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Autonomous Cars and Mathematical Traffic Models Could Improve Driving Fluidity

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【Summary】Autonomous cars can improve traffic flow by applying specific mathematical models that reduce road congestion. One of these solutions is called queuing model, which is used to predict waiting times and length of lines. Various principles, such as First-in-First-Out (FIFO), Last-in-First-Out (LIFO) and Priority, are applicable in queuing models.

Michael Cheng    Nov 15, 2016 5:52 AM PT

Human drivers are not efficient in maintaining traffic flow, which is why public roads are highly prone to congestion. According to Lorna Wilson from CityMetric, basic mathematical models can be applied to ensure cars don't contribute to bottlenecks while driving (also known as "phantom traffic jams"). For example, keeping vehicles moving within variable speed limits, would boost consistency on the road.

Unfortunately, such driving methods are extremely difficult to apply with traditional cars.

This is because humans are often quick to step on the gas when the traffic light turns green (or when there aren't any cars around) and react wildly to other cars on the road by tapping or aggressively stomping on the brakes. This widespread method of driving actually increases fuel consumption and results in longer traveling times. External factors, including heightened emotions and mental fatigue, negatively impacts traffic flow because it causes drivers to make bad decisions behind the wheel – especially during morning and afternoon peak periods.

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Mathematical Models

Autonomous cars can improve traffic flow by applying specific mathematical models that reduce road congestion. One of these solutions is called queuing model, which is used to predict waiting times and length of lines. Various principles, such as First-in-First-Out (FIFO), Last-in-First-Out (LIFO) and Priority, are applicable in queuing models. For more complex traffic scenarios, a grid model may be applied. This solution incorporates grouping cars in grids with specific rules or criteria that must be met before the vehicle can move to the next grid cell.

"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," said Wilson.

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Reducing Randomness

Human drivers are the main culprits when it comes to contributing to traffic jams. In order to improve road conditions, random or external factors must be greatly reduced. The rise of autonomous vehicles is the solution to this global issue. They will drive at regular speeds, regardless if you're running late or had a rough day at the office. Even after being on the road all day, driverless cars will always perform in the same manner and will not engage in actions outside of its developed features.

On the road, cooperative behavior decreases traffic. While driverless cars are clearly a solution to this concern, they can also be the problem. As clarified earlier, there are several mathematical models that can be applied to improving fluidity. Car manufacturers may have different algorithms in their controlling software to achieve such goals. With multiple traffic-reducing models being applied on the road, reaching full optimization could be difficult.

"Some car makers expect that eventually we will stop viewing cars as possessions and instead simply treat them as a transport service," explained Wilson. "Again, by applying mathematical techniques and modelling, we could optimise how this shared autonomous vehicle service could operate most efficiently, reducing the overall number of cars on the road."

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