The Wrong Side of my Car

A blog about Auckland City, its streets, and culture shock

2 Dec 2015

The unavoidable traffic infarct conjecture

What is it with cities that always causes them to suffer from congestion all the time?

Auckland is still quite OK compared to what we’re used to in Belgium, but it’s catching up fast:

It seems unavoidable that as a city grows, its traffic grinds to a halt. But why?

You could argue that this happens because there are not enough roads. You’d be right, but why don’t we just build more roads as the city grows? Judging from the discussion about rate increases for the next 10-year plan in Auckland, one issue seems to be funding.

It got me thinking. Why is that? Are we doing something wrong? Or is it just a consequence of how cities work?


OK, suppose we have a small city. As it grows it needs new infrastructure. The more people living in the city, the more houses, schools, parks, utilities, roads and streets etcetera it needs.

How much money do we have for all of that? If a city gets twice as large, you could expect it to have twice the ratepayers, and so twice the budget. So we could say, our budget scales up linear with our population, O(n). That’s an underestimate, as things like agglomeration benefits come into play. That’s the entire point of building a city in the first place. But let’s go with that for now.

The more people, the more we need to build. House to live in, for example. If population doubles, we need double the amount of houses. Demand for housing is O(n), nicely in line with our funding (although often land prices are a whole different issue). Many other kinds of infrastructure scale up that way. We need double the amount of schools, and daycare for our kids. We would like double the amount of local parks so we can hang out and maybe meet some neighbours.


What about roads? To understand this one, we have to step back to think about what makes a city a city. A city of 100,000 people is very different from 20 towns of 5,000 people laid together back-to-back. The key thing is proximity. In our city, we can look for jobs in the entire city. If we have some exotic illness, we may go to the best hospital in the entire city. If I have a business which appeals to only a small fraction of the population, I can attract customers from the entire city, and not just the 5,000 people in the part of the city I happen to live in.

The infarct

But that assumes we can actually get there easily. We build (usually) roads to get around these days. So, how does that scale up? In a small town, probably we can get around on foot, which makes transport very cheap. As the town grows bigger, we probably rely on cars for getting around.

As a city gets larger, the journeys we want to make get longer. If we don’t increase the density of our city, then the area will increase proportional with our population *1. So basic geometry dictates that this distance scales up with the square root of the size of your city. The total distance our citizens want to travel scales up by O(n∙√n). We not only need to build new roads in the new suburbs, we also need to widen the roads or build new roads in the other parts to meet the new demand for cross-town traffic.

Of course this is also an underestimate. High land prices and the fact that normally most places are already built up in our city make any expansion in capacity difficult and more expensive. And as distance grows, we need faster transport which is probably also more expensive.

So maybe both curves are an underestimate, but I think you can still assume that the cost of all our roads is growing faster than the budget we have to build them:

O(n) funding vs O(n∙√n) traffic

Starting from this assumption, you can explain a lot of observations in cities:


Yes, I know about the apartment towers in city centres. But usually growth occurs both in those densely populated centres, and as lower density suburbs on the edge of the city. It can go both ways.

Corollary 1: induced demand

This funding gap means a large city is always short of transport capacity, manifesting itself in things like congestion on roads, and crowding on trains. New infrastructure will quickly fill up and get crowded as well. This is part of what urbanists call that the law of induced demand.

And now we can also put to rest a lot of nonsense about all these big new transport projects: Whenever anyone tells you that any of these…

…will achieve any of these…

Then you know he’s selling you snake oil. New infrastructure will just meet a little more of the existing demand out there. It enables growth. They for example will allow more people living on the edge to the city to commute to places further away from their homes.

Corollary 2: Once congestion sets in, we’re screwed

It can take a while for that O(n∙√n) need to catch up with that O(n) budget. But when it does, things deteriorate fast. Once a road is saturated, even a small increase in traffic will make congestion much worse. So that congestion will set in suddenly, and above all, irreversibly.

Auckland appears to have reached this point now. You can in some places almost watch the congestion get worse every year.

Corollary 3: land is scarce

So, we don’t have enough transport infrastructure to let our people reach any parts of town easily. So what happens next? The central parts of our city have the best connections. For employers, this is where they can reach the most potential employees. On the edge of the city? Not so much, as on one side you have the more rural areas, with way less people. And what if you happen to live on that edge? probably you’ll have to contend with the worst congestion if your job is more centrally located.

So the more central areas of the city will be the most desirable, but they are by definition scarce. Which means expensive. No amount of available land around the city will change that.

Beating O(n∙√n)

Dealing with this funding gap is a thankless task. You can’t increase rates too much without angering people. But you can’t just sit on your hands and let congestion get worse without angering people. Probably you’ll anger people for both reasons at the same time.

(1) Avoid the increase in distance

One obvious way to beat this increase in total travelled distance, is to not increase the distance between destinations. Increase the density, rather than the area.

Sometimes the opposite happens, and the majority of growth happens as low-density sprawl on the edges. That is of course not going to help our problem.

But with more density also comes more traffic concentrated in the same area. So you had better…

(2) bet on the right system

Some systems scale up better than others.

We like our cars. They go door to door, any time we need want. At least they will when the parking problem is fixed, right? But this scales up particularly poorly in cities. Did I say land is scarce in the centre? Well, for cars you need lots and lots of it. Big motorways, the parking all the people using that road need, and the even bigger interchanges. And there is this other observation: all those cars have a way of dominating the streets of your city, making it a rather ghastly environment for humans.

Public transit, especially with trains, scales up much better. A double-tracked railway can carry more people than a 2×10 lane motorway, and only needs a station to let people on and off. But it has a different problem. It’s often caught in a catch-22 between no people wanting to take the bus, and no buses to pick any people up. Public transit scales down pretty badly. You can’t cater for 100 people per day travelling along a given route in a meaningful way. An empty bus every 15 minute is too expensive, while having a bus only every 2 hours would be a crippling limitation for those people. Unlike a road network, it’s really difficult to build up a useful transit network gradually.

But at some point you have to seriously think which kind of investment allows enough growth without bankrupting the city, so…

(3) have courage

Building a public transit network is not going to be popular. What’s your experience with taking the bus? Unless you’re really lucky, it’s probably in the lines of hurry the bus is almost there and the next bus is only in an hour, wait forever for a connecting bus, and generally taking 2 hours instead of the usual 20 minutes to get home. Maybe you think that’s just how public transport works, and the congestion on the roads should be “fixed”.

But there is overwhelming empirical evidence that the latter completely impossible. At some point, you really have to start investing in an alternative with better economies of scale, and preferably before you pile up a crippling debt by building ‘just one more motorway and then it will be fixed’.

And of course, don’t forget…

(4) walking is the cheapest

Yes of course it is! You’d think everybody knows that. However:

Botany mall, uh, “town centre”.

Oops. Most planners seemingly don’t realise this. Auckland is full with warts like these. Mangere. And Albany. It’s a self-fulfilling prophecy. If you assume everybody will drive in, you have to build a lot of parking. If you surround your centre with these seas of parking, then walking there will be a quite unpleasant experience at best, and just too far at worst. So instead of a slightly wider footpath, you get to build a 6-lane road instead. I think you can guess which one is cheaper.

Same problem with some shop owners. Even in the middle of the city centre.

This also comes back to density. A high enough density means a lot of daily chores, like grocery shopping, can be done on foot. That saves you a lot of money on parking and roads.

(5) …followed by cycling

The aversion to cyclists here in Auckland is almost comical. Too bad, as cycling infrastructure is quite the bargain at the moment. There is a proposal to spend $1 billion on just one road along the Mangere inlet. We could probably have 10% extra capacity on our entire street network for less than that. I would definitely know what to choose.

So, in conclusion

So if you happen to be planning or lobbying for another road to be built here in Auckland: You had better think long and hard before going ahead. The chances of it having those benefits you hope for are pretty slim.

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