Tag Archives: headways

Thinking Big? Let’s Think “Realistic” First

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The MBTA’s Fiscal and Management Control Board, according to their slides, wants to “think big.”

Thinking big is a laudable goal. The only problem is that big thinking requires feasibility, and it is a waste of everyone’s time and energy if the big thinking is completely outside the realm of what can reasonably occur or be built.

Case in point: combining Park Street and Downtown Crossing into one “superstation.” The first reason this won’t happen is that it doesn’t need to happen: with the concourse above the Red Line between the two stations, they are already one complex. (#Protip: it’s faster to transfer between the Red Line at Park and the Winter Street platform on the Orange Line—trains towards Forest Hills for the less anachronistic among us—by walking swiftly down the concourse rather than getting on the train at Downtown Crossing.) But there are several other reasons why this is just not possible.

Tangent track

To build a new station between Park Street and Downtown Crossing would require tangent, or straight, track. If you stand at Park, however, you can’t see Downtown Crossing, because the tracks, which are separated for the center platform at Park, curve back together for the side platforms at Downtown Crossing. This curve is likely too severe to provide level boarding, so the track would have to be realigned through this segment. So even if it were  easy to build a new complex here, the tracks would have to somehow be rebuilt without disrupting normal service. That’s not easy.

Winter Street is narrow. Really narrow.

The next, and related, point: Winter Street is very narrow: only about 35 feet between buildings. Park Street Station is located under the Common, and the Red Line station at Downtown Crossing is located under a much wider portion of Summer Street: those locations have room for platforms. Winter Street does not. Two Red Line tracks require about 24 feet of real estate: this would leave 5.5 feet for platforms on either side before accounting for any vertical circulation, utilities and the like. Any more than that and you’re digging underneath the century-old buildings which give the area its character. That’s not about to happen. And Winter Street would be the only logical location for the station; otherwise it would force long walks for transferring passengers.

Summer Street (foreground) is wide.
Winter Street (background) is narrow.
The fact that so many streets change names crossing Washington?
Well, that’s just confusing.

Note the photograph to the right. The current Downtown Crossing station is located between Jordan Marsh on the left and Filene’s on the right (for newer arrivals: the Macy’s and the Millenium building), where Summer Street is about 60 feet wide, enough for two tracks and platforms, and it’s still constrained, with entrances in the Filene’s and Jordan Marsh buildings. Note in the background how much narrower Winter Street is. This isn’t an optical illusion: it’s only half as wide. The only feasible location for such a superstation would be between the Orange and Green lines, but the street there is far too narrow.

Passenger operations

The idea behind combining Downtown Crossing and Park Street is that it would simplify signaling and allow better throughput on the line operationally. But any savings from operations would likely be eaten by increased dwell times at these stations. At most stations, the T operations are abysmal regarding dwell times; Chicago L trains, for example, rarely spend as much time in stations as MBTA trains do, as the operator will engage the door close button as soon as the doors open. At Park and Downtown Crossing, however, this is not the case. Long dwell times there occur because of the crowding: at each station, hundreds of passengers have to exit the train, often onto a platform with as many waiting to board. This is rather unique to the T, and the Red Line in particular, which, between South Station and Kendall, is at capacity in both directions. Trying to unload and then load nearly an entire train worth of passengers at one station, even with more wider doors on new cars, just doesn’t make sense.

If Park and Downtown Crossing were little-used stations, it would make no sense to have two platforms 500 feet apart, and combining them, or just closing one, would be sensible. (Unlike New York and Chicago, the Boston Elevated Railway never built stations so close that consolidation was necessary.) But they are two of the busiest stations in the MBTA system, both for boardings and for transfers. Given the geometry of the area, both above and below ground, calling this a big idea is risible. Big ideas have to, at least, be somewhere in the realm of reality. Without a 1960s-style wholesale demolition of half of Downtown Boston, this is a distraction. The FMCB has a lot to do: they should not spend time chasing unicorns.

Better Headways? Geometry gets in the way, not just signals.

In addition to a spending time on infeasible ideas like combining Park and Downtown Crossing, the FMCB and T operations claims that it would only take a minor signal upgrade (well, okay, any signal upgrade wouldn’t be minor) to allow three minute headways on the Red Line. Right now, trains come every 4 to 4.5 minutes at rush hour (8 to 9 minutes each from Braintree and Ashmont); so this would be a 50% increase. Three minute headways are certainly a good idea, but the Red Line especially has several bottlenecks which would have to be significantly upgraded before headways can progress much below their current levels. New signals would certainly help operations, but they are not the current rate limiting factor for throughput on the line.

There are four site-specific major bottlenecks on the line beyond signaling: the interlocking north of JFK-UMass (a.k.a. Malfunction Junction), the Park-Downtown Crossing complex, the Harvard curve, and the Alewife terminal. (In addition, the line’s profile, which has a bi-directional peak along its busiest portion, results in long dwell times at many stations.) Each of these is it’s own flavor of bottleneck, and it may be informative to look at them as examples of how retrofitting a century-old railroad is easier said than done. This is not to say that a new signaling system shouldn’t be installed: it absolutely should! It just won’t allow for three minute headways without several other projects as well. From south to north:

JFK-UMass

This is likely the easiest of the bottlenecks to fix: it’s simply an interlocking which needs to be replaced. While the moniker Malfunction Junction may not be entirely deserved (the Red Line manages to break down for many other reasons), it is an inefficient network of special track work which dates to the early 1970s and could certainly use an upgrade. In fact, it probably would be replaced, or significantly improved, with the installation of a new signal system.

Park/Downtown

Right now, Park and Downtown Crossing cause delays because of both signaling and passenger loads. For instance, a train exchanging passengers at Downtown Crossing causes restricted signals back to Charles, so that it is not possible for trains to load and unload passengers simultaneously at Park and Downtown Crossing. Given the passenger loads at these stations and long dwell times at busy times of day, it takes three or four minutes for a train to traverse the segment between the tunnel portal at Charles and the departure from Downtown Crossing, which is the current rate-limiting factor for the line. If you ever watch trains on the Longfellow from above (and my new office allows for that, so, yeah, I’m real productive at work), you can watch the signal system in action: trains are frequently bogged down on the bridge by signals at Park.

A new signal system with shorter blocks or, more likely, moving blocks would solve some of this problem. A good moving block system would have to allow three trains to simultaneously stop at Park, Downtown Crossing and South Station. So this would be solved, right? Well, not exactly. Dwell times are still long at all three of these stations: as they are among the most heavily-used in the system. Delivering reliable three-minute headways would help with capacity, but longer headways would lead to cascading delays if trains were overcrowded. There’s not much margin for error when trains are this close together. Given the narrow, crowded stairs and platforms at Park and Downtown crossing, the limiting factor here is probably passenger flow: it might be hard to clear everyone from the platforms in the time between dwells. And it is not cheap to try to widen platforms and egress. A new signaling system would help, but this still may be a factor in delivering three minute headways.

The Harvard Curve and dwell times

Moving north, the situation doesn’t get any easier to remedy. When the Red Line was extended past Harvard, the President and Fellows of Harvard College would not allow the T to tunnel under the Yard, so the T was forced to stay in the alignment of Mass Ave. This required the curve just south of the station, which is limited (and will always be limited) to 10 miles per hour. The curve itself is about 400 feet long, but if any portion of the train (also about 400 feet long) is in the curve, it is required to remain at this restricted speed. So the train has to operate for 800 feet at 10 mph, which takes about 55 seconds to operate this segment alone. Given that with Harvard’s crowds, it has longer dwell times due to passenger flow, traversing the 800 feet of track within the station and tunnel beyond takes more than two minutes under the best of circumstances.

Would signaling help? Maybe somewhat, but not much. Even a moving block signal system would not likely allow a train to occupy the Harvard Platform with another train still in the curve. Chicago has 25 mph curves on the Blue Line approaching Clark/Lake and operates three minute headways, but they also frequently bypass signals to pull trains within feet of each other to stage them, something the T would likely be reticent to do. It may be possible to operate these headways but with basically zero margin for error. Any delay, even small issues beyond the control of the agency, would quickly cascade, eating up any gains made from running trains more frequently. This is a question of geometry more than anything else: if trains could arrive and leave Harvard at speed, it wouldn’t be an issue. But combining the dwell time and the curve, nearly the entire headway is used up just getting through the station.

Alewife

The three issues above? They pale in comparison to Alewife. Why? Because Alewife was never designed to be a terminal station. (Thanks, Arlington.) The original plan was to extend the Red Line to 128, with a later plan to bring it to Arlington Heights. But these plans were opposed by the good people of Arlington, and the terminal wound up at Alewife. The issues is that the crossover, which allows trains to switch tracks at the end of the line, didn’t. It wound up north of Russell Field, along a short portion of tangent track between the Fitchburg Cutoff right-of-way and the Alewife station, and about 900 feet from the end of the platform. If a train uses the northbound platform, it can run in to the station at track speed (25 mph, taking 50 seconds), unload and load at the platform, and allow operators to change ends (with drop back crews, this can take 60 seconds), and then pull out 900 feet (25 mph, taking 30 seconds) and run through the crossover at 10 mph (45 seconds). That cycle takes 185 seconds, or just about three minutes, of which about a minute is spent traversing the extra distance in and out of the station. If the train is crossing over from one track to the other would foul the interlocking, causing approaching trains to back up. And since this is at the end of the line, there’s significant variability to headways coming in to the station, so trains are frequently delayed between Alewife and Davis waiting for tracks to clear.

Without going in to too much detail, the MBTA currently has a minimum target of about 4 minute headways coming out of Alewife. Without rebuilding the interlocking—and there’s nowhere to do this, because it’s the only tangent portion of track, and interlockings basically have to be built on tangent track—there’s no way to get to three minute headways. In addition, the T is in the enviable position of having strong bidirectional ridership on the Red Line. In many cities, ridership is unbalanced: Chicago, for example, runs three minute headways on their Red Line from Howard at peak, but six minutes in the opposite direction from 95th (this results in a lot of “deadheading” where operators are paid to ride back on trains to get back to where they came from). The T needs as many trains as it can run in both directions, so it has to turn everything at Alewife (never mind the fact that there’s no yard beyond; we’ll get to that). This also means that T has to run better-than-5-minute headways until 10 a.m. and 8 p.m. to accommodate both directions of ridership. While this means short wait times for customers, it incurs extra operational costs, since these trains provide more service than capacity likely requires and, for instance, we don’t need a train leaving Alewife every four minutes at 9:30, except we have to put the trains somewhere back south.

In the long run, to add service, Alewife is probably unworkable. But there is a solution, I think. The tail tracks extend out under Route 2 and to Thorndike Field in Arlington. The field itself is almost exactly the size of Codman Yard in Dorchester. Assuming there aren’t any major utilities, the field could be dug up, an underground yard could be built with a new three-track, two-platform station adjacent to the field (providing better access for the many pedestrians who walk from Arlington, with Alewife still serving as the bus transfer and park-and-ride), a run-through loop track, and a storage yard. I have a very rough sketch of this in Google Maps here.

Assuming you could appease local population and 4(f) park regulations, the main issue is that field itself is quite low in elevation—any facility would be below sea level and certainly below the water table. But if this could be mitigated, it would be perhaps the only feasible way to add a yard to the north end of the Red Line. And it is possible that a yard in Arlington, coupled with some expansion of Codman (which has room for several more tracks) could eliminate the need for the yard facility at Cabot Yard in Boston, which is a long deadhead move from JFK/UMass station. While the shops would still be needed the yard, which sits on six acres of real estate a ten minute walk on Dot Ave from Broadway and South Station, could fetch a premium on the current real estate market.

This wouldn’t be free, and would take some convincing for those same folks in Arlington, but operationally, it would certainly make the Red Line easier to run. Upgrades to signals and equipment will help, but if you don’t fix Alewife, you have no chance of running more trains.

Overall, I’m not trying to be negative here, I’m just trying to ground ideas in realism. It’s fun to think of ways to improve the transit system, but far too often it seems that both advocates and agencies go too far down the road looking in to ideas which have no chance of actually happening. We have an old system with good bones, but those bones are sometimes crooked. When we come up with new ideas for transit and mobility, we need to take a step back and make sure they’ll work before we go too much further.

Today’s glossary:

  • Deadhead: running out of service without passengers. All the cost of running a train (or, if an operator is riding an in-service train, all the costs of paying them), none of the benefits.
  • Headway: the time between train arrivals
  • Tangent track: straight track

Editor’s note: after a busy first half of the semester, I have some more time on my hands and should be posting more than once every two months!

Where could the MBTA implement unscheduled short turns?

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I recently wrote about short turning a bus on the EZRide Shuttle route. People will ask: “why doesn’t the T do this, my bus is always bunched?!” The answer is a) it’s not easy to do, b) they are way too understaffed to do so, and c) their schedules are so much more complex that there are many more moving parts. At rush hours, the T has four dispatchers watching 100 buses; my office has one or two watching nine (although it’s not our only job, sometimes it demands full attention). The need for short turns arises at times when there is heavy traffic and ridership. At those times, it’s all the dispatchers can do at that time to keep some semblance of order among the 250 buses they’re watching, not turn their attention to one particular part of one single route.

And also: there are only so many places and times you can successfully execute a short turn. Our route has a lot of twists and turns which make it easy for a bus to take a right instead of a left and go from outbound to inbound, but often a short turn may require a bus to go around a narrow block in traffic, and you certainly don’t want a bus getting stuck on a narrow corner where it doesn’t belong. There are more issues with the T: we know our drivers are on one route and that their shifts end around the same time. I’ve actually had times where a driver couldn’t cover an extra run because he or she had to be at another job; this is more frequent at the T where shifts start and end in a very complex scheme and at all hours of the day; a driver might finish one trip and set out on a different route, so a short turn would find them far away from where they needed to be. And finally, the T has thousands of drivers, so there is no way for a dispatcher to know whether a driver is familiar with the route and where to make a turn, or whether it’s his first day in the district and he or she is following the route for the first time.

Trains? Buses are much easier than trains. Trains require operators to change ends, change tracks—often at unpowered switches—and obtain a ton of clearance to do so, especially on the older sections of the MBTA system which don’t have the kind of new bi-directional signaling systems that, say, the DC Metro has. If the T had pocket tracks in the right places, it might be easier. But without them short turns would only save time in a few circumstances and a few areas.

And on a train you’re dealing with even more passengers. I’ve been on trains expressed from Newton Highlands to Riverside. Even with half a dozen announcements, a couple of stray passengers won’t pay attention (buried in their phone, perhaps) and then wonder why the train is speeding past Waban. I’ve heard of crews at Brigham Circle, after switch the train from one side to the other, walking through the car rousing passengers who are on another planet (or just staring at their phones). If you can’t run a short turn expediently, it’s not worth doing at all.

That being said, I have a couple of thoughts on routes which could benefit from more active management and, perhaps, some short turns. Both are frequent “key” routes, both experience frequent bunching, and both carry their heaviest loads in the middle of the routes, so that the passengers from a mostly empty bus in the trailing half of a pair could be transferred forwards without overcrowding the first bus. The are (drumroll please): the 1 and the 39. Let’s take a quick look:

Actual NextBus screen shot for the 1 bus.

1. The 1 Bus is one of the busiest routes in the system (combined with the CT1, the Mass Ave corridor has more riders than any other such route except the Washington Street Silver Line) and frequent headways of 8 minutes at rush hours. There is no peak direction for the route; it can be full at pretty much any time in any direction. And it is hopelessly impacted by crowding and traffic, such that bunching is almost normal, and on a bad day, three or even four 1 buses can come by in a row, with a subsequent service gap. (It could benefit, you know, from bus lanes and off-board fare collection, but those are beyond the purview of this post.)

But the 1 has a couple of features that make it a candidate for short turning. First of all, its highest ridership is in the middle of the route. The route runs from Dudley to Harvard, but the busiest section is between Boston Medical Center and Central Square. Going outbound (towards Harvard) many passengers get off at Central to transfer to the Red Line or other buses, inbound (towards Dudley), many passengers get off at Huntington Avenue and the Orange Line to make transfers. So here’s a relatively frequent scenario:

The black lines show the actual headways. The red
shows what could be accomplished by short-turning
one of the bunched buses at Central Square.

An outbound 1 bus gets slightly off headway, encounters heavy crowds, is filled up, and runs a few minutes behind schedule. Meanwhile, the bus behind encounters fewer passengers, spends less dwell time at stops, and catches the first bus. The first bus may have 60 passengers on board and the second 30. The buses remain full past MIT and pull in together to the stop at Central Square, where two thirds of the passengers disembark (and few get on: it’s faster to the the Red Line to Harvard or beyond). So now, the first bus has 20 passengers on board, and the second 10. In the mean time, since the first bus is behind schedule, there is now a 20 minute service gap: the first bus should have looped through Harvard by now, and if the buses proceed as a pair, the first bus will pull right through the loop and head out late and with a heavy load, and even if the second bus has a few minutes of recovery, it will quickly catch the first, and the process will repeat inbound.

You won’t be shocked by this, but I went to Nextbus, pulled up the map for the 1 bus, and at 10:15 p.m. on a weeknight, found this exact scenario. See the map to the right. The first bus has gotten bogged down with heavy loads, so there is a 22 minute gap in front of it, while there is another bus right behind. The bus in front should be going inbound at Central right now, but instead both will continue to Harvard, loop around, and start the route bunched: the second bus will lay over for about three minutes and, most likely, after passing several vacant stops, be right on the tail of the first.

This is what the 1 bus route should look like
without any bunching. This is somewhat rare.

And the loop is a particular problem since there is not time or space there for the route to have recovery time, so if a pair of buses enters bunched, they are likely to leave bunched as well. Instead of having proper recovery time at each end, only Dudley serves to even out headways. So bunches are much more likely on the inbound (Harvard-Dudley) having occurred going outbound. And given the traffic, passenger volume and number of lights on this route, bus bunching is likely.

But what if, magically, that bus could be going inbound? Well, it could, and it wouldn’t be magic. It would be a short turn. If a dispatcher were paying special attention to the route, the operators could consolidate all passengers on to one bus in Central Square. At this point, the empty bus could loop around and resume the trip inbound from Central (even waiting in the layover area for a minute or two if need be to maintain even headways), where the bulk of the passengers will be waiting. The bus with passengers will continue to Harvard. On the subsequent trip, every passenger’s experience will be improved. Anyone waiting for a bus inbound from Central will have service 10 minutes earlier—on a proper headway. And passengers between Harvard and Central will have a bus show up when it would have, except instead of quickly filling up as it reaches stops which have had no service for 22 minutes and subsequently slowing down, it will operate as scheduled.

Note that one bus is catching the other. This is the start
of the bunch. 10:09 PM. It’s not too late to short turn!

I watched the route for a while longer, and as predicted, the pair of buses looped through Harvard together, and then traversed the entire inbound route back-to-back, meaning that everyone there waited ten extra minutes, only to have two buses show up together. Every inbound passenger experienced the wonders of a 22 minute headway when the route is scheduled for 12. However, with one dispatch call and a transfer of a few passengers in Central, the headways could have been normalized, and the route could have been kept in order. An issue which was apparent at 10:09 (see the screen capture to the right) could have been fixed at 10:15; instead it lasted until nearly 11:00 (see below):

Now, is this easy? Hell, no, it’s not easy. First of all, the drivers have to know that it might happen. Then, they have to be able to clearly communicate it to the passengers. (If you focused on a couple of routes, you could have Frank Ogelsby, Jr. record some nice announcements. Imagine that deep baritone saying “In order to maintain even schedules, this bus is being taken out of service. Please exit here and board the next bus directly behind.” Oh, and of course, “we apologize for any inconvenience this may have caused.”) You’d have to be damn sure that there was another bus behind and its driver was instructed to pick up the waiting passengers. And a thank you Tweet (@MBTA: Thank you to the passengers of the 1 bus who switched buses so we could fill a service gap at Central) would be in order.

Would it be perfect? No. Sometimes you’d have an issue with a passenger who didn’t want to get kicked off the bus. If a bus had a disabled passenger on board, the driver could veto the short turn based on that fact, since the time and effort to raise and lower the lifts would eat in to the time saved by the turn. But most of the time, if executed well, the short turn would save time, money, and create better service for most every rider.


39. The 39 bus is similar. It is heavily used, and it bunches frequently. It also has its heaviest loads in the middle: the stretch between Back Bay Station and Copley is mostly a deadhead move, the bus only really fills up in the Longwood area, and the bus is mostly of empty of passengers along South Street from the Monument in JP to Forest Hills. So at either of these locations, a similar procedure could take place. If two buses were bunched going inbound, the first could drop off in Copley, take a right on to Clarendon, a right on to Saint James and begin the outbound route, rather than looping in to Back Bay and then out again to backtrack to Berkeley before beginning the route. Back Bay is necessary as a layover location when buses are on schedule, but there’s no reason to have a bus go through a convoluted loop when it could be short turned and fill a gap in service.

At the other end, two bunched buses could consolidate passengers on Centre Street in Jamaica Plain, at which point one could loop around the Monument (already the layover point for the 41) and begin a trip inbound, while the other would serve the rest of the route to Forest Hills.

So those are my two bus routes that could be short-turned and unbunched. Combined, they carry 28,000 passengers per day: the busiest routes in the system. I would propose a pilot study where the T figured out when these routes are most frequently bunched (they have these data) and then assign a dispatcher to watch only these two routes during these times and, when necessary, short-turn a bus to maintain headways, along with some driver training to ensure proper customer service and expedient routing. It could also record messages, put up some signs, and make sure to have some positive outreach to passengers. This could be done for a period of time, and the results analyzed to see the effect of actively dispatching such routes. If it were deemed a success—if there were fewer bunches and service gaps (data could show this)—the program could be expanded, and perhaps automated: any time buses were detected as being bunched, a dispatcher could be notified, and then make a decision on whether it would be appropriate to short-turn the bus, or not.

The passengers—well, we’d certainly appreciate it, too.

How schedule adherence affects headways

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There’s an article on TheAtlanticCities which is bouncing around the office about how painful it is to wait for a train (I’d add: especially if you don’t know when it might come). But even with the proliferation of countdown timers (except, uh, on the Green Line), any disruption to the published (or, at least, idealized) headways can cause headaches. And when headways get at all discombobulated, passenger loading becomes very uneven, resulting in a few very crowded trains that you, the passenger, are more likely to wind up waiting for and squeezing aboard.

For instance, let’s say that you ride the Red Line in Boston. The published headway is 4.5 minutes (two lines, 9 minute headways for each line). Assuming you’re going south through Cambridge, the agency should be able to send out trains at the exact headways from the two-track terminus, barring any issues on the outbound run. You’d expect that, upon entering the station, you’d have an average wait of 2:15, and the longest you’d ever wait for a train would be 4:30 (if you walked in just as the doors were closing and the train was pulling out of the station).

In a perfect world, this would be the case. In the real world, it’s not. In fact, it probably seems to many commuters that their average wait for the train is more in the four-minute range, and sometimes as long as seven or eight minutes. And when a train takes eight minutes to come, the problem compounds as service bunches: the cars get too full, and dwell times increase as passengers attempt to board a sardine-can train and the operator tries to shut the doors.

Here’s the rub: even if most services run on a better-than-average headway, passengers are more likely to experience a longer wait. Here’s an extreme example. Imagine a half hour of service with five trips. With equal headways, one would arrive every six minutes, and the average wait time would be three minutes. Now, imagine that the first four services arrived every 2.5 minutes, and the final one arrived after 20 minutes. The average headway is still six minutes. However, the experienced average is far worse. Unless the services operate at that frequency due to load factors, passengers likely require the service at a constant (or near-constant rate). Imagine that one passenger shows up each minute. The first ten are whisked away quickly, waiting no longer than three minutes. The next 20 wait an average of 10 minutes, with some waiting as long as 20. In this case, even with the same average headway, 14 passengers—nearly half—wait longer than the longest headway if the service was evenly-spaced.

I used the Red Line as an example because I have experience with this phenomenon, and also data. Back when I first collected Longfellow Bridge data, I tracked, for two hours, how often the trains came. It turns out that the headway is actually 4:10 between 7:20 and 9:20, more frequent than advertised. However, nearly half of the trains come within three minutes, which means that there is a long tail of longer headways which pulls the average down. So instead of an average wait time of 2:05, the average user waits quite a bit longer.

Assuming that each train carries all passengers from each station (not necessarily a valid assumption), the average customer waits 2:32. This doesn’t seem like a long time, but it means that while the trains are run on approximate four minute headways, the actual experience is that of five minutes, a loss of 20% of the quality of service. Five minute headways aren’t bad. The issue is that there are several periods where customers wait far longer than five minutes, resulting in overcrowding on certain trains, and longer waits for the same ones. The chart below shows wait times for each minute between 7:23 and 9:23. Green is a wait of 2:15 or less, yellow 4:30 or less (the advertised headway). Orange is up to 6:45, and red is longer. About one sixth of the time a train is running outside of the given headways. And three times, it is longer than 150% of the advertised headway.

Another personal observation is that, try as I might, I seem to always get caught on a packed-full train. This is due to the same phenomenon. Of the 30 trains noted, only eight of them had headways of more than 4:30. Those 8 trains—which, assuming a constant flow of riders, accounted for 27% of the passengers—served 56 of the 120 observed minutes, carrying 47% of the ridership! Ten trains came within 2:30 of the previous trains. These trains accounted for 33% of the service, but only served 19% of the ridership. So while one-in-three trains is underloaded, you only have a one-in-five chance of getting on one of those trains. And while only about a quarter of services are packed full, you have a nearly 50% chance of riding one of those trains. So if you wonder why it always seems like your train is packed full, it’s because it is. But there are just enough empty services that once a week you might find yourself in the bliss of a (relatively) empty train car.

Overall, I mean this as an observation of headways, not as an indictment of the MBTA. Running a railroad with uneven loads (especially at bus- and commuter rail-transfer stations), passengers holding doors and the like can quickly cascade in to a situation where certain trains are overloaded, and others pass by with plenty of room. Still, it’s infuriating to wait. But it’s interesting to have data, and to visualize what it looks like during the course of what seems to be a normal rush hour.

(On the other hand, there are some services, like the 70 bus, which have scheduled uneven headways and where the actual level of service is significantly impacted, but that’s the subject of another post entirely.)