This is why building new roads can make the network less efficient – and make traffic congestion worse

Congestion in action. Image: Flickr/Wendell, CC BY-ND.

It’s not been a good year so far for major transport projects in Australia’s capital cities. 

The scale of disagreements over the merits of Melbourne’s proposed East West Link was such that the Victorian Government recently paid out $339m simply for the project not to be built. In Queensland, Annastacia Palaszczuk became the fourth successive Premier to completely throw out her predecessor’s signature infrastructure project – in this case the Bus and Train (BaT) Tunnel.

And while Sydney’s WestConnex project is still going ahead, recent reports concluded that it will either substantially increase traffic on the much-maligned Parramatta Road, or maybe decrease it. It all depends on which report you believe.

I am not going to debate the relative merits of these schemes: my background is in applied mathematics and not in transport planning. As such, my interest is less in the conclusions of some of these predicted usage studies and more in the consequences of the assumptions made in the modelling.

How can one report filed with the NSW Major Project register predict 20,000 fewer cars per day on a section of Parramatta Road, while other reports within the Roads and Maritime Services state that no significant reductions are likely to be seen?

It is very easy to chalk up some of these differences either to wildly overoptimistic developers potentially misleading themselves and others to get a project approved. Similarly, it is sometimes alleged that feasibility studies might be influenced by political biases or pre-established views on the merits of roads or public transport schemes.

While these factors may well influence some decision making, one thing that is often missed in the reporting of such studies is the sheer complexity associated with analysing such networks. Assuming all roads are connected, the behaviour of a whole network can be hyper-sensitive to how individual parts, even seemingly minor ones, function.

A poor estimate of traffic flow in one section of a network can lead to hugely different behaviour across the whole system. Furthermore, even the simplest networks can have the potential to function in some extremely surprising and often counter-intuitive ways.

It is very easy to believe that, if a traveller is offered the choice of two routes for a journey, the addition of a third choice should not worsen his/her travel time. If the new route is slower, the traveller could simply ignore the new route and make the same choice as before.

But as the German mathematician Dietrich Braess pointed out, this is not always the case. Increasing the capacity of a network can, perhaps surprisingly, decrease the efficiency of journeys around it even without increasing the number of trips made, as was pointed out in a recent article.

The Braess’s Paradox

To take a closer look at the reasoning behind this paradox, consider the case illustrated below. There are two major cities, labelled as the Start and End locations for a journey.

Travellers between the two cities have two choices of route, either via Town A or via Town B. The roads from Start to Town A and from Town B to End are both highways, which can handle any number of cars and allow them to make each leg of the journey in 105 minutes.

The roads from Start to Town B and from Town A to End are smaller roads, which are slower when busy. When there are N cars on the road, each leg of the journey takes N minutes. There is an old road linking Town A to Town B with a journey time of 100 minutes. This road is sufficiently slow that no traveller from Start to Finish would choose a route that involves it.

Network illustrating Braess’s Paradox. Travel times along routes are listed in minutes.

If we assume that 100 cars are travelling at the same time from Start to End, then there is no advantage to going via Town A vs going via Town B. The traffic will split approximately 50/50 between the two routes and each car will do the journey in 155 minutes. This is the fastest route. In reality, the split of cars might not be exactly 50/50, but unless the ratio is heavily imbalanced, the average travel time across the network will be 155 minutes.

A driver cannot help the overall network without suffering for it in the form of a slower journey

Now suppose now that the network is “improved” by upgrading the road between Town A and Town B. Rather than taking 100 minutes to travel between the towns, it now takes only 2 minutes.

The fastest route now is for all drivers to go from Start to Town B in 100 minutes, take the 2 minute trip to Town A, then travel from Town A to End in another 100 minutes. This journey now takes 202 minutes – but that’s 47 minutes longer than on the old road layout.

There is no incentive for any driver to choose an alternative route. Opting for either of the 105 minute roads will only lengthen their trip. A driver can improve travel times for all others by selflessly choosing the slowest roads, but cannot help the overall network without suffering for it in the form of a slower journey. This, of course, is not an option which many will choose.

While the old road between Town A and Town B was hugely inefficient, this inefficiency actually ensured that the network as a whole remained reasonably efficient. It served to distribute traffic evenly between the two routes from Start to End. But by improving this relatively unimportant road, it simply redistributes traffic more unevenly and worsens the overall system.

Even more counter-intuitively, Braess’s Paradox is observed in simple physical systems as well as transport networks.

The video (above) illustrates a system whereby a weight is suspended on two springs connected both in series (by an initially tense string) and in parallel (by initially slack strings). Removing the string which is in tension actually leads to the weight being lifted upwards.


This is actually a reverse of our traffic example. The distance the weight hangs represents the longer journey time of the traffic – remove the central string (the new road) and the hanging distance is reduced as is the journey time for the traffic.

Paradox in action

This paradox is not simply a mathematical quirk, or one which can be neglected by network analysts. There are a number of examples where removing roads – rather than building news ones – has improved transport networks.

Probably the most famous example of this comes from South Korea. When the motorway network around Seoul was reworked to remove some of the 1960s-built roadways, the the result was significantly reduced transit times throughout the city. This was not because of fewer journeys through the city, rather a more efficient distribution of cars across the remaining network.

Similar phenomena have been observed during road closures in New York City in the United States and in Stuttgart in Germany.

As Braess’s Paradox points out, even a slight change to a relatively unimportant part of the whole network can lead to massive changes in travel times. While planning reports might focus on headline stories – new road X will cut travel times by Y minutes – the underlying modelling must be more robust and look at the uncertainty around such estimates.

As painstaking as this modelling may be, it is unquestionably something that needs to be answered as fully and as correctly as possible, admitting its own limitations.

A multi-billion dollar infrastructure project cannot afford to fail simply because someone didn’t do their sums correctly. The financial consequences of incorrect projections can be financially catastrophic.

Both Sydney’s Cross City Tunnel and Lane Cove Tunnel drove their initial operators into receivership. The developers of Brisbane’s Clem Jones Tunnel fared no better.

The issue is not just limited to Australia, of course. Of the 15.9m journeys expected to be taken between London and Paris during the Channel Tunnel’s first year of operation, a mere 18 per cent of those actually occurred.The Conversation

Stephen Woodcock is lecturer in mathematics at University of Technology, Sydney.

This article was originally published on The Conversation. Read the original article.

 
 
 
 

CityMetric is now City Monitor! Come see us at our new home

City Monitor is now live in beta at citymonitor.ai.

CityMetric is now City Monitor, a name that reflects both a ramping up of our ambitions as well as our membership in a network of like-minded publications from New Statesman Media Group. Our new site is now live in beta, so please visit us there going forward. Here’s what CityMetric readers should know about this exciting transition.  

Regular CityMetric readers may have already noticed a few changes around here since the spring. CityMetric’s beloved founding editor, Jonn Elledge, has moved on to some new adventures, and a new team has formed to take the site into the future. It’s led by yours truly – I’m Sommer Mathis, the editor-in-chief of City Monitor. Hello!

My background includes having served as the founding editor of CityLab, editor-in-chief of Atlas Obscura, and editor-in-chief of DCist, a local news publication in the District of Columbia. I’ve been reporting on and writing about cities in one way or another for the past 15 years. To me, there is no more important story in the world right now than how cities are changing and adapting to an increasingly challenging global landscape. The majority of the world’s population lives in cities, and if we’re ever going to be able to tackle the most pressing issues currently facing our planet – the climate emergency, rising inequality, the Covid-19 pandemic ­­­– cities are going to have to lead the way.

That’s why City Monitor is now a global publication dedicated to the future of cities everywhere – not just in the UK (nor for that matter just in the US, where I live). Our mission is to help our readers, many of whom are in leadership positions around the globe, navigate how cities are changing and discover what’s next in the world of urban policy. We’ll do that through original reporting, expert opinion and most crucially, a data-driven approach that emphasises evidence and rigorous analysis. We want to arm local decision-makers and those they work in concert with – whether that’s elected officials, bureaucratic leaders, policy advocates, neighbourhood activists, academics and researchers, entrepreneurs, or plain-old engaged citizens – with real insights and potential answers to tough problems. Subjects we cover include transportation, infrastructure, housing, urban design, public safety, the environment, the economy, and much more.

The City Monitor team is made up of some of the most experienced urban policy journalists in the world. Our managing editor is Adam Sneed, also a CityLab alum where he served as a senior associate editor. Before that he was a technology reporter at Politico. Allison Arieff is City Monitor’s senior editor. She was previously editorial director of the urban planning and policy think tank SPUR, as well as a contributing columnist for The New York Times. Staff writer Jake Blumgart most recently covered development, housing and politics for WHYY, the local public radio station in Philadelphia. And our data reporter is Alexandra Kanik, whose previous roles include data reporting for Louisville Public Media in Kentucky and PublicSource in Pittsburgh, Pennsylvania.

Our team will continue to grow in the coming weeks, and we’ll also be collaborating closely with our editorial colleagues across New Statesman Media Group. In fact, we’re launching a whole network of new publications, covering topics such as the clean energy transition, foreign direct investment, technology, banks and more. Many of these sectors will frequently overlap with our cities coverage, and a key part of our plan is make the most of the expertise that all of these newsrooms combined will bring to bear on our journalism.

Please visit citymonitor.ai going forward, where you can also sign up for our free email newsletter.


As for CityMetric, some of its archives have already been moved over to the new website, and the rest will follow not long after. If you’re looking for a favourite piece from CityMetric’s past, for a time you’ll still be able to find it here, but before long the whole archive will move over to City Monitor.

On behalf of the City Monitor team, I’m thrilled to invite you to come along for the ride at our new digs. You can follow City Monitor on LinkedIn and on Twitter. If you’re interested in learning more about the potential for a commercial partnership with City Monitor, please get in touch with our director of partnerships, Joe Maughan.

I want to thank and congratulate Jonn Elledge on a brilliant run. Everything we do from here on out will be building on the legacy of his work, and the community that he built here at CityMetric. Cheers, Jonn!

To our readers, on behalf of the City Monitor team, thank you from all of us for being such loyal CityMetric fans. We couldn’t have done any of this without you.

Sommer Mathis is editor-in-chief of City Monitor.