Complex Numbers

With the Flow

So, okay, I'm still not completely coherent, but I'm not going to break my streak now.

Why a Traffic Flow Suddenly Turns Into a Traffic Jam  
Those aggravating slowdowns aren’t one driver’s fault. They’re everybody’s fault.

I've always wondered about this, myself, and I've taken actual traffic engineering classes.

Few experiences on the road are more perplexing than phantom traffic jams.

I can think of a couple, like when cops pull you over because you have out of state tags and therefore they figure you're not going to come back to contest the ticket.

Because traffic quickly resumes its original speed, phantom traffic jams usually don’t cause major delays. But neither are they just minor nuisances. They are hot spots for accidents because they force unexpected braking. And the unsteady driving they cause is not good for your car, causing wear and tear and poor gas mileage.

Okay, that's a stretch.

In contrast, macroscopic models describe traffic as a fluid, in which cars are interpreted as fluid particles.

When I was in engineering school, I learned both fluid mechanics and traffic engineering. I noted then that the equations used to model traffic flow were the discrete versions of the continuous equations used to model fluid flow. Such an epiphany made me feel a whole lot smarter than I actually was.

This observation tells us that phantom jams are not the fault of individual drivers, but result instead from the collective behavior of all drivers on the road.

You know, there's a metaphor in there somewhere. Like... pick a societal problem. Any problem. Poverty, racism, global warming, whatever. It's no individual's fault, but the result of all of our collective behavior.

It's not a great metaphor, but there it is.

However, in reality, the flow is constantly exposed to small perturbations: imperfections on the asphalt, tiny hiccups of the engines, half-seconds of driver inattention, and so on. To predict the evolution of this traffic flow, the big question is to decide whether these small perturbations decay, or are amplified.

And this bit reminds me of the difference between laminar and turbulent flow. I can't be arsed to explain that right now. Google it.

Besides being an important mathematical case study, the phantom traffic jam is, perhaps, also an interesting and instructive social system.

Like I said. Metaphor. I mean, really, you have to read the article to get the full effect; I've had a few beers tonight and thus I'm probably not making nearly as much sense as I think I am. But this one's been hanging out in my queue for a while, and I'm pretty sure that I'm saying what I wanted to say about it.

Hopefully tomorrow I'll be more clear, but right now there's a turbulent traffic jam in my neurons.