otherwise) and start slowing well in advance to an oncoming red followed by accelerating briskly when red turns to green if not blocked by other users of the road.
The vast majority of the other users have the opposite speed profile. They go well above the speed limit (60+ is not uncommon to see), often passing me at the last second before safely or not so safely stopping at a red and then take their sweet time getting up to the limit (and then beyond) after a green. The fact that most of them drive enormous apartments on wheels perhaps explains some of this behavior.
The main hypothesis I am interested in is that their strategy of speeding to the next red light and lazily getting going at green (if they notice the light change) is actually counter productive to throughput and maximizing average speed. The speeding and the bunching at red coupled with glacial acceleration up to and beyond the limit is far slower than keeping to the speed limit, gradual slowing down (sometimes catching red->green before stopping) and brisk speed up is the winner, assuming not blocked by lumbering behemoths.
That is, stopping is slower than speeding is fast.
> then take their sweet time getting up to the limit (and then beyond) after a green
I know this is bad for my fuel/electric efficiency, but I enjoy being the first car at the stop bar during a red light because of this. Means I can accelerate faster and merge lanes without waiting for other drivers to make a spot, even if those other cars ultimately end up passing me a mile later.
> If, after fixing all the intersections, flow is improved, people who were making do with something other than driving at the peak rush, will show up to consume the new capacity.
I fail to see the problem with "we built something and people used it because they preferred it to their other options"
It's not cost effective to have a bus line that stops at everybody's house.
However, when you start to have 3 lanes of traffic then a lot of that traffic can be handled by a bus at a cheaper cost to both the drivers and the relevant department of transportation than expanding the road to handle the current traffic.
In addition to the sibling comments, Braess's paradox actually goes beyond this. You can add capacity and every actor acts rationally as you describe and the net result is an objectively worse situation for everyone, in which the decisions made are still the rational ones.
His premise there was "why simply adding more lanes won't fix the problem of congestion". He didn't claim that it won't lead to more cars using the road.
The problem with this is that if your goal is to build a liveable city where people can reach their destinations in predictable time without pulling their hair out, simply building more lanes does not usually help, for the reasons outlined very clearly in the article.
And that isn't exactly a wild guess, we have decades of data on the subject.
> If a straight stretch of road has 4 intersections with stop lights for cross traffic, and one of those lights is green for 20 seconds for the straight road and green for 40 seconds for the cross traffic, then the end-to-end throughput of that road (ignoring turns on/off for the sake of simplicity) is 1/3 of its hourly capacity, or 600 cars per hour. Widening the road won’t fix that intersection.
I don't see how the intersection affects road-widening calculations at all. Doubling the lanes will double the throughput, to 1200 cars per hour. We weren't expecting widening the road to also eliminate red lights.
The lane widening and whatnot basically acts as a cache for the bottleneck intersection (or other feature).
A good example is getting the small % of left turning traffic out of a lane where much of the traffic wants to go straight and there is much oncoming traffic. When there's a break, you've got a car cached right there. When there's not you can push any left turning traffic into the cache for later. Massive improvement, even if all the out flows from the light are the same throughput.
is the relationship between lanes and throughput linear? even where it's illegal people will change lanes and do all sorts of suboptimal things with the additional space; particularly if people need to shift multiple lanes to be in the correct legal lane.
author here, you are right, I missed that. In my pathetic defense, the normal argument around here (Cambridge, MA) is about literal lane widening and narrowing, and not adding and subtracting.
Problems I face WRT Traffic / Commutes / Related factors:
* Drivers who can't just drive at at _least_ the speed limit. Flow is mentioned several times in the article, but flow is also a major part of traffic issues I face daily. Every time drivers refuse to merge right to allow others to pass (state law here). Every time drivers slow down instead of speeding up because they're unsure. Every time there's traffic enforcement for revenue rather than enforcing the laws that would promote a smooth and steady commute. That causes the rate of flow to decrease. It lets other slower drivers merge into the gaps opened in front (which pushes the stack of cars further back and further slows the flow, compared to just going down the road). The only way to clear a log jam in a river is to get the logs out, down the river in the case of traffic. After the block clears up traffic should go slightly _faster_ to pull the flow forward, removing the pressure and restoring safety and expediency for drivers behind.
* Freeways built to hub and spoke main city designs, when I need to cross around major geographic features (lakes, 'very big hills' with a couple mounts along the most obvious paths).
* No where NEAR enough housing built in the last 40+ years anywhere near jobs. (Solution: have good building codes and auto approval if code conditions are met, and build build build.)
* Family with roots in an area far from where jobs are today... the suburbia of my childhood is not a center of well paying white collar jobs. (That's what hub and spoke to the big city used to be; before businesses escaped to other outlying areas.)
> Drivers who can't just drive at at _least_ the speed limit.
I don't mind people who drive under the speed limit (it is, after all, meant to be a limit and not a minimum speed), but they need to not hang out in the passing lane. Nobody should be hanging out in the passing lane in general, but you especially don't get to do it if you aren't even driving the speed limit.
Hi, author of the article. I'm assuming urban traffic speeds, which is what I observe all the time myself, but you can look at the video of those kids, and count, and look at the seconds. 125 bikes in 45 seconds, between 0:02 and 0:47. Understanding it is another issue, but it's a fact. (This is one of those things that I do myself and would not claim that I exactly understand the details, I just do it.)
There have been more academic studies. e.g. https://nacto.org/wp-content/uploads/5_Zhou-Xu-Wang-and-Shen... estimates 2512 bicycles per hour per meter of road width, or 7536 bikes per hour on a 3-meter (10 feet) wide lane. That's only 4.2x car throughput, versus those kids who managed 5.5x.
You are right about the trailers, but at least where I ride, they are not common-case for carrying things, lots more cargo bikes instead, and those are "better" than trailers -- it's possible to ride two cargo bikes side-by-side even in a US protected lane (specifically on Garden Street in Cambridge, MA), though this of course assumes competent riders.
Optimizing them for speed makes them flexible: when they're not full, you can go fast, and when they're full, they can degrade gracefully to 30-35 mph.
In London, the M25 (outer ring road) has variable speed limits. Perhaps it's to improve throughout on the M25, or to increase the capacity of the M25 to absorb traffic from nearby roads.
This doesn't mention the most economically sound and complete solution to traffic: dynamic congestion pricing on roads.
Due to the effects described in the article, entering a road that's close to congested imposes negative externalities due to the delay on everyone behind you, even higher if you are pushing the road below optimal throughput. Push that externality into the price, and suddenly drivers will change their behavior in the desired fashion:
1. People will move their travel to less expensive times. Even if no other change occurs than people waiting for prices to fall, the roads operate at much higher throughput due to never getting into the region of diminishing throughput.
2. People will carpool/vanpool/mass transit- no need for any special treatment for transit, a bus with 50+ people can simply outbid most cars on the road for space, even accounting for the difference in road space taken by the bus. With the economic incentive in place, you'd even expect private buses/etc to pop up spontaneously. Right now, its rarely worth it to pool/bus- it adds extra time for you, but the benefit to the road you never see. With proper pricing, its still faster to take a car, but a lot more expensive- and the carpool/bus/etc is still probably faster than driving would be with congested roads.
3. Similarly, the high prices will incentivize alternatives such as biking, subways, etc, and give very good information on exactly what routes are in high demand when, estimates of how much an improvement would be worth, etc.
Naw, the most economic solution is to make bigger bumpers and let cars push each other forward.
Think about a hose. If you have it at a certain flow and then increase the flow the water doesn't go out faster because it wants it. It flows faster because it's being pushed.
Same thing with cars, as more cars get onto the highway you want them to go at a higher speed so that the throughput matches the on ramp. We just need to cut down the number of 4 lane highways so that we have space to put exit ramps on both sides of a 2 lane highway but the increased speed will make up for it.
How do you propose people find out the cost of traveling if the pricing is dynamic? People won’t check beforehand, and they’ll already be in their cars when they find out the cost
How do people find out how much traffic congestion there will be for an upcoming drive when they need to be at their destination at a specific time?
Induction, typically.
guess, and many people are frequently late.
Google Maps
Navigation/maps providers like Google/Apple maps, etc, will incorporate price estimates as well as time estimates- they can even show multiple options if there are price-time tradeoffs available.
This exists already and generally they post prices both online, and on digital signage well before the entrance ramp.
This will only affect poor people. Rich people will continue driving everywhere they want as if it didn't exist.
At high demand times, you have to be very rich indeed to outbid a full bus without even thinking about it. There aren't enough people who can do that.
But say this does happen a lot-this means rich people pay enormous road use fees, which can then be used for road maintenance, construction, and improvement, as well as other transit infrastructure!
So, the rich willingly subsidize infrastructure for everyone? Seems like a win-win!
That's a nice pipe dream, but what would happen in reality is that all of the congestion fees would go to the rich (perhaps in the form of tax cuts), who would use it to buy more stock, bribe some politicians to ban buses, and then triple the congestion charge because fuck you.
The congestion fees would go to the government responsible for the roads. Of course, they could be captured by the rich, but most governments spend most of their money not on the rich.
You'd set the congestion charge, by law (at least on public roads), to the minimum required for efficient road use- not the revenue maximizing price, which would likely be much higher due to monopoly.
I mean, they exist in many places (London and New York are notable examples) and this has not happened
London in particular uses congestion pricing money to fund more buses and ridership exploded as a result
>perhaps in the form of tax cuts
Why do people insist on this tired unimaginative trope. We have the past and present to look at. We know how these things work.
The rules will be crafted, the commas in the laws placed, the contracts handed out, to support those who supported the endeavor. If the plumber's trade group agrees to support it their vans will be exempt. If Palantir supports it, the RFP will be written to make it nigh on impossible to not buy their stuff. No matter how flagrant the badness of the system, if the tech industry makes even a cent, the comment section full of techies will engage in olympic level mental gymnastics and not just do bending over backwards but doing full on backflips to justify the goodness of the system. If the bus drivers have such a comment section they'll do it too.
This is how things were. This is how they are. This is how they will be. Well, right up until the point where the rest of society gets sick of our shit and leaves us in a big communal hole or gives us a free shower or whatever happens to the fashionable way to do that thing is at that point in the future...
But I suppose maybe you're right and they'll throw a few pennies of tax cuts at it if they just need a little upper middle class support to drag it across the finish line.
There is a floor to this; there are people so poor they can't afford the ongoing expense of a car at all.
The poor are on the bus which is stuck in traffic it could outbid if the road were priced fairly.
The same can be said of any tax meant to curb a behavior (sin tax).
What traffic-reducing policy would you suggest such that all people are affected equally?
absolutely none, which is why ideas like this will never see the light of day…
I think it's worth pointing out that congestion pricing is a policy that already exists in several cities around the world including New York City.
And also in essentially any relevant private market for goods and services where capacity is limited, especially when there are more and less desirable times.
In a very weak form, yes- and yet it still seems helpful and even popular after people saw the effects of implementation.
[dead]
This blog post has a lot of good ways to think about traffic.
There is on particular phenomenon I ponder about my commute to work on 45 MPH "stroads" involves the interplay between speeders, slugs and the many stop lights.
I strictly keep to the speed limit during day light and good weather (slower otherwise) and start slowing well in advance to an oncoming red followed by accelerating briskly when red turns to green if not blocked by other users of the road.
The vast majority of the other users have the opposite speed profile. They go well above the speed limit (60+ is not uncommon to see), often passing me at the last second before safely or not so safely stopping at a red and then take their sweet time getting up to the limit (and then beyond) after a green. The fact that most of them drive enormous apartments on wheels perhaps explains some of this behavior.
The main hypothesis I am interested in is that their strategy of speeding to the next red light and lazily getting going at green (if they notice the light change) is actually counter productive to throughput and maximizing average speed. The speeding and the bunching at red coupled with glacial acceleration up to and beyond the limit is far slower than keeping to the speed limit, gradual slowing down (sometimes catching red->green before stopping) and brisk speed up is the winner, assuming not blocked by lumbering behemoths.
That is, stopping is slower than speeding is fast.
> then take their sweet time getting up to the limit (and then beyond) after a green
I know this is bad for my fuel/electric efficiency, but I enjoy being the first car at the stop bar during a red light because of this. Means I can accelerate faster and merge lanes without waiting for other drivers to make a spot, even if those other cars ultimately end up passing me a mile later.
It depends on how long they're above the speed limit and you're below it.
If you want to win the race, max acceleration, max speed, max deceleration. Anything else is sub optimal.
> If, after fixing all the intersections, flow is improved, people who were making do with something other than driving at the peak rush, will show up to consume the new capacity.
I fail to see the problem with "we built something and people used it because they preferred it to their other options"
From the article, the problem is "removing a road segment, would block the competition, and actually improve overall flow".
Ie. we built something, people used it because they preferred it, and now everyone gets a worse experience.
The problem is cost efficiency.
It's not cost effective to have a bus line that stops at everybody's house.
However, when you start to have 3 lanes of traffic then a lot of that traffic can be handled by a bus at a cheaper cost to both the drivers and the relevant department of transportation than expanding the road to handle the current traffic.
In addition to the sibling comments, Braess's paradox actually goes beyond this. You can add capacity and every actor acts rationally as you describe and the net result is an objectively worse situation for everyone, in which the decisions made are still the rational ones.
Assuming nobody actually wants to move slower.
His premise there was "why simply adding more lanes won't fix the problem of congestion". He didn't claim that it won't lead to more cars using the road.
The problem with this is that if your goal is to build a liveable city where people can reach their destinations in predictable time without pulling their hair out, simply building more lanes does not usually help, for the reasons outlined very clearly in the article.
And that isn't exactly a wild guess, we have decades of data on the subject.
> If a straight stretch of road has 4 intersections with stop lights for cross traffic, and one of those lights is green for 20 seconds for the straight road and green for 40 seconds for the cross traffic, then the end-to-end throughput of that road (ignoring turns on/off for the sake of simplicity) is 1/3 of its hourly capacity, or 600 cars per hour. Widening the road won’t fix that intersection.
I don't see how the intersection affects road-widening calculations at all. Doubling the lanes will double the throughput, to 1200 cars per hour. We weren't expecting widening the road to also eliminate red lights.
You're right that paragraph is misleading.
The lane widening and whatnot basically acts as a cache for the bottleneck intersection (or other feature).
A good example is getting the small % of left turning traffic out of a lane where much of the traffic wants to go straight and there is much oncoming traffic. When there's a break, you've got a car cached right there. When there's not you can push any left turning traffic into the cache for later. Massive improvement, even if all the out flows from the light are the same throughput.
is the relationship between lanes and throughput linear? even where it's illegal people will change lanes and do all sorts of suboptimal things with the additional space; particularly if people need to shift multiple lanes to be in the correct legal lane.
author here, you are right, I missed that. In my pathetic defense, the normal argument around here (Cambridge, MA) is about literal lane widening and narrowing, and not adding and subtracting.
Problems I face WRT Traffic / Commutes / Related factors:
* Drivers who can't just drive at at _least_ the speed limit. Flow is mentioned several times in the article, but flow is also a major part of traffic issues I face daily. Every time drivers refuse to merge right to allow others to pass (state law here). Every time drivers slow down instead of speeding up because they're unsure. Every time there's traffic enforcement for revenue rather than enforcing the laws that would promote a smooth and steady commute. That causes the rate of flow to decrease. It lets other slower drivers merge into the gaps opened in front (which pushes the stack of cars further back and further slows the flow, compared to just going down the road). The only way to clear a log jam in a river is to get the logs out, down the river in the case of traffic. After the block clears up traffic should go slightly _faster_ to pull the flow forward, removing the pressure and restoring safety and expediency for drivers behind.
* Freeways built to hub and spoke main city designs, when I need to cross around major geographic features (lakes, 'very big hills' with a couple mounts along the most obvious paths).
* No where NEAR enough housing built in the last 40+ years anywhere near jobs. (Solution: have good building codes and auto approval if code conditions are met, and build build build.)
* Family with roots in an area far from where jobs are today... the suburbia of my childhood is not a center of well paying white collar jobs. (That's what hub and spoke to the big city used to be; before businesses escaped to other outlying areas.)
> Drivers who can't just drive at at _least_ the speed limit.
I don't mind people who drive under the speed limit (it is, after all, meant to be a limit and not a minimum speed), but they need to not hang out in the passing lane. Nobody should be hanging out in the passing lane in general, but you especially don't get to do it if you aren't even driving the speed limit.
Please update the link to the post: https://dr2chase.wordpress.com/2025/09/01/understanding-traf...
That way when people visit from the future, they dont get the most recent article
If you email hn@ycombinator.com and they will quickely fix the link
Link should be https://dr2chase.wordpress.com/2025/09/01/understanding-traf...
I don't understand the bicycle density numbers in the article.
At high speeds, bicycles also have to spread out. Add the bike trailers mentioned, and it seems even more unlikely.
Hi, author of the article. I'm assuming urban traffic speeds, which is what I observe all the time myself, but you can look at the video of those kids, and count, and look at the seconds. 125 bikes in 45 seconds, between 0:02 and 0:47. Understanding it is another issue, but it's a fact. (This is one of those things that I do myself and would not claim that I exactly understand the details, I just do it.)
There have been more academic studies. e.g. https://nacto.org/wp-content/uploads/5_Zhou-Xu-Wang-and-Shen... estimates 2512 bicycles per hour per meter of road width, or 7536 bikes per hour on a 3-meter (10 feet) wide lane. That's only 4.2x car throughput, versus those kids who managed 5.5x.
You are right about the trailers, but at least where I ride, they are not common-case for carrying things, lots more cargo bikes instead, and those are "better" than trailers -- it's possible to ride two cargo bikes side-by-side even in a US protected lane (specifically on Garden Street in Cambridge, MA), though this of course assumes competent riders.
> Car throughput is maximized at around 30-35mph
That's funny. That means that the interstates are optimized for speed, not throughput. I believe it, it's just counter-intuitive.
Optimizing them for speed makes them flexible: when they're not full, you can go fast, and when they're full, they can degrade gracefully to 30-35 mph.
In London, the M25 (outer ring road) has variable speed limits. Perhaps it's to improve throughout on the M25, or to increase the capacity of the M25 to absorb traffic from nearby roads.
That makes sense, since they're not often near capacity between cities.