Variable Speed Limits: An Informative Piece

I wanted to write a post on Variable Speed Limits or (VSL) because I feel that they can be used to effectively reduce traffic on freeways. So to start off;

• What are Variable Speed Limits?
• They are speed limit signs that can change. Instead of having a posted speed limit on a metal sign that never changes, VSL sign's are able to change to based on current road conditions either weather or traffic conditions.
• Are they Effective?
• VSL have been shown to not only reduce travel times in congested traffic¹ , but also to increase safety on the road ways².
  

Variable Speed Limits can be very useful for reducing congestion or implementing safer speed limits based on weather conditions. When traffic comes to a halt in one location on the freeway (due to an accident or just a general slow down) it's possible to have cars continually braking back upstream. The transition of these stopped cars to the braking cars can be considered to be a wave moving. Similar to how domino's fall, where the upright dominoes representing the moving cars, and the knocked over dominoes representing the stopped cars, there is a transition zone that moves along the freeway. The speed of this "wave" has been shown to travel as fast as 8-10 mph. The speed of the wave ultimately depends on the density of cars per mile. The density of cars can again be related to dominoes. The closer the dominoes are placed together, the wave of them being knocked down travels faster. If the dominoes are spaced further apart, the wave knocking them down travels slower³. Essentially, the dominoes has to fall for a smaller amount of time before it transfers it's energy to the next dominoes.
Similarly, spacing between cars has an effect on the backward traveling wave. A higher density of cars, or stated another way; cars close together, continue to have cars stop quickly for slowing cars. For cars that are more spaced out, a wave does not travel as quickly to cars upstream.
By adjusting the speed limit upstream of the slow down, can reduce the number of people entering the jam. This helps decrease density, which helps with dispersing the wave. Optimizing the upstream speed to just the right value can essentially dissolve the wave moving upstream. These changes in speed would remain until the traffic improves to free flow conditions.
There has been two main approaches to finding how to calculate the speed of the Variable speed limit signs. One approach is to try to make the local speed of the highway uniform. Basically, looking at an average of the speed way over a few miles ahead, and a few miles behind the current location. This aims to reach 1 overall speed limit that all cars ad hear to. This method however tends to reduce travel time, by imposing speed limits that are much lower than normal, and does not seam to improve safety. The second method tries to prevent the highway from becoming too congested and over populated. This method of reducing density has been shown to be more efficient⁴.
I really feel Variable Speed Limit signs are great, because they are dynamic to the current road conditions. Rather then having a static sign posting 65 mph, even when the highway does not support such speeds, it can help future traffic utilize the full capacity of the highway.⁵

So implementation of VSL seams like a good idea, but it not widely used, especially in the US. This is most likely due to two reasons, besides obvious money and time constraints.

1. Drivers need to know about VSL. They need to know that the speed of the freeway can change. This was alot of the motivation for this post.
   
2. Even if drivers do know how VSL works, they still must remember the new speed limit. Changing the speed limit of a freeway, normally to be found with a speed of 65 mph, can be a little difficult to become acclimated to, as well as remembering the new speed limit for the time being⁶.
   

Well I hope this clarifies what Variable Speed Limit's are and that you too become a proponent of using them!

Update: Implementation in Seattle and it's effects: http://www.howwedrive.com/2010/09/16/traffic-and-algorithms-in-seattle/

notes

¹ P.Breton, A. Hegyi, B. De Schutter, and H. Hellendoorn, "Shock wave
elimination/reduction by optimal coordination of variable speed
limits," Proceedings of the IEEE 5th international conference on
intelligent Transportation Systems (ITSC'02), Singapore, pp. 225-230,
Sept. 2002

² Chris Lee, Bruce Hellinga, Frank Saccomanno, "Evaluation of Variable speed limits to improve traffic saftey", Transportation Research Part C 14 (2006) 213-228

³ Falling Dominoes: Problem 71-19, by B. G. McLachlan, G. Beaupre, A. B. Cox and L. Gore SIAM Review © 1983 Society for Industrial and Applied Mathematics.

⁴ P.Breton, A. Hegyi, B. De Schutter, and H. Hellendoorn, "Shock wave
elimination/reduction by optimal coordination of variable speed
limits," Proceedings of the IEEE 5th international conference on
intelligent Transportation Systems (ITSC'02), Singapore, pp. 225-230,
Sept. 2002

⁵ As a side note: It can also be seen as cars are the thief of roadway, where each car try's to consume as much roadway as possible. Since most drivers are selfish, they try to consume every piece of roadway available. VSL put a limitation on this robbery, and restrict these cars from only consuming so much roadway per hour.

⁶ Juha Luoma and Pirkko Rama, "Effects of variable speed limit signs on speed behavior and recall of signs", Traffic Engineering + Control pp. 234-237