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January 9, 2007

Traffic and Anti-traffic, applying wave theory to bust traffic jams

Posted by: Brian — January 9, 2007 at 1:20 am

http://amasci.com/amateur/traffic/traffic1.html

I hate traffic.  In fact, I've renounced it.  My commute to work now is a 30-40 minute drive down quiet country roads.  If I find myself behind two cars, it's a heavy day.  I still have to deal with it now and again, but those times are fewer and farther between.   And yet I found the linked article really very interesting.  The premise is that most heavy traffic is essentially composed of traveling, standing or shock waves, and that by applying principles of physics and mathematics, those waves can be smoothed or eliminated.

The basic premise is that by simply refusing to "go with the flow" of traffic one can not only ease personal stress, but actually reduce or eliminate the traffic jam for those behind.  Instead of moving with the wave, accelerating when the wave expands and braking as it compresses, the author recommends finding the average speed of the wave and holding there.  It might be, no it will, be slower than the speed of the expansion, but it's also going to be faster than the speed of the compression.  Your constant speed will essentially eliminate the compression wave for you and any who choose to follow you.  Because compression waves make flow less efficient, eliminating the compression actually increases the capacity and efficiency of the medium.  In this case that means that the road can carry more cars more effiiciently.  Even though maximum speed has been redcued, AVERAGE speed is increased (which is arguably much more important because trip time is directly related to average speed, not isloated instances of maximum speed.) 

The other aspect of the article I found interesting was the concept of carrying "anti-traffic" into jams, though I'm not sure most physicists or mathematicians would actually approve of the term "anti-traffic" in this sense.  The idea here is to leave very long spaces in front of you.  We were all taught the "2 second rule", but for safety, not flow and since we've become more confident and arguably better drivers than we were at sixteen, we've largely allowed it to float away.  But there is, it seems, another very good reason for the two second rule and even larger spaces, namely that if you carry a large space into one of these unexpected compression waves, the space you bring allows the compression to dissipate before you arive, and if you don't have to slow dramatically when you arrive at the compression point, the wave can not propagate. 

This area of "anti-traffic" also allows for the free movement of traffic between lanes.  When someone changes lanes in front of you, now there is plenty of room and no need for braking, which could cause (or contribute to) a new compression wave.  It seems counter intuitive, but increasing the amount of empty space on a highway will actually increase capacity.

Now your first reaction to this might be the same as mine, which was "But if I leave a space, people will just butt in!"  And in lighter traffic, they probably will… there is nothing to inhibit agressive drivers from whipping around between lanes.  In heavier traffic though something interesting happens.  The agressive drivers immediately behind the car leaving space will try to pass, accelerate to the end of the open space and rejoin the wave.  Similarly, a few drivers from the adjoining lanes will do the same.  Eventually, however a pocket of drivers who are content to allow the negative space to exist forms around the space and the space can grow.  In some cases, drivers in neighboring lanes begin to (at least subconciously) join in the creation of negative space and the entire roadway has its compression wave countered.  What begins as one driver trying to even out his or her commute winds up easing the congestion for the entire highway.

 Anyway, the entire series of articles are a good read. 

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