The End of Traffic Jams
Being stuck in miles of halted traffic is not a relaxing way to start or finish a summer holiday. And as we crawl along the road, our views blocked by by slow-moving roofboxes and caravans, many of us will fantasize about a future free of traffic jams.
As a mathematician and motorist, I view traffic as a complex system, consisting of many interacting agents including cars, trucks, cyclists and pedestrians. Sometimes these agents interact in a free-flowing way and at other (infuriating) times they simply grind to a halt. All scenarios can be examined – and hopefully improved – using mathematical modeling, a way of describing the world in the language of maths.
Mathematical models tell us for instance that if drivers kept within thevariable speed limits sometimes displayed on a motorway, traffic would flow consistently at, say, 50 mph. Instead we tend to drive more aggressively, accelerating as soon as the opportunity arises – and being forced to brake moments later. The result is greater fuel consumption and a longer overall journey time. Cooperative driving seems to go against human nature when we get behind the wheel. But could this change if our roads were taken over bydriverless cars?
Incorporating driverless cars into mathematical traffic models will prove key to improving traffic flow and assessing the various conditions in which traffic reaches a traffic jam threshold, or “jamming density”. The chances of reaching this point are affected by changes such as road layout, traffic volume and traffic light systems. And crucially, they are affected by whoever is in control of the vehicles.
In mathematical analysis, dense traffic can be treated as a flow and modeled using differential equations which describe the movement of fluids. Queuing models consider individual vehicles on a network of roads and the expected time they spend both in motion and waiting at junctions.
Another type of model consists of a grid in which cars’ positions are updated, according to certain rules, from one grid cell to the next. These rules can be based on their current velocity, acceleration and deceleration due to other vehicles and random events. This random deceleration is included to account for situations caused by something other than other vehicles – a pedestrian crossing the road for example, or a driver distracted by a passenger.
Adaptations to such models can take into account factors such as traffic light synchronization or road closures, and they will need to be adapted further to take into account the movement of driverless cars.
In theory, autonomous cars will typically drive within the speed limits, have faster reaction times allowing them to drive closer together and will behave less randomly than humans, who tend to overreact in certain situations. On a tactical level, choosing the optimum route, accounting for obstacles and traffic density, driverless cars will behave in a more rational way, as they can communicate with other cars and quickly change route or driving behavior.