The science of traffic and its awfulness

If only the guy in front of you would drive better, perhaps you wouldn’t be stuck in traffic. Slow, fast, break. Slow, fast, break. Shift lanes. Whoever it is, that driver sucks.

That’s what the driver behind you thinks about you, and what the driver behind that driver thinks about him, and so on. It’s traffic congestion, and it’s bad for everyone.

There are two aspects of congestion to be explored here in very brief detail: its physical results and its economic causes. Only once we understand the economic causes will we be able to figure out a solution.

Traffic makes roads terrible

Roads move traffic at a rate governed by a very simple model: the density of the vehicles per mile times their speed. But there is a trade-off. As the density of vehicles goes up, their speed goes down as drivers become more cautious. There’s a balancing point where density and speed allow a road to move the most vehicles. Shift the density a bit either way, and you don’t move as many vehicles, and you’re not getting your money’s worth out of the road. The relationship looks like this:

When traffic gets bad, roads exist on right-hand side of the diagram. Drivers like being on the left-hand side where speed is pretty high,, and taxpayers should want to be right in the middle, getting the most for their money. Image from ACCESS magazine [1]

When traffic gets bad, roads exist on right-hand side of the diagram. Drivers like being on the left-hand side where speed is pretty high,, and taxpayers should want to be right in the middle, getting the most for their money. Image from ACCESS magazine [1]

So, traffic congestion is when the road is operating somewhere on the right side of the curve. Basically, at rush hour, there are too many people that want to use the road all at once, increasing density way past the efficient level, making everyone slow down and the roads awful. This video does a good job of showing how this works. It’s boring, but stick with it [2]:

Basically, everyone slows everyone else down by trying to use the road all at the same time. Every additional vehicle on the road slows everyone else down just a little bit, which adds up to a lot. Past the balancing point, each additional vehicle also makes the road less efficient. Just how much is something we can quantify.

Time is money

When someone is slowed down in traffic, they get to wherever they’re going later than they’d hoped. This might cost maybe a few minutes, but when multiplied out over everyone stuck in (and causing) that traffic it ends up being a lot of person-hours. Economists, measuring a whole host of factors [3], translate this time cost into a monetary cost. Every vehicle “pays” a certain amount of time (alongside gas, maintenance, and tolls) which is the average cost of using the road. When someone new comes into the road, that average cost goes up just a little bit at the margins. This is called marginal cost of using the road. Each driver feels only the average cost; the marginal cost is divided up evenly between everyone else around them on the road. It’s like when someone cuts in line: everyone behind them is slowed down a bit.

In short, every vehicle faces the average cost and forces everyone else to “pay” a little bit more. Brendan O’Flaherty writes:

The final major kind of external cost that drivers impose on each other is congestion. On an otherwise deserted country road, or even on most city streets at four o'clock in the morning, it's difficult for one car to get in the way of another car or to impede its progress, and so congestion is not a problem. But when tens of thousands of cars an hour are converging on the Lincoln Tunnel during rush hour, they get in each others' way, and since the number of cars that can go through the tunnel in any minute is less than the number that want to go through, each car that enters the tunnel during rush hour is forcing all the cars behind it in the queue to wait a few seconds. Because drivers don't bear the cost of the congestion they cause, they cause too much of it.
I'm not saying that drivers don't bear the costs of congestion. Of course they do; being stuck in a traffic jam is unpleasant and time-consuming. But I don't bear the costs of the congestion I cause; instead I bear the costs of the congestion you cause, and so you have no incentive not to cause it. Or more starkly, think about a line of cars going through the Lincoln Tunnel. The first car may encounter no congestion, but if it were vaporized, every other car would get through the tunnel more quickly; and so the first car is causing a lot of congestion. The last car, by contrast, is encountering a lot of congestion, but causing none (if it were vaporized no one else would get through the tunnel sooner). [4]

O’Flaherty goes on to also describe how people shift their schedule around to avoid traffic, which has its own cost, and how people sometimes just grin and bear it, choosing to drive in traffic and pay that cost on the road instead. [5]

But all this cost is just in terms of time. It’s wasted, lost to everyone. If there were a way to shift that cost into dollars, then it would be possible to put that cost to productive use, or to return it to the people who need money more than time.

Anti-congestion toll

This is where congestion pricing, or demand pricing, or surge pricing, or whatever you want to call it, comes in. In essence, it’s a toll that charges people what they would otherwise pay in terms of time as well as the cost they impose on other users of the road (the marginal cost). This smooths out demand, so the road never gets clogged, and allows the money to be put to better use. The tolls collected could also be returned to poor drivers as a refundable tax credit. (I would have the electronic toll collector contractor, i.e. FasTrak, mail out a tax form to each of its customers itemizing the amount paid in anti-congestion tolls by month, which the customer could report on their taxes as a credit contingent upon income.)

The goal would not be to return the road to free-flow speed, but rather to the balancing point, where a road moves the most cars per hour possible. More people would therefore be able to get through the system at rush hour, meaning the whole driving system would be more efficient. Any money not returned as a tax credit could sponsor public transit or road improvements.

The London tolling plan, which did not include the tax credit, saw travel times fall and then stabilize within the controlled area, though traffic volumes continued to fall significantly. [6] London also saw the number of crashes and traffic deaths fall significantly. [7] The Stockholm plan saw the similar results but, intriguingly, drivers who were interviewed after the toll went into effect didn’t think they had changed their travel behavior. [8]

This is the only way to ensure congestion doesn’t occur without a recession because, as discussed above, people normally don’t feel the cost they impose on everyone else on the road and so they overuse it. With a toll like this, people will feel the full cost of their road use and so allow society to get the most out of the investment in roads.

Of course, people don’t like to be charged for what they previously got for free, especially when that would represent an unknown change. Stockholm residents, for instance, hated the idea of a congestion charge until it was attempted. [9] Manhattan has tried for years to implement a charge only to be blocked by state lawmakers. [10] When San Francisco talked about doing something on the Golden Gate Bridge, then-San Rafael mayor Al Boro called it a “Marin commuter tax.” [11]

Nevertheless, given that it is the only way to permanently resolve traffic, it is worth exploring how big the charge would be and what is possible with that income. That’s what we will explore next time.

Works Cited

[1] Richard Arnott, “A Bathtub Model of Downtown Traffic Congestion,” ACCESS Magazine, June 1, 2015.

[2] Washington State Department of Transportation, Doug MacDonald - Rice and Traffic Congestion, 2007.

[3] J. Hewitt, “The Calculation of Congestion Taxes on Roads,” Economica 31, no. 121 (1964): 72–81, doi:10.2307/2550927; Roberto Ayala, “The Value of Travel Time Savings: Departmental Guidance for Conducting Economic Evaluations Revision 2 (2014 Update)” (Washington, DC: US Department of Transportation, July 9, 2014).

[4] Brendan O’Flaherty, “Congestion,” in City Economics, 1st ed (Cambridge, Mass: Harvard University Press, 2005), 52.

[5] Ibid., 56.

[6] Transport for London, “Public and Stakeholder Consultation on a Variation Order to Modify the Congestion Charging Scheme Impact Assessment” (London, UK, January 2014).

[7] Alex Davies, “London’s Congestion Pricing Plan Is Saving Lives,” Website Type, Wired, (March 10, 2015).

[8] Jonas Eliasson, How to Solve Traffic Jams (Lausanne, Switzerland: TEDxHelvetia, 2012).

[9] Ibid.

[10] Ben Fried, “Factchecking Cuomo’s Revisionist History of NYC Road Pricing,” Streetsblog New York City, February 18, 2015.

[11] Michael Cabanatuan, “Bridge Raises Tolls, Denies Doyle Dr. Funds,” SFGate, March 15, 2008.