Saturday, May 26, 2012

Does the Downs-Thomson Paradox apply in Boston?

While looking at some Google Map directions I started thinking about the "in current traffic" time projections offered along with the turn-by-turn steps.  Could these be gathered and statistically analyzed in a coherent way? And if so, could they be used to study the Downs-Thomson Paradox as it may apply to commuting travel in Boston? From Wikipedia:
[The] equilibrium speed of car traffic on the road network is determined by the average door-to-door speed of equivalent journeys by (rail-based or otherwise segregated) public transport.
It follows that increasing road capacity can actually make overall congestion on the road worse. This occurs when the shift from public transport causes a disinvestment in the mode such that the operator either reduces frequency of service or raises fares to cover costs. This shifts additional passengers into cars. Ultimately the system may be eliminated and congestion on the original (expanded) road is worse than before.
In other words, when there is a highway competing with a separate public transit way, the congestion on the highway builds up until the average travel time matches the trip time on public transit. If the highway gets worse, then commuters shift onto public transit. If the highway gets better, then they shift back into cars.

There are plenty of caveats to this equilibrium. For one thing, there needs to be adequate, well-patronized public transportation available. It needs to be separate from the roadways so that effects of automobile traffic congestion do not interfere with its operation. There is also an assumption that the cost of driving (and parking) is within reach of enough commuters to make a difference. And there could be many peculiarities of geography or design which tilt the balance.

For the design of this study I chose 8 points of interest near Commuter Rail stations in the Greater Boston region. I mapped out travel directions to a selected point in the Financial District, and gathered travel times at 4 moments in the morning rush hour: 7:00am, 7:30am, 8:00am and 8:30am. So far, this data has been collected over the course of two weeks, but is continuing. I then analyzed the schedules for those Commuter Rail stations and came up with the equivalent public transportation trip times to the same location downtown. I added average lateness (or earliness) to each trip based on my real-time Commuter Rail data set.

All of the charts presented show travel times in minutes as measured over the course of the morning peak period, from approximately 6am to 9am.

The above 6 charts show a convergence between driving time (in red) and public transit time (in blue). Middleborough and Kingston are part of the "Old Colony" expansion. Attleboro is on the Providence line, Forge Park is the end of the Franklin line. Both Salem and Lowell are on the north side, which means that their trip via public transit includes a transfer at North Station to the Orange line. Salem in particular receives very good service in the morning, because it sits at the junction of Newburyport and Rockport branches. As a result of that, and also the relative inconvenience of driving, it has a high ridership, despite requiring the transfer at North Station. In Feb 2009 the MBTA estimated that 2,010 people board at Salem station every workday on their way to Boston; only a few stations on the Providence line have better numbers.

These 4 charts show cases where there doesn't seem to be an equivalence between driving and public transportation times. Each of these four examples is dysfunctional in its own way. The Fitchburg line is currently undergoing heavy renovation that will be finished soon: that will speed up journey times by 20 minutes -- bringing it into line with traffic and hopefully adding later trains as well. Framingham trains almost achieve parity with traffic: it too will see some improvements in upcoming years when CSX Beacon Park closes and that portion is double-tracked. Needham Heights is an odd case because the Needham line actually turns sharply and nearly backtracks to get there. That adds a good 10 minutes to the travel time which is simply out-of-the-way. But that's why I included it, to see what effect that might have. Finally, Lawrence is very close to the New Hampshire state line and suffers from an excess of single-tracking which is supposed to be partially fixed as part of a stimulus project.

I can think of a few criticisms of this highly unscientific study. The Google-based traffic data has the problem of being dependent on a hidden prediction model. Is it reasonably accurate? I've heard reports that it may be slightly optimistic, but I don't have the resources to go and gather my own data. Other problems include the assumption of downtown commutes -- obviously there is more than one job center in Boston -- although the Commuter Rail does serve that market best. There's some loose ends regarding parking and other costs, too. I picked a destination near some downtown garages, but I don't have any figures on how long it takes to navigate inside of the garages to a final parking space -- or whether that's even important, psychologically. It's generally accepted that taking the commuter rail is cheaper than driving, but how much exactly depends on many specifics. That cost may also cause commuters to choose one mode over another, but it may not be enough to overcome the equilibrium effect caused by traffic congestion.

Still, the initial results do seem to indicate that, at peak congestion, the average travel time of driving to work does tend to approach the equivalent public transit trip time, and that may mean that the Downs-Thomson Paradox does apply here in Boston. This has ominous implications when considering the effect of service cuts and other proposed cost "saving" measures: they may in fact make things worse in the overall economic picture.

(also see: Rapid Transit)


  1. Oh, this is great! It is also a microcosmic example of something I've been thinking about for the past couple of weeks, namely, building a database of Google's "in current traffic" estimates. This would not only paint a much-needed picture of when traffic gets bad where, but also show how variable it is. For instance, I was driving 93 north of the city (northbound, thank goodness) and it was jammed at 10 a.m. How frequent is this?

    And how much variability is there in traffic? It might be the case that transit, on average, takes a bit longer than driving, but driving has many more outliers (i.e. a longer tail) from accidents, weather, or the random traffic jam from hell. (And yes, I know the train is sometimes late, too.)

    Anyway, love the idea. Are you pulling these data by hand, or have you written a script to grab it? It seems that it would be pretty simple (load source code, find the string "in current traffic" and grab the number after that). Any interest in expanding this?

    1. It's basically a script as you describe. I have a set of saved Google directions which it checks with a cron job. I can add additional entries easily, which I did for the second part of this article, but it's not terribly comprehensive.

      There probably is a database out there of traffic data over time, maybe measured in expected minutes of delay per road. Google offers a layer which summarizes the current state, but I didn't see anything historical. Still, knowing them, they probably save everything.

      In terms of variability, there's a bunch of factors which are difficult to account for, and I suspect most folks just go by 'feel' anyhow. For example, besides traffic, there may be different results depending upon exactly where your home is, presuming you don't live at the train station. And the exact amount of time it takes for you to park your car and walk to your actual workplace is very specific. But I don't think people spend a lot of time thinking about those things, they just go with whatever seems to be the fastest. Maybe they value driving so much they don't care it's slower, or maybe they value working on the train they don't care it takes longer, or maybe the cost of one option is too much to consider. Anyway, it's a highly 'unscientific' study, so I'm just hoping that those effects cancel each other out a bit in the larger picture.