As millions prepare for holiday travel, many will find themselves enduring long hours in traffic jams. This congestion not only drains time, fuel, and patience but also heightens pollution and burdens transport networks.
If you’ve ever felt tempted to switch lanes, thinking it will get you home faster, you’re not alone. Many believe this tactic works, but mathematics often proves this intuition wrong.
As an applied mathematician, my research focuses on predicting and controlling complex systems under uncertainty—a concept applicable to both holiday traffic and quantum technologies.
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We commonly assume traffic jams are caused by accidents, roadworks, or lane closures. However, many frustrating queues, known as phantom traffic jams, occur without any clear cause. These are stop-start waves that move backward through traffic, even as vehicles move forward.
In 2008, Japanese researchers conducted an experiment with 22 drivers on a circular track, maintaining constant speed and safe distance. Minor differences in braking and reaction times quickly escalated into a stop-start wave circulating the track, despite the absence of any road obstacles.
The reason is straightforward: one driver brakes slightly more than necessary, the following driver reacts a bit later and brakes harder, and this pattern continues. The disturbance grows as it moves backward, forcing drivers much further back to stop completely, with no apparent cause for the queue.
The mathematics behind traffic
Instead of focusing on individual drivers, mathematicians view traffic as a continuous flow, akin to water flowing through a pipe, borrowing concepts from fluid dynamics.
A fundamental relationship in traffic flow theory is q = ρv, where q represents traffic flow (vehicles passing a point per hour), ρ is traffic density (cars on the road), and v is their average speed.
This simple equation reveals a counterintuitive phenomenon: adding more vehicles initially boosts traffic flow, but eventually, the increase in vehicles slows everyone down, reducing overall flow.
The equation indicates an optimal traffic density that maximizes vehicle passage per hour. Exceeding this point decreases road efficiency and increases travel time.
This same mathematics explains why lane switching is often ineffective. Each lane change creates a small disturbance that other drivers react to, which can accumulate and form traffic waves, making conditions worse overall.
Can maths help reduce traffic jams?
In my research on probabilistic mathematical methods, I explore strategies that combine prediction, decision-making, and feedback to stabilize complex systems, even with incomplete or noisy information.
In traffic, we aim to prevent stop-start waves that lead to phantom traffic jams. In other systems, these disturbances might manifest as power failures or communication bottlenecks.
Rather than crafting solutions for single issues, applied mathematicians create general frameworks that can be applied to various problems, including traffic. Each mathematical tool has a specific role:
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Signal processing converts data from road sensors and vehicles into useful information.
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Stochastic modelling accounts for uncertainties from driver behavior, weather, and traffic demand.
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Machine learning identifies patterns and predicts where congestion might occur.
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Control theory guides how traffic systems respond, adjusting lights, speeds, and routes.
The goal is not just to optimize one driver’s journey but to enhance the entire traffic network’s efficiency.
A significant example occurred in 2018 when researchers replicated the Japanese circular-track experiment with a twist: they introduced an autonomous car programmed for smooth acceleration and braking.
Amazingly, this single vehicle, less than 5% of the traffic, was sufficient to reduce the stop-start wave, enhancing traffic flow and cutting fuel consumption for all drivers.
Tips for your next car journey
Traffic congestion is likely to persist due to population growth, rising travel needs, and unpredictable human behavior.
However, mathematics is shifting the focus from reacting to avoiding congestion.
A key aspect is understanding how networks can make coordinated decisions using limited local information, without knowing the whole system’s state. These principles are vital for intelligent transport systems, where vehicles and infrastructure work together to ease traffic.
Before your next holiday drive, consider these three mathematically supported tips to reduce time in traffic:
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Keep a safe distance from the car ahead;
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Accelerate and brake smoothly;
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Avoid frequently changing lanes for small gains.
Applied mathematics reveals that reaching your destination quickly isn’t about aggressive driving but maintaining stability in the traffic system.
This article was originally published on The Conversation. Read the original article.
