Speaker A
This is a traffic jam wave with no apparent cause, yet it drains fuel, time, and safety from everyone stuck inside it.
Explores phantom traffic jams: how they form from driver reactions, how a few smart drivers can dissolve them, and how damped oscillator physics explains driving behavior.
Key Takeaways
- Phantom jams are real and arise from driver reactions alone, without accidents or roadworks.
- A small share of smoothing drivers or autonomous vehicles can stabilize traffic and save fuel for all.
- Gradual communication of speed changes can prevent jam formation with no change to driver behavior.
- Damped oscillator models offer a physics-based framework for designing better driving strategies.
What the video covers
- Phantom traffic jams can form with no visible cause, arising from driver reactions on a ring road, as shown in a 2018 experiment.
- Jam waves can fade over time; in the experiment, only six drivers using a quiet smoothing strategy were enough to reduce waves for everyone.
- Even perfectly smooth followers can turn tiny disturbances into full traffic waves, so calm following alone is not sufficient.
- Traffic can be metastable: nearly identical disturbances (e.g., braking to 8% vs 7.5% speed) can either fade or grow into jams.
- Time-space diagrams act like seismographs for traffic, revealing jam waves as backward-moving bands of congestion.
- A brief speed-limit change can trigger jams long after the cause is removed; gradual, spread-out communication of speed changes can prevent them.
- Driver behavior can be modeled as a damped oscillator settling into equilibrium, with speed matching and a safety gap as the equilibrium pair.
- Newton's second law and damping terms give the equation of motion, which can be analyzed via simulation or analytically.
- Anticipating the leader's behavior and braking gently and earlier improves stability, with the damping ratio providing a key criterion.
- Even a small fraction of globally aware or autonomous 'wave damper' vehicles can dampen jams and improve flow and fuel efficiency for everyone.
Chapters
- 00:00Introduction to Phantom Traffic Jams
- 01:34Traffic Waves and the Ring Road Experiment
- 03:03Why Good Drivers Still Cause Jams
- 04:39Time-Space Diagrams and Jam Fingerprints
- 05:55Variable Speed Limits and Communication
- 08:00Drivers as Damped Oscillators
- 12:00Equations of Motion and Anticipation
- 18:40Autonomous Wave-Damping Vehicles and Optimal Flow
Full Transcript — Download SRT & Markdown
Speaker A
And this mathematical model captures the essence of that phenomenon, though today it comes with two surprises.
Speaker A
These cars drive on a ring road, each reacting to the one ahead. At first, everything stays quiet, until, with no outside cause, waves appear, growing until cars come to a stop.
Speaker A
This kind of jam, forming out of nowhere, is called a phantom jam. Here's footage from a 2018 experiment, showing exactly this behavior.
Speaker A
It wasn't the first, but along with others, it proved that phantom jams are real, and don't need visible causes like accidents or roadworks.
Speaker A
So it's all about how drivers react, and that's what causes these waves. But here, we add another twist.
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After a while, the backward-moving jams start to change. Gradually, they thin out, and eventually disappear again.
Speaker A
One might think everyone just learned to drive better, and we'll calculate what "better driving" mathematically means.
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But in fact, only six drivers used a quiet trick. Which shows that on a shared resource, here, a single lane, a small number of drivers can smooth out traffic for everyone...
Speaker A
which means fuel savings for everyone. Of course, ideally, you'd want to have fewer cars in total.
Speaker A
But with the complexity of everyday life and a mix of traffic modes, making cars consume a bit less fuel could still be worth it.
Speaker A
But it's not that simple, because traffic waves can be counterintuitive. Are you really sure all these drivers are just "bad drivers"?
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If you have a driver who catches up perfectly smoothly to the car ahead, without any overshooting or overreacting, and you put many of these perfect drivers in a row, they nonetheless turn the tiniest disturbances into full-blown traffic waves.
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So it turns out, just following calmly isn't enough. And traffic waves are even more complex.
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There are situations where, with the same number of cars, a tiny difference in disturbance leads to completely different results.
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On the left, one car temporarily brakes to 8 percent of its speed; on the right, to 7.5 percent.
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Both trigger an initial wave, but on the left, it fades; on the right, it grows.
Speaker A
So even with identical congestion, traffic can fall into a stable or unstable situation. To see why that is, we'll go back to how these jams really form, which will then tell us how to drive better.
Speaker A
But even if you know how to do it, not everyone will do it. So, how many percent of good drivers does it take to stabilize highways or cities full of lazy drivers?
Speaker A
And what can you do if nobody plays along? This video is sponsored by Brilliant. More at the end.
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Imagine a straight road... with a single lane, and hundreds of cars arriving in a steady stream.
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Now, if you want to catch a jam in the act of forming, you can do it by tracking each car's position over time.
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This creates a time-space diagram, almost like a seismograph for traffic. And you'll notice, with all cars starting out calmly, the diagram shows straight, parallel lines.
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But as the road is too crowded, the situation tips, and waves appear. For instance, this car here has to slow down to avoid a collision, covering less distance in the same time.
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By doing that, it unknowingly helps seed a jam wave. So, minutes later, when another car arrives, it runs straight into a fully formed jam.
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Now, in theory, these waves can travel at different speeds. They always move backward relative to the cars, but at some point, backward relative to the road itself.
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But this here is an idealized simulation with a very calm beginning. In real life, it often takes just one driver braking a little harder to directly trigger a strong wave.
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And when you look at many of these waves together, you realize they all look strikingly similar, like an inherent feature of dense traffic.
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And they're not just inconvenient. Every sudden brake comes with the risk of someone missing it, and that's how collisions happen in these waves.
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It's a reminder that phantom jams don't just waste fuel and time. And when we look at them through that time-tracking lens, we get a kind of fingerprint of the whole situation, letting us instantly see what's happening even as things get more complex.
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Like here: on this road, the density is lower, so waves don't form on their own.
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But then, there's a short maintenance job, some landscaping, and a variable speed limit sign reduces the allowed speed.
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The work is done and the speed limit is lifted after just five minutes. But by then, it's already too late.
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Several minutes later, jam waves force cars to a stop, long after the actual event.
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As a driver, arriving much later, you might wonder why you're stuck when there's nothing causing it.
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But the beauty of this fingerprint is that if we change anything, we instantly see the effect.
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For instance, it's obvious that hard braking at the slow zone is the trigger. After all, without a disturbance, there wouldn't be a wave.
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So, we're probably in a "metastable" regime, just like in the intro, where small disturbances fade, but larger ones grow.
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Well then, could we do better by announcing the speed reduction more gradually? On this road, there are multiple variable speed signs and the more we spread out the news, the smoother the flow, until eventually, no jams form at all.
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Even though it gets impractical, notice: we haven't changed anything about the drivers, just how we communicate the information.
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Comparing the two extremes: With jam waves, you spend more time moving quickly between stops.
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Without waves, you spend more time at lower speeds overall. So in this special case, the average speed might be similar.
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One notable benefit, though, is fuel savings. Here, these drivers save over 10 percent fuel, by avoiding costly re-accelerations.
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Now, there's a lot more you can do by changing the road network. But let's look at how drivers themselves can react better...
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starting with a not-so-great driver, who follows the car ahead with some delay and eventually settles into a kind of "rest" state, the equilibrium.
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And that equilibrium really is a pair: matching the leader's speed, and keeping a safety gap ahead, which itself depends on how fast you're going.
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So if you put the follower's speed on one axis and the gap on the other, you can watch the driver spiral into equilibrium.
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That picture is what's called a phase diagram. And some of you may already recognize this spiral.
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It looks just like a classical damped oscillator, which also settles into equilibrium the same way.
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Well then, if our drivers behave like damped oscillators, why not treat them as such?
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These systems are well-studied in physics, and they might hold clues for how to damp traffic oscillations more effectively.
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Now, the oscillator also has an equilibrium pair: its position comes from the balance of gravity and spring force, and its velocity must match the anchor point's velocity, which here is zero.
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But how does the oscillator get there, how does it return to equilibrium? That's where Newton's second law comes in: mass times acceleration equals the net force.
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At equilibrium, gravity is already balanced. What remains is the spring force from being displaced away from that balance point, plus damping like friction or air resistance.
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In the simplest case, we have a viscous damping force, which is velocity-proportional. Combine those, and you get the oscillator's equation of motion, basically, a recipe for how it settles back to equilibrium.
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And to calculate that motion, the displacement function x(t), there are two options. One is to start with some initial displacement and velocity, calculate the acceleration, and then update everything step by step, which is the essence of a computer simulation.
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You look at the current state of the system, predict how it changes over a short time, and then repeat the prediction again and again.
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Or, instead of simulating step by step, we can extract insights directly by looking at the equation of motion.
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If we divide everything by the mass and relabel the coefficients, the dynamics don’t change, but now the solution for the lightly damped case can be written as this function.
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And if you want to check it yourself, you can plug this solution back into the equation of motion and see that there’s no contradiction.
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So, that position function really does describe possible oscillator motion. And it comes with four parameters: the initial amplitude and phase, which you set when you first kick off the mass, and the natural frequency and damping ratio, which are properties of the system itself.
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For instance, a more viscous damper gives a higher damping ratio, while a stiffer spring gives a higher natural frequency.
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So this relabeling of coefficients is quite useful, because these two numbers, the natural frequency and damping ratio, fully characterize the system’s inherent behavior.
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Which means you can read off how the system behaves just by looking at those coefficients.
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It’s right there, you don’t need a lengthy calculation! But how can we use these two factors?
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In our mechanical oscillator, the damping ratio is always positive, that’s what’s called local stability.
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It means that after a disturbance, the mass always returns to equilibrium. If the damping were negative, the motion would blow up, unstable.
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And if it reaches the critical value of one, the mass returns without any oscillation at all.
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So, by equating the relabeled coefficients with the original ones, we can calculate exactly how to set the mass, the spring stiffness, and the damper to get the damping ratio we want.
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In fact, here I simply increased the damping coefficient c by mixing in a higher amount of glycerol with water, until I got a damping ratio of one.
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Great! With this procedure, we can tune the oscillator to oscillate, or not oscillate, just the way we want.
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Which makes you wonder: Can we bring our car-following model into the same mathematical form, and then ask: what kind of driver behavior gives us a damping ratio of at least one, and no oscillations at all?
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We’ll see in a moment if that’s enough. To get there, we need an equation of motion for a driver.
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In most of my simulations I use a fairly complex car-following model. But for intuition, let’s build a simpler one.
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To make our driver–car system respond, it needs to accelerate or decelerate. But when, and by how much?
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Suppose our driver wants to stay safe by aiming for an ‘optimal’ velocity, one that gives them a tau-second safety gap to the car ahead.
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So the difference between this optimal velocity and the current one becomes the signal to accelerate.
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If we’re below optimal, we speed up; if we’re above, we slow down. And with a bit of rearranging, this can be written in the same form as the oscillator’s equation of motion, which we then simulate just like before.
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Now, if we make this reaction weaker, by scaling down this parameter alpha, the driver follows less quickly, less... agile.
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But that leads to lots of oscillation, which isn’t really how a ‘less agile’ driver behaves in real life.
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So, to make the model more human, think how you would approach a much slower car in real life.
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You would anticipate the leader velocity and brake not at the last moment, but gently and a bit sooner.
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That’s why it makes sense to also react to the velocity difference with the leader.
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This leads to the so-called Full Velocity Difference Model, one of the simplest models that already lets you control three things: safety, agility, and anticipation.
Speaker A
You could add reaction time to make it even more human, but even this simple model already shows some counterintuitive behavior, as we’ll see.
Speaker A
Now, to make this driver model exactly match the mechanical oscillator, we temporarily ignore the motion of the leader car.
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In that case, the follower oscillates right through the leader, because without a leader velocity, the tau-second gap also becomes zero.
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But you can simply think of it as an offset point for the calculation, sitting just behind the actual leader car.
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The point is, it still shows the oscillatory nature of the follower. And in this simplified setting, we can once again equate the coefficients and find an inequality that tells us how to drive without oscillations.
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All it takes is making sure that safety, agility, and anticipation, when combined, produce a damping ratio of at least one.
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If we map this out in 3d, over the three parameters, we get a surface where the damping ratio is exactly one.
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So, for example, with this particular parameter setting, the driver quickly settles into position, without any oscillation at all.
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If the damping is below that surface, oscillations reappear. If it’s above, things get even calmer.
Speaker A
Which is exactly what we wanted, right? So, if we put many of these ‘damping ratio one’ drivers in a row, we should get perfectly damped traffic.
Speaker A
Hm. Interesting. Because even though every driver is tuned to settle without oscillations, the whole chain starts oscillating?
Speaker A
If every driver is locally stable and fully damped, shouldn’t the entire traffic flow stay calm?
Speaker A
Apparently not! It turns out, a damping ratio of one, just isn’t enough. But then, how can these waves still develop?
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Let’s watch the time evolution of the gaps between a few cars. Starting from a calm state, the gaps suddenly begin to oscillate as soon as an initial wave arrives.
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And if you look closely, each follower’s gap oscillates with a slightly larger amplitude, amplifying the wave as it moves down the chain.
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Up to now, we’ve only asked how a car settles once the leader stops disturbing it.
Speaker A
But here, every leader keeps oscillating. So with a damping ratio of one, why don’t the followers just absorb those incoming oscillations, instead of making them bigger?
Speaker A
If you give a follower just a position disturbance, it damps out without oscillations, just like we saw before.
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But if you also give it a little velocity kick on top, you suddenly get an overshoot, just from that extra bit of momentum.
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And after that overshoot, once it’s reduced again to a pure position disturbance with zero relative velocity, it calmly settles back with no further oscillations.
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So, maybe the leader’s oscillations are somehow feeding that extra bit of momentum into the follower, and that’s why we see amplification?
Speaker A
Let’s look back at the damped oscillator. Instead of disturbing it once and letting it settle, imagine we now move the anchor point, the leader, up and down with a fixed amplitude.
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Then, the mass, the follower, oscillates too, but with a smaller amplitude. And if you pass that smaller motion to the next car, it shrinks again, and so on.
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So, this wave would just get damped away. But that’s not true for every frequency.
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At very low frequency, changes are so slow that the mass just copies the anchor point one-to-one.
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But as we increase the frequency, something interesting happens: the timing lines up just right, so the anchor keeps pumping energy into the mass’s motion.
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That’s a resonance, and it’s where the extra momentum gets stored. And once that extra momentum outweighs the damping, the oscillations grow instead of fade.
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And if each follower amplifies just a little, a wave can grow along the chain, leading to stop-and-go traffic.
Speaker A
It just takes enough cars. So it was never just about damping what’s left after a disturbance, it’s about not amplifying ongoing oscillations.
Speaker A
That’s something different. But then, could we just crank up the damping until there’s no amplification at all, at any frequency?
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If we plot amplification as a function of frequency, the goal is: it should always stay below one.
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Only then would no oscillation, of any frequency, ever grow along the chain. To calculate that, we need to remember: both the spring and the damper forces depend on the relative motion between the mass and the now moving anchor point.
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For instance, if the anchor and the mass move up by the same amount, the spring feels nothing new and generates the same force.
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This adds a few terms to the equation of motion, terms that used to be zero when the anchor was fixed.
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And one more thing: both the leader and the follower now oscillate almost like perfect sine waves, each with its own amplitude, and a small time delay between them.
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So whenever the anchor point moves, the mass follows, just a little later. If we now relabel the coefficients, assume pure sine motion, and push through the math, we can express the amplitude ratio, the amplification, as a function of excitation frequency.
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And just like the relabeled equation of motion, it depends on the two system properties: the damping ratio and the undamped natural frequency.
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Now, at a certain frequency, the amplification reaches a peak, the resonance, where the system gathers the most extra momentum.
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So, can we tune the parameters to push this peak below one? Changing the undamped natural frequency only shifts the resonance left or right, but doesn’t change its height.
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It seems like all we need is more damping, right? If you start with zero damping, the maximum amplification is infinite.
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But as you dial the damping ratio higher and higher, the peak shrinks, but it never dips below one.
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Why? Because this damper isn’t between the mass and the ground, it’s between the mass and the anchor.
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So the harder it tries to fight the relative velocity, the more it just forces the mass to copy the anchor’s motion...
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to copy its amplitude. Which brings us back to cars: does that mean we’re always prone to traffic waves?
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If you look back at the full car-following equation of motion, you’ll notice something subtle: the coefficients in front of the velocity terms aren’t the same.
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That means we can’t just merge them into a single ‘relative velocity’ term with one neat coefficient, like we did for the oscillator.
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Only the follower’s own velocity term can be relabeled that way. The leader’s velocity comes with a different weight, so it has to stay separate.
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And that difference is exactly what gives us an independent, third characteristic parameter, the anticipation.
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For position, it’s different: the coefficients match, so relabeling one automatically relabels both. And all of this carries straight into the amplification function.
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And now, here’s a breakthrough: For a given natural frequency and a given level of anticipation, there actually is a finite damping ratio where the amplification peak just touches one, right at zero frequency.
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That point marks the threshold for what’s called string stability. At every non-zero frequency, the amplification is then below one, so no wave ever snowballs along the chain.
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But notice: if you change the natural frequency or the anticipation, that threshold shifts as well.
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So the ordinary damping ratio loses its uniqueness, it’s no longer the one parameter that decides stability.
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Instead, we need a new measure. Remember earlier, when we found the condition for ‘no local oscillations’ by equating coefficients?
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Now we can do something similar, by enforcing that the amplification peak stays at zero frequency.
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And that condition guarantees string stability. And just like before, we can map this out over safety, agility, and anticipation, again forming a surface.
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And with that surface, you can invent a new, unique stability measure: the closest distance from any driver behavior to that surface, with the sign telling which side you’re on.
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A “string damping ratio,” if you will. And here’s the surprising part: You can actually have drivers who locally overshoot, a damping ratio below one, yet still form a string-stable chain, a string damping ratio above zero.
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How is that possible? Well, let’s scroll through this ‘safety slice’ of the parameter space, changing agility and anticipation, and watch what happens to the gap after a single disturbance, and to how much the waves get amplified.
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At low agility and low anticipation, these are the really bad drivers: they overshoot a lot, and waves blow up as they move down the chain, if the cars don’t crash first.
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But then, in this funny region, things look different. A sudden gap jump may cause an overshoot, but each follower smooths it further toward something more visibly wave-like.
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And since all these waves eventually fade, the chain is nonetheless stable. And somewhere in this plane, there’s a fascinating point: just by nudging either agility or anticipation, you step into one of four fundamentally different regions.
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Two of them are ‘boring’: Locally fully damped drivers who also form a stable chain.
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Or locally oscillating drivers who also make an unstable chain. But the other two... that’s where it gets interesting.
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You can have locally fully damped, seemingly ‘good’, drivers, who nonetheless produce an unstable chain.
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Or locally oscillating, seemingly ‘bad’, drivers, who, in a chain, are string stable. That’s a level of complexity I honestly didn’t expect.
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So, the classical damping ratio and string stability are really two different things. And a whole line of cars with string stability never amplifies waves.
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If every driver used these parameters, yes, traffic would stay calm. Now, the story often goes: “Even if everyone drove like you, we’d still be stuck in a jam.” But honestly... if you drive safely, with enough agility and anticipation,
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then in a world full of drivers like you, things would improve. If you already drive like that, this is your moment for a little self-high five.
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And if not... that’s exactly the point. After a long day, hardly anyone drives at their best.
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So, what happens when... nobody drives well? Who, then, is left to dampen the jams?
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Let’s imagine there’s at least one driver willing to drive in a special way, so jams dissolve, or maybe never form at all.
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What would that look like? On this overloaded ring road, using the more complex driver model again, we see that for a while, everyone can drive steadily, until oscillations creep back in.
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So, as a wise driver, what’s the simplest way to stop those waves before they grow?
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By not reacting! Instead of copying every tiny imperfection from the car ahead, this driver just holds a steady pace, and gives the following car an absolutely smooth driving experience.
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In theory, they can even nudge up the average speed, gradually catching the end of the chain, which is the physical speed limit, because at higher speeds, followers keep larger safety gaps.
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Now, of course, this ring road isn’t real life. Here, the inflow is set by the outflow, not by the external traffic demand.
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But the implications are interesting. This trick works only because the wise driver knows exactly how the imperfect followers behave, and also knows what the next wise driver will do.
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Because that next wise driver... is this driver! So even a single globally aware driver already benefits everyone.
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But of course, you can’t really do this once a jam has already formed. How do you erase a wave if you’re stuck right in the middle?
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Well, you have to be able to drive through all the oscillations, and for that, you need extra space ahead.
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You could dial up safety, agility, and anticipation, but there’s something else: we also want to show the car behind us as smooth a drive as possible.
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So, we add another term to our acceleration rule, trying to reduce the speed difference to the following car.
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And now you’re acting as a wave damper. You’re not just anticipating what happens in front, but also what those behind you will do with it.
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And yes, this makes the jam look temporarily worse. But after just one lap, the wave is gone.
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We’re back at the physical speed limit, and soon overtaking the jammed case in terms of both average speed and fuel use.
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And this isn’t just theory. You can see it here in the real ring experiment.
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The wave damper car holds a steady speed, and the jam around it begins to dissolve.
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And if we’re lucky, the other drivers even share our joy in this mathematically elegant solution, and appreciate that we’re creating this ‘healing jam’ just to help everyone.
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Of course, in practice, a great solution has to go unnoticed. Ideally, it should look as if the jam dissolves on its own.
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And one driver alone can’t quite pull that off, you need a few more to join in.
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Here, with just six wise drivers, following a slightly different, globally aware acceleration rule (as discussed in the coding tutorials), the jam vanishes as if by magic, and nobody knows who did it.
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So, does that mean we always need a handful of wise human drivers? Not quite.
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Because without them, the thinner traffic still jams. Which means: this jam full of ordinary drivers can be resolved just by adding a handful of wise autonomous vehicles.
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A small fleet of wave dampers, so to speak. Of course, you don’t really want more cars on already full roads, but upgrade the existing ones instead.
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But the point is, you don’t need everyone to drive an autonomous vehicle to make it work.
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Even at low percentages, they can already have an effect on jams, helping everyone. And that’s worth thinking about, because it’s not all or nothing.
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So, let’s try this in a slightly more realistic scenario, the straight road from the beginning, where a sudden speed limit triggered stop-and-go waves.
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Now, suppose every twentieth car is autonomous. Their acceleration rule is designed so that they respond directly to the next autonomous vehicle ahead, with a safety gap stretched by a factor of at least 20, to still give space for all the others.
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Dynamically, we’re pretending the traffic only consists of a twentieth as many vehicles, each pulling along a little string of ordinary drivers.
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So, when a disturbance hits, the next autonomous vehicles immediately reacts, creating enough room to glide smoothly over the wave.
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And because the system dynamically behaves as if traffic were thinner, it’s naturally more stable, and oscillations don’t get amplified.
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In the end, the traffic flows just as smooth as with those frankly, impractical distributed speed limits.
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In other words, by giving some cars global awareness, basically turning them into self-driving speed-limit signs, waves are damped before they even form.
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And even if this virtually thinned-out traffic does develop waves, they scale up by the same factor, so the wavelengths are much longer, and the oscillations so gentle they’re practically irrelevant.
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Of course, for safety, the autonomous rule can always be overridden to react to the immediate leader.
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Now, if you want to measure how much this really improves traffic flow, things get interesting.
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Running the simulation without a slow zone and without autonomous vehicles, the tiny initial disturbances don’t grow into waves.
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In that case, a certain number of cars calmly pass this measurement point per hour.
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But if the very first car drives a bit slower, everyone behind also has to slow down.
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At the lower speed, though, they don’t need as much safety gap. Which means that, in the same time, more cars pass this point.
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So the higher density actually overcompensates for the lower speed, and traffic flow rises. And because everyone drives slower, fuel consumption per traveled distance also drops.
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This works, up to a critical density. Beyond that, even small disturbances start to grow into jam waves, which causes two problems: The traffic flow drops sharply because the waves reduce the average speed, and fuel consumption rises noticeably.
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At higher densities, the flow keeps falling until, at maximum density, nobody moves at all.
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So there seems to be an optimal density for maximum flow, right at the edge of string stability.
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Or so it seems. If you repeat the same simulations with a stronger initial disturbance, jam waves appear at lower density already.
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That creates a metastable region: With small initial disturbances, the chain is string stable; with larger ones, it isn’t.
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But wait, didn’t we just show that if amplification stays below one for all frequencies, nothing grows?
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How can that be true and false for this equally dense traffic? Well, our string stability analysis used a car-following model, where position and velocity only appear as linear terms with the coefficients to equate, never squared, or more complicated.
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Now, with a more general acceleration rule, the stability can’t be derived that way. So, either you simulate and observe...
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or you find linearized substitute rules that are roughly valid for a given amplitude range, and calculate stability for that range.
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As it turns out, string stability depends on the disturbance amplitude. Which brings us to the key question: What happens if just 5% of cars are autonomous, even under strong initial disturbances?
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Well... As density increases, there’s no sudden loss of string stability. Although the traffic will get stuck eventually, it all happens without jam waves.
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Those autonomous vehicles damp out even large disturbances at any density, achieving a better optimum in traffic flow with a lower fuel consumption.
Speaker A
Of course, there are far more effective modes of transportation. But since major shifts in acceptance take time, saving fuel by driving a little differently in the meantime could still be worth it.
Speaker A
Now, damping out waves to make highway traffic behave more like a train is just part of the story.
Speaker A
In a city, things fundamentally change. From a dynamical systems perspective, city car traffic is technically ‘stable,’ because waves form mostly as the result of strong external triggers like traffic lights, so wave damper cars don’t really work here.
Speaker A
And honestly, maybe solving traffic has always been as much a psychological problem as a technical one.
Speaker A
Maybe the best first ‘foot’ step is to get people educated. Because it’s one thing to know that traffic waves are inefficient, but once you play with the simulations yourself, you realize how little it can take to change an entire traffic system.
Speaker A
And that’s the heart of problem solving: understanding a system well enough to know exactly what to tweak.
Speaker A
And if you’re a little scared of the code, having a brilliant teacher makes the journey a lot more fun.
Speaker A
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Speaker A
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Speaker A
If you want to build that kind of intuition yourself, try Brilliant’s Thinking in Code course.
Speaker A
You can explore how iterative systems behave, just like we did here, only now you’re the one tweaking the variables and discovering the principles that make the whole thing work.
Speaker A
To learn for free on Brilliant, go to brilliant.org/braintruffle, scan the QR code onscreen, or click on the link in the description.
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Brilliant’s also given my viewers 20% off an annual Premium subscription, which gives you unlimited daily access to everything on Brilliant.
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Thanks for watching, and thank you for your support!
Topics:traffic jamsphantom jamstraffic wavesdamped oscillatortraffic flowautonomous vehiclesstring stabilityfuel efficiencycar-following modeltraffic physics
