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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…):
“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.
October 30, 2009
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