Heading for a world-wide traffic jam

Some traffic jams have clear causes, such as an accident, road works, or an upcoming on-ramp. However, some traffic jams seem to occur for reason at all. Such phantom jams can even occur on completely visible roads at low speeds (see also the paper by Yuki Sugiyama et al., 2008 and their video). The script on this page (open script in separate tab) simulates traffic flow on a six-lane circular road. Cars are exactly the same in the way they accelerate and decelerate, but differ in the speed at which they want to travel. The script allows you to experiment to determine what causes phantom jams and how they can be dissolved. The controls for this script are explained at the bottom of the page.
The JavaScript on this page makes use of HTML5.

Going around in circles

The script on this page simulates cars that drive along a circular road while keeping a safe distance from other cars. Each simulated car has a preferred top speed that it will try to achieve. However, since some cars have a higher preferred speed than others, the fast driving cars will occasionally get too close to a car ahead, and will have to hit the brakes. In the simulation, cars always brake with the same intensity. This means that cars will sometimes brake more intensely than necessary, and drop its speed below the speed of the car ahead. Together with the small variation in the preferred top speed of cars, these effects can cause a ripple in the traffic flow that cause a phantom jam.

In addition to variations in speed and braking too intensely, the simulation has a number of other features that can make phantom jams worse. Firstly, cars that have stopped moving will not pull up immediately when the car ahead of them starts moving. Instead, cars wait a little while until the distance is large enough. Additionally, when cars want to accelerate but cannot because of a car ahead of them, they may decide to change lanes. Although a car can help to clear up a phantom jam in a lane by changing to another lane, changing lanes can cause another jam in the lane they are entering.

The script above has a graph that allows you to keep track of phantom jams by plotting the percentage of jammed cars, which are cars that have come to a complete halt, and the average speed of cars. The average speed of cars is plotted as a percentage of the speed at which these cars prefer to drive. By running the script, you will find that phantom jams can occur for a lot of different settings of the sliders. But are there ways to prevent phantom jams, or to dissolve them after they have already happened? For example, does it help to lower the speed limit, or to force cars to stay in their lanes? And what can drivers do themselves to avoid and solve phantom jams? Are the solutions that avoid phantom jams the same as those that avoid these jams?

Controls

• Summary graph: After every change in the situation on the road, the graph updates to show the new percentage of jammed cars, which are currently standing still, and the average speed of cars, as a percentage of their top speed.
• Car count slider: This determines the number of cars on the road, with a range of 75 to 175 cars.
• Average top speed slider: This slider determines the preferred driving speed or top speed of cars. The value represented by this slider is the average top speed across all cars. That is, individual cars differ in their actual top speed.
• Variation top speed slider: This slider determines the range of individual variation in the top speed of cars. More variation means that faster cars more often have to brake due to slower cars ahead.
• Acceleration slider: This slider determines how quickly cars accelerate to their top speed.
• Preferred deceleration slider: This slider determines at what speed cars prefer to brake. A lower value of the preferred deceleration means that cars that encounter a slower car ahead will be faster to brake and bring their own speed down more gradually. A higher value means that cars tend to brake more abruptly.
• Lane changing slider: This slider determines the likelihood that a car will change lanes. A car will only consider changing lanes when it is prevented from accelerating because of a car ahead.
• Zoom slider: This slider controls the magnification of the road.
• Simulation speed slider: This shows how quickly time passes on the road.
• Reset field: Resets the cars by spreading them out approximately equally across the tarmac.
• Road: By double-clicking the road, you can switch representations of the road. In the more schematic representation with white cars, you can additionally select a car to follow its behaviour more easily.

The sprites for this script have been adapted from the sprites of the 1999 computer game Grand Theft Auto 2 by Rockstar Games.