Mike the Mad Biologist

humorous pictures

One of the enduring mysteries of Boston’s transit system is why is the Red Line always fouled up. I can understand why the Green Line is squirrelly: parts of the Green Line run above ground and intersect with traffic, the above ground stops take much longer at the stations (to prevent people sneaking on without paying, only the front door of each car opens), and, inbound, there are four different Green Lines that merge into one. In other words, the Green Line is a guaranteed clusterfuck.

But the Red Line has none of these problems. So why is it almost always screwed up, even when it doesn’t break down? (equipment failure is a topic for a separate post–I’ve been following this and there are roughly two delays every day due to equipment failures).

Thank goodness WE HAZ TEH SCIENTISMZ!!

A recent article in PLoS ONE asks the question “Why Does Public Transport Not Arrive on Time?” Basically, the problem is that it is nearly impossible to maintain “equal headway”, which is when trains arrive at regular intervals (e.g., every five minutes, not four, then six):

….the configuration where the headways are equal is unstable. This is because of the following: if one vehicle is delayed, then there will be a shorter headway with the vehicle behind and a longer headway with the vehicle in front. Longer headways lead to more passengers waiting at stations, which lead to more delays. Also, shorter headways lead to less passengers waiting. Thus, vehicles moving behind a delayed vehicle will go faster than average. Even if a minimum waiting time at stations is established, during times of high passenger demand, slower vehicles will be reached by faster ones. After some time, several vehicles will be “platooning”, i.e. traveling together. This makes the service inefficient, since people need to wait more time for a platoon to arrive than if the vehicles were equally spaced in time. Moreover, when a platoon arrives at a station, there will be much more people waiting, delaying the platoon flow….

The problem of having an equal headway instability is that it makes transport inefficient. Many vehicles are used below their capacity and adding more vehicles does not improve the situation, as they simply aggregate to platoons. This leads to large wastes of infrastructure and fuel. Moreover, from the passenger’s viewpoint, platoons of public transport cause greater delays and make travel less comfortable, as many passengers accumulate within few vehicles.

And there’s a figure that illustrates the problem (although if you regularly use the Red Line, you probably don’t need it…):

HeadwayDeviation.graffle
“A” is good, equal headway, B and C are not

Then the authors do some math and computer simulations, which I won’t repeat here. To solve this problem, you have to optimize two things:

1) The minimum station waiting time, which will keep a train at the station even if there are no passengers waiting. This prevents faster trains from stacking up behind slower ones (typically, the first train in a ‘stack’ travels slowly because it is overcrowded as passengers, tired of waiting for a train, all cram into the first one).

2) The minimum station waiting time, which means a train must leave a station after a certain amount of time, even if people want to get onto the train. This prevents the ‘stack of trains’ from forming in the first place.

The optimization of these two parameter leads to the “adaptive maximum model” which restores equal headway, but can adjust to varying amount of people. Based on this model, the authors recommend (italics mine):

For passengers:

•If a crowded vehicle arrives at a station after a long waiting time, it is very probable that empty vehicles are coming close behind. Do not board the crowded vehicle, contributing to its further delay and of all the passengers within. If even some people follow this advice, it is likely that crowded vehicles will be able to go relatively faster, allowing the vehicles behind them also to go faster, improving the performance of the whole system. Waiting at the station for another vehicle might actually contribute to a faster trip. [Mad Biologist: On the T, they always try this. Nobody ever listens]

•Give way to people descending a vehicle before boarding. Trying to “win” and enter before others will delay everybody. Sometimes waiting for a second or a third vehicle is faster than attempting to board a crowded one (especially in transport systems that allow passing).

•Inside a crowded vehicle, go far from the doors. Giving space to ascending and descending people will accelerate the travel. Make way to the doors not too long before exiting.

For engineers:

•It makes little sense to add vehicles if these are not regulated to maintain an equal headway.

•Design methods to regulate equal headways. This will improve considerably the system performance. The most common method is to have scheduled arrival and waiting times at stations, with margins for adjustment along the route and also at terminals.

•Educate passengers with publicity campaigns to promote equal headways. In many cases these cannot be achieved because of passenger behavior. Explain to passengers the equal headway instability phenomenon, indicating that following certain norms will help them arrive earlier and more comfortably at their destination. Suggest recommendations as those outlined above, adapted to the local culture.

“Adapted to the local culture?” Obviously, the authors have never ridden the T. And that’s before one considers the tourists….

But the concept is quite sound.

Cited article: Gershenson C, Pineda LA, 2009 Why Does Public Transport Not Arrive on Time? The Pervasiveness of Equal Headway Instability. PLoS ONE 4(10): e7292. doi:10.1371/journal.pone.0007292

Comments

  1. #1 Rugosa
    October 30, 2009

    For this you need scientists?

    My current commute doesn’t involve the trains, but the same happens on the buses. It would help a great deal if passengers knew that the following bus would actually stop and pick them up. Too often, the following bus leapfrogs the first one, no matter how many people are at a stop. In this situation, it makes sense for passengers to cram on to the first bus because they don’t know if the second bus will actually stop. It doesn’t even out over the course of the route because passengers are clustered at certain stops – near the hospitals, for example.

  2. #2 llewelly
    October 30, 2009

    … (to prevent people sneaking on without paying, only the front door of each car opens) …

    Here Salt Lake City the trains just open all the doors. Nobody checks your ticket as you board, which saves time. However, about 1 trip in 20 (depending on the length of your trip), your car will be boarded by a security person, who will check everyone’s ticket while the train is in motion. If you don’t have a valid ticket, you get fined $120 (first offense).

  3. #3 Eric Lund
    October 30, 2009

    It doesn’t even out over the course of the route because passengers are clustered at certain stops

    Same goes with a rail-based transit system. There will always be more passengers at transfer points; for example, at Park Street the Red Line has to absorb not only the people who are starting there, but also passengers who started out on the Green Line and whose destinations are along the Red Line. The result is that a deviation from equal headway on one line can propagate to another line: if there happens to be a platoon of Green Line trains coming through, the pax load on the next Red Line train will be increased.

    The northbound Red Line also has the merging branch problem, though not as severe as what the Green Line has. Some Red Line trains originate at Ashmont, others at Braintree. The paths are of rather different lengths (Ashmont is well within Boston city limits, Braintree is well out into the ‘burbs), so I would expect problems north of the merge point. The westbound Green Line can smooth things out a bit because some of the trains originate at Government Center, but the instability is still there.

  4. #4 Hilary
    October 30, 2009

    “Let the passengers off the train first.”

    “Move right along the carriage, use all the available space.”

    “The train is being held briefly at this station and will be moving again shortly.”

    These are all standard announcements which regular passengers on the London Underground (aka Tube) hear every day. Almost without exception, Londoners observe the first rule instinctively and (usually American) tourists really get up our noses when they try to barge onto trains without first standing aside to let others off. Observance of the second rule is a bit patchier, but still fairly widespread.

    On the buses, you’ll sometimes get “The bus is being held briefly at this stop in order to regulate the flow” so passengers can understand the logic of not moving off immediately even though they can see there’s no traffic in the way.

    I’m surprised these simple messages are news to other transport services.

  5. #5 Tony P
    October 30, 2009

    I rode the southbound Red Line to Braintree for four months. Only one incident that I can recall. Otherwise it was smooth sailing, especially coming home at night, those cars were speeding along the track.

    But I know the Ashmont service was always packed. In the mornings I’d be standing in South Station and could see the crowds on the platform waiting for the Red Line into that area.

    Very little goes to Braintree.

  6. #6 Jim Thomerson
    October 30, 2009

    I think only occasionally checking for tickets is common in Europe. The trains in England had a sign which said if you were caught without a ticket, people would look at you. I did not understand why this would deter. I always bought a ticket, except once in Berlin, when I did not have change.

  7. #7 Carlos Gershenson
    October 30, 2009

    For the record, I lived in Boston for 18 months, so I suffered from delays on the Red Line… the MBTA “solution” is mentioned in the paper…

  8. #8 Jen
    October 30, 2009

    I ride the Green E, though I am only there for 2 days or so every 4-6 weeks. Even with that, I’d say about half the time, getting on at Museum of Fine Art, I’ve gotten a free ride at night. Perhaps, had I been made to pay, I would think about waiting for the next one or two, since at this time, I really have no worries about getting anywhere at any time. If I had to pay, I would definitely choose getting a seat, or at least not being squished up against a drunken Northeastern student (I ride on Friday nights).

  9. #9 Julie Stahlhut
    October 31, 2009

    I lived in the Boston area for 17 years, and remember the Red Line exactly as you described it. In fact, the Mass. Ave. bus line behaved in much the same way. One night, a combustible mix of a bus backlog, a crowd of passengers who might by that time have been envying canned sardines their defensible space, and a bad-tempered driver resulted in a friend of mine (who was on crutches at the time after recent knee surgery!) getting hit in the face with a bus door by the driver for no discernible reason. My startled friend hauled off and punched the bus door so hard he broke the glass. The driver was prevented from retaliating by the rest of us at the bus stop, since we all managed to remain calm, surround the driver, describe in detail how we’d witnessed his hitting a guy on crutches with the bus door, and note that several of us had recorded his badge number.

    Just another night on greater Boston public transport ….

  10. #10 Min
    October 31, 2009

    Japanese subways and trains run on time. Here is an opportunity for a little cross-cultural research. :)

  11. #11 sue
    November 2, 2009

    I live in the Los Angeles area. My family visited Boston last year, I just loved the public transport there – my son and I went everywhere, and our fellow commuters were always helpful.

    I’m green with envy…. riding convenient, albeit crowded, mass transit beats sitting in traffic on the 405 fwy any day.

  12. #12 Kaleberg
    November 4, 2009

    They used to call this the bus clumping problem. You don’t really need much in the way of reinforcement, just Poisson noise.

    Good luck getting more cooperative passengers in Boston. I lived in Boston for years, and Bostonians are the nastiest people you are likely to run into. The New York subway always seemed rather mellow, even during rush hour. It might have been just as crowded, but the people were calmer and nicer.

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