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December 28, 2014  |  Traffic wiz, traffic viz  |  6050 hit(s)

I found an interesting intersection recently of two things I think about a lot. One is traffic, a topic of perennial interest to me. The second is data visualizations, something that I'm comparatively new to but very interested in.

Let me back up slightly. Not long ago (maybe in 2013?), the state of Washington introduced variable speed limits in a some areas that are prone to congestion, like on I-5 northbound approaching Seattle:

[source, license, cropped slightly and reduced]

I was traveling with someone (my daughter, I think) who asked "Does that work?" To which my answer was that it could, if people actually obeyed these variable limits[1]. (Which they don't at all.) What's the theory?

On their website, the state explains variable speed limits this way:
Ideally, approaching traffic will slow down and pass through the problem area at a slower but more consistent speed reducing stop and go traffic. By reducing stop and go traffic we’re also reducing the probability of an accident by giving drivers more time to react to changing road conditions. This helps drivers avoid the need to brake sharply as they approach congestion.
Hmmm. This sort of describes the theory, but only in general terms. I also found the following on a different state site, which explains the theory even less, but does include a curious bonus reason (emphasis mine) for variable speed limits:
Variable speed limits offer considerable promise in restoring the credibility of speed limits and improving safety by restricting speeds during adverse conditions.
So let me give it a shot. Imagine that you want to go to the movies. You go to the ticket booth and buy tickets. Let's say that this transaction takes 30 seconds. Just as you finish, someone else walks up to buy their ticket. Just as they finish their 30-second transaction, a third person walks up, and so on. As long as people don't arrive at the ticket booth any more frequently than every 30 seconds, there's never a line.

But let's say that 15 seconds after you started buying your tickets, someone gets in line behind you. That person has to wait 15 seconds. And let's say people arrive at the ticket booth every 15 seconds from then on, but the ticket vender can't go any faster than one transcation per 30 seconds. The result is that the line grows, and it continues to grow as long as people arrive at the queue faster than they can buy tickets. The ticket booth is a bottleneck, and the queue is congestion.

Make sense? Congestion results from people being added to a queue (or otherwise approaching a bottleneck) faster than they can leave it. This is as true for people buying movie tickets as it is for cars approaching a slowdown. If you can prevent people from joining the queue faster than they can leave it, you can reduce the delay. If you're selling movie tickets, I don't know how you prevent people from getting in line. But if you're managing traffic, you can try to keep people out of the congestion by slowing down how fast they get to the point where the slowdown occurs.

Some people have understood this for a long time, and voluntarily slow down when it looks like traffic is heavy ahead. William Beaty has a great article (undated?) in which he dives deep on ways that even a few drivers who behave intelligently in congestion and during merges can improve flow for everyone. And while his suggestions undoubtedly work, they rely on people engaging in non-intuitive behavior, like allowing people to merge (gasp!) and leaving long-ish gaps ahead of them.

Since most people don't have the benefit of Beaty's insights, the state has decided to try variable speed limits: if people won't regulate their own speed in reaction to congestion ahead, the state (the state's computers) will attempt to do it for them.

This brings me to the visualization part of our story. Lewis Lehe is a graduate student in transportation engineering who's created a beautiful, interactive visualization that illustrates bottlenecks. (The viz is actually about the difference between bottlenecks, which I'm interested here, and gridlock.) Lehe's visualization shows cars arriving at and leaving a bottleneck, and you can adjust the arrival rate to see interactively how congestion grows if cars arrive faster than they can leave (or vice versa). Click the link and then play with the viz to get a great sense of how variable speed limits could work.

An interesting promise of self-driving cars, like the one apparently forthcoming from Google, is that they could be a whole lot smarter than human drivers about driving in congested conditions. Assuming, of course, that humans aren't allowed to take control of a car that's driving—per their own sense—exasperatingly slow. That remains to be seen.

[1] In fact, the minimum speed (perhaps by federal law?) is 40 MPH, so there's definitely a bottom limit to when variable speeds could be effective.