Millions of people will hit the road this holiday season, only to end up spending frustrating hours sitting in their cars. traffic jams. Traffic jams cost drivers time, fuel and patience, while increasing pollution and putting enormous pressure on transport networks.
If you’ve ever found yourself staring longingly at the lane next to you, convinced that it’s moving faster, you’re not alone. Most of us instinctively believe that changing lanes will get us home faster. But mathematics suggests that this intuition is generally wrong.
As an applied mathematician, much of my research is motivated by a single question: how can we predict and control the behavior of complex systems operating under uncertainty? And this can apply to both holiday traffic and emergent traffic. quantum technologies.
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We tend to think that traffic jams require a trigger: an accident, roadworks or a lane closure. Yet some of the most frustrating queues have no obvious cause. These are known as phantom traffic jams-stop-start waves that back up in traffic even as each vehicle moves forward.
In 2008, Japanese researchers asked 22 drivers to navigate around a circular track while maintaining a constant speed and a safe distance from the vehicle in front of them. Within minutes, tiny, unavoidable differences in braking and reaction times turned into a wave of stops and starts that spread continuously across the circuit, even though there were no obstacles in the road.
The explanation is surprisingly simple. A driver brakes a little more than necessary. The driver behind reacts a little later and brakes a little harder. The next driver does the same.
In this way, the small initial disturbance grows as it backs up until drivers hundreds of meters behind are forced to come to a complete stop, even though no one can identify the initial cause of the queue.
The mathematics behind traffic
Rather than modeling each driver individually, mathematicians treat traffic as a continuous flow – borrowing ideas from fluid dynamics, where the movement of vehicles is analyzed in the same way as the flow of water in a pipe.
One of the simplest relationships in traffic flow theory is q = ρvOr q is the traffic flow (the number of vehicles passing through a point each hour), r is the traffic density (number of cars on the road) and v is their average speed.
This deceptively simple equation explains a counterintuitive phenomenon. First, adding vehicles obviously increases the overall traffic flow, as more vehicles travel on the road.
But as soon as the road gets too busy, everyone has to slow down. Ultimately, this reduction in speed outweighs the increase in the number of vehicles so that the overall flow is reduced.
The equation shows that there is an optimal traffic density that maximizes the number of vehicles traveling on the road each hour. Beyond this point, adding cars reduces the efficiency of the road and increases the time it takes for everyone to reach their destination.
The same math explains why constantly changing lanes is rarely worth it.
A lane change creates a small disturbance to which neighboring drivers must react. If many drivers behave in the same way, these disruptions accumulate and increase the likelihood of traffic waves. So what seems like a smart decision for one driver can ultimately make conditions worse for everyone.
Can mathematics help reduce traffic jams?
In my research on probabilistic mathematical methodsI develop approaches that combine prediction, coordinated decision-making and feedback to maintain the stability of complex systems, even when the available information is incomplete or “noisy” (full of superfluous data).
In traffic, the disruptions that we seek to avoid are the waves of stops and starts which create phantom traffic jams. In other complex systems, these may include power outages, communication bottlenecks, or unstable autonomous systems.
Rather than designing solutions for a specific application, applied mathematicians develop general mathematical frameworks. This is one reason why ideas originally developed for engineering systems can also help us think differently about traffic – with each of our mathematical tools playing a different role:
Signal processing transforms measurements from road sensors, cameras and connected vehicles into useful information.
Stochastic modeling takes into account uncertainty arising from driver behavior, weather conditions and changes in traffic demand.
Machine learning identifies patterns in all this data and predicts where congestion is likely to develop.
Control theory It then closes the loop by determining how traffic systems should respond, whether by adjusting traffic light schedules, introducing adaptive speed limits, recommending alternative routes, or coordinating autonomous vehicle fleets.
Rather than optimizing a driver’s journey, the goal is to improve the performance of the entire traffic network.
Perhaps the most striking demonstration took place in 2018, when researchers repeated the Japanese circular track experiment with one key difference. They replaced one of the human-driven vehicles with a single self-driving car, programmed to accelerate and brake smoothly.
Remarkably, this single vehicle, less than 5% of the traffic, was enough to cushion the wave of stops and starts across the entire circuit, thereby improving traffic flow and reducing fuel consumption for each driver involved.
Tips for your next road trip
It is unlikely that traffic jams will ever disappear completely. Population growth, increasing demand for travel and the unpredictability of human behavior will always put pressure on our roads.
But mathematics helps us move from reacting to congestion to preventing it.
An important aspect is to understand how large networks of interacting agents can coordinated decisions using only local informationwithout requiring each component to know the state of the entire system. These ideas are at the heart of the design of intelligent transportation systemswhere connected vehicles and infrastructure must cooperate to improve traffic flow.
In the meantime, if you’re getting ready to go on a driving vacation, here are three driving tips all backed by solid mathematical proof. If everyone adopts them, it should reduce the time you spend in queues.
Maintain a safe distance;
Accelerate and brake smoothly;
Resist the temptation to keep changing paths in search of small gains.
Applied mathematics shows that the quickest way to reach your destination is not to drive more aggressively. This is to help maintain the stability of the entire system.
This article was originally published on The conversation. Read the original article.
