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.

 
 
 
 

The Thessaloniki dig problem: How can Greece build anything when it’s swarming with archaeologists?

Archaeological finds on display in an Athens metro station. Image: Gary Hartley.

It’s fair to say that the ancient isn’t much of a novelty in Greece. Almost every building site quickly becomes an archaeological site – it’s hard to spin a tight 360 in Athens without a reminder of ancient civilisation, even where the city is at its ugliest.

The country’s modern cities, recent interlopers above the topsoil, serve as fascinating grounds for debates that are not just about protecting the ancient, but what exactly to do with it once it’s been protected.

The matter-of-fact presentation that comes with the many, many discoveries illustrates the point. Athens often opts to display things more or less where they were found, making metro stations a network of museums that would probably take pride of place in most other capitals. If you’re into the casual presentation of the evocative, it doesn’t get much better than the toy dog on wheels in Acropolis station.

That’s not even close to the extent of what’s available to cast an eye over as you go about your day. There are ruins just inside the city centre’s flagship Zara store, visible through the glass floor and fringed by clothes racks; Roman baths next to a park cafe; an ancient road and cemetery in an under-used square near Omonia, the city’s down-at-heel centre point.

Ruins in Zara. Image: Gary Hartley.

There is undoubtedly something special about stumbling upon the beauty of the Ancients more or less where it’s always been, rather than over-curated and corralled into purpose-built spaces, beside postcards for sale. Not that there isn’t plenty of that approach too – but Greece offers such sheer abundance that you’ll always get at least part of the history of the people, offered up for the people, with no charge attached.

While the archaic and the modern can sit side by side with grace and charm, economic pressures are raising an altogether more gritty side to the balancing act. The hard press of international lenders for the commercialisation and privatisation of Greek assets is perhaps the combustible issue of the moment – but archaeology is proving something of a brake on the speed of the great sell-off.

The latest case in point is the development of Elliniko – a site where the city’s decrepit former airport and a good portion of the 2004 Olympic Games complex sits, along the coastal stretch dubbed the Athens Riviera. With support from China and Abu Dhabi, luxury hotels and apartments, malls and a wholesale re-landscaping of several square kilometres of coastline are planned.

By all accounts the bulldozers are ready to roll, but when a whole city’s hovering above its classical roots, getting an international, multi-faceted construction job off the ground promises to be tricky – even when it’s worth €8bn.


And so it’s proved. After much political push and shove over the last few weeks, 30 hectares of the 620-hectare plot have now been declared of historical interest by the country’s Central Archaeological Council. This probably means the development will continue, but only after considerable delays, and under the watchful eye of archaeologists.

It would be too easy to create a magical-realist fantasy of the Ancient Greeks counterpunching against the attacks of unrestrained capital. The truth is, even infrastructure projects funded with domestic public money run into the scowling spirits of history.

Thessaloniki’s Metro system, due for completion next year, has proved to be a series of profound accidental excavations – or, in the immortal words of the boss of Attiko Metro A.E., the company in charge of the project, “problems of the past”.

The most wonderful such ‘problem’ to be revealed is the Decumanus Maximus, the main avenue of the Byzantine city – complete with only the world’s second example of a square paved with marble. Add to that hundreds of thousands of artefacts, including incredibly well-preserved jewellery, and you’ve a hell of a haul.

Once again, the solution that everyone has finally agreed on is to emulate the Athens approach – making museums of the new metro stations. (Things have moved on from early suggestions that finds should be removed and stored at an ex-army camp miles from where they were unearthed.)

There are other problems. Government departments have laid off many of their experts, and the number of archaeologists employed at sites of interest has been minimised. Non-profit organisations have had their own financial struggles. All of this has aroused international as well as local concern, a case in point being the U.S. government’s renewal of Memorandums of Understanding with the Greek state in recent years over protection of “cultural property”.

But cuts in Greece are hardly a new thing: lack of government funding has become almost accepted across society. And when an obvious target for ire recedes, the public often needs to find a new one.

Roman baths in Athens. Image: Gary Hartley.

Archaeologists are increasingly finding themselves to be that target – and in the midst of high-stakes projects, it’s extremely hard to win an argument. If they rush an excavation to allow the quickest possible completion, they’re seen as reckless. If they need more time, they’re blamed for holding up progress. 

Another widely-told but possibly-apocryphal tale illustrates this current problem. During the construction of the Athens Metro, a construction worker was so frustrated by the perceived dawdling of archaeologists that he bought a cheap imitation amphora in a gift shop, smashed it up and scattered the fragments on site. The worthless pieces were painstakingly removed and analysed.

True or not, does this tale really prove any point about archaeologists? Not really. They’re generally a pragmatic bunch, simply wanting to keep relics intact and not get too embroiled in messy public debates.

It also doesn’t truly reflect mainstream attitudes to cultural capital. By and large, it’s highly valued for its own sake here. And while discoveries and delays may be ripe for satire, having history’s hoard on your doorstep offers inconveniences worth enduring. It’s also recognised that, since tourists are not just here for the blue skies, good food and beaches, it’s an important money-maker.

Nonetheless, glass malls and shiny towers with coastal views rising from public land are good for the purse, too – and the gains are more immediate. As the Greek state continues its relentless quest for inward investment, tensions are all but guaranteed in the coming years. 

This is a country that has seen so many epic battles in its time it has become a thing of cliché and oiled-up Hollywood depiction. But the latest struggle, between rapacious modernity and the buried past, could well be the most telling yet. 

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