Why mathematicians are the finest drivers

September 15, 2016

Over the years, there are very few people whom I know that have described Mathematics as their thing. Actually, mathematics is not be the first thing on most people’s mind turns to when they are caught in a traffic jam. A recent engagement with a fellow coder led me to understand why mathematics holds the key to understanding how traffic congestion develops, and how to prevent it.Is there a country where major cities don’t experience traffic jams?I don’t think so. In the context of a road network, he explained that there is the seemingly counter intuitive result that even without an increase in traffic, building a new road can actually make every single journey slower.This can arise because the distribution of cars in a network is determined by the individual decisions of many drivers, each acting to reduce their own personal travel time instead of working as a group to reduce travelling times overall. Such behaviour often results in suboptimal use of the road network.In fact, when President Barack Obama visited Kenya last year, there stories on social media on how closing roads during his visit improved traffic congestion.This highlights that there is a lot of very interesting, challenging, and important mathematics that is involved in efficiently transporting human beings around a modern city.My friend argues, public transport should be scheduled to minimise people’s travel times and traffic signals operated to reduce congestion. When and where should cities build new roads matters a lot. As populations continue to increase, tackling the transportation problem becomes ever more challenging. In his view, mathematics has recently yielded some significant gains.In Finland, use of mathematical control of the traffic lights at the entrances of freeways has already increased travel speeds by more than 20% during the morning peak hour. And this was achieved without the cost of building extra lanes.As regular commuters know all too well however, significant challenges remain.

In addition to economic costs, there is also the negative impact congestion has on the environment, and on people’s quality of life.Luckily, there are researchers around the world working on these issues.Understanding the kinds of behaviour that can emerge from large collections of self driven particles is an active area of theoretical physics that can be applied on motorists.It has been found that there are many common features in the way jams form in flows of such self driven particles, regardless of whether the particles are insects or people. To borrow from physicists, the onset of jamming is an example of a phase transition.On a more immediately practical level, much recent effort within the mathematical community has been expended on improving the efficiency of the transport networks. Breakthroughs in this direction are due in part to technological advances, which allow detailed information on traffic conditions to be constantly collected and processed.Even more crucial, however, has been the development of improved mathematical models and algorithms to process and harness the new data.Using smartphone technologies, an app can efficiently match passengers with vehicles using optimisation algorithms and smart user interfaces. The vehicles used in such schemes could be private cars, but they could also be buses that are routed adaptively, to make sure there’s a bus when and where you need it. An even broader vision would be to schedule all transport. If drivers notified the transport system each time they started a journey, it could then schedule road use to balance out traffic across the road system and minimise congestion. Simulations suggest even with a small percentage of drivers using the system, users could halve their travel times.So the next time you find yourself in bumper to bumper traffic, instead of being angry, try pondering some mathematics because it could also save you a lot of time.

Contador Harrison