At both TransitMatters and my ongoing Northeast Corridor high-speed rail timetabling project, one question we face is how to mix local and express trains on the same line. I blogged about this years ago, but that was from first principles and this is from a much better position of using Devin Wilkins’ code and analysis of recent research on rail timetabling to evaluate alternatives.

Most of this post is going to be about the Worcester Line in Boston, which we used as a test case; thus, the following two sections cover how to modernize the line, which will be covered in greater detail in an upcoming TransitMatters report, and you can skip them if you genuinely don’t care about Boston. But much of the analysis generalizes, especially when it relates to the issue of American commuter suburbs and their land use. This land use makes neat express patterns hard to justify in most cases, and the outcome in historic American planning has often been irregular patterns, which in postwar suburban New York led to regularizing around zonal express trains, designed to be usable only by rush hour suburb-to-city commuters and nobody else. Nonetheless, it’s still possible to run coherent timetables that make suburb-to-city commutes convenient while also making other trips viable – it just requires running fewer express trains in most cases.

The Worcester Line’s current situation

The Worcester Line connects Boston and Worcester. It is 71 km long and double-track and has 17 stops on the way. There is a planned infill station within Boston at West Station in Allston, and one to four potential infill locations on the way (Newton Corner is the most interesting; the other three are US 20 and the poorly-named Plantation Street in Worcester and Parsons Street in Faneuil). On the way, it passes largely through commuter suburbs of Boston, with one intermediate city, Framingham, station #12 out of Boston, at km-point 34.4, dividing the line into an inner and outer zone. Atypically for a Boston commuter line, seven stations in the inner zone not only don’t have level boarding, but also don’t even have a railcar length’s worth of high platform for wheelchair accessibility (called “mini-highs” in Boston).

All trains are pulled by diesel locomotives. Currently, off-peak and on weekends, all trains make all stops, running roughly hourly. At rush hour, trains either run local between Framingham and Boston, or express between Worcester and Boston, the latter trains running nonstop between the last station in Boston (Boston Landing, #3) and West Natick (#11) and running local beyond; each of the two patterns ran roughly half-hourly before corona, but currently runs roughly every 45 minutes.

Exceptionally, reverse-peak and some midday trains do not stop at the Newton stations (#4-6), where not only are the platforms low but also they only serve one track, and so the peak trains use the track with Newton platforms and the reverse-peak trains use the track without; they switch to the usual right-hand running farther west, the line running infrequently enough it can be scheduled. However, a project to build high platforms on both tracks at these stations is currently in design, and all future modernization assumes it will be completed by then; the current pattern is so atypical that what should generalize is the timetable after completion, not the current one.

Worcester Line modernization and timetabling

Modernization of the Worcester Line means, at a minimum, high platforms at all stations and electrification. This is the starting point of everything that follows; while the North American rail network has practically no electrification measured by route-length, the electrified share measured by ridership is fairly high (nearly all ridership in metro New York is on electric lines, for one).

The combination of those two, plus the improvements in reliability that would follow permitting less timetable padding, would make trip times much faster. Where today, locals to Framingham take 58 minutes and expresses to Worcester take 1:26, EMUs would do these trips in 35 and 46 minutes respectively even with infill stations, or maybe slightly more with schedule padding. This would induce higher ridership, requiring higher frequency – not to mention that at stations 15-20 minutes out of Boston, which the Newton stations will be if this is implemented, increasing frequency from a train every 30 minutes to a train every 15 or ideally less would increase ridership in and of itself.

Then, there’s planning for intercity trains beyond Worcester, to Springfield, which is called East-West Rail in Massachusetts. The plans have gotten some funding, but it isn’t enough, and the current plans are still measured in diesel trains per day and not electric trains per hour. But for future planning, we look at space for faster trains, running even faster than Boston-Worcester express trains. Internally in meetings, Devin has come to calling the three patterns local (current locals), local-express (current expresses, so named because they run local between Framingham and Worcester), and Heart-to-Hub (trains running express between Framingham and Worcester, named after a daily express train that got a lot of love from Worcester boosters but not much ridership). The Heart-to-Hub’s ridership was low and therefore its main use is to speed up Boston-Springfield trips. We express frequency in trains per hour at rush hour in both directions, in the order above: 4/4/0 means the local and local-express patterns run every 15 minutes and there are no Heart-to-Hubs, 4/2/2 means the locals run every 15 minutes and the other two run every 30 minutes, etc.

To boost frequency to 4/4/0 or 4/2/2, even with very fast EMU acceleration rates, requires additional infrastructure. The options are to rebuild Framingham from an at-grade two-track station to an elevated four-track station, so that locals could terminate while local-express and Heart-to-Hub trains continue west, and to add a third track in Wellesley (current stops #7-9, the overtake done toward the east). An ongoing plan to triple-track both Wellesley and Natick is budgeted at $400 million, including four station rebuilds; even net of the rebuilds, it’s expensive, and being able to build a shorter triple-track section would save a lot. (Another option is a modified 4/0/4, with the locals running all the way to Worcester; close to 100% of the riders from the local outer-zone stations would transfer at Framingham.)

Anything beyond eight trains per hour requires too much extra infrastructure – at a minimum, both quad-tracking Framingham and triple-tracking Wellesley, and even then the timetable would be fragile. A coherent 4/4/2 pattern would even require an additional passing track around Southborough (stop #14): the issue is that local-express and Heart-to-Hub trains have narrow windows to depart between pairs of local trains, so if there are four local trains per hour and six express trains, then two pairs of express trains have to be closely spaced, forcing an overtake on the outer section even though the speed difference between them is small.

Thankfully, the Worcester Line can live with eight peak trains per hour indefinitely: it’s a doubling over current frequency, and modernization stands to raise ridership by more than that but largely off-peak, as the modal split at rush hour is healthy.

Short-turn trains

Eight trains per hour on the Worcester Line, four running local to Framingham and four running express to Framingham and continuing on to Worcester, is solid. But are there other ways to shove more trains in? This is where the compromises that lead to irregular express patterns become apparent.

The first possibility is to add short-turn trains: those are trains that run short of the outer terminal. Technically, Framingham locals can be thought of as short-turns, but it’s perhaps better to think of Framingham as the outer terminal of local trains, and then conceive of local trains turning short of that. Newton is a good candidate for short-turns: it is on the dense side for an American suburb, it’s close to Boston, and there’s a place for trains to short-turn off the track via a disused connection to Riverside, where the Green Line D branch terminates. But this still doesn’t work, for a subtle reason that generalizes.

The generalization is that instead of the three names for future Worcester Line trains, we will have more patterns, so let’s refer to them by letters. Local trains are L; local trains that turn short are M. Express trains are X (local-express) and Y (Heart-to-Hub), but in the most general case, it’s fine to think in terms of just L, M, and X, since on the inner zone, X and Y make the same stops.

The issue is that X and Y trains still have to fit between L trains or between L and M trains. Under the 4/2/2 option, with Framingham overtakes and no short-turns, outbound departures look roughly as follows:

:00 X
:02 L
:15 Y
:17 L
(Repeat every half hour)

L is allowed to take at most 11 more minutes to get to the overtake point than X/Y, otherwise X/Y have to be slowed down. Under our current assumptions, this is the exact difference. So there’s no space for additional trains unless they turn short, enough that by the time they’d be overtaken mid-line, they’re on the spur to Riverside. This leads to the following principle: if short-turn locals are added to a line with local and express trains, the express train must run behind a short-turn local and not a full-line local. Concretely, where would M short-turns fit? It would look roughly as follows:

:00 X
:02 L
:07 M
:15 Y
:17 L
:22 M
(Repeat every half hour)

This shoves more frequency on the line, which is good for residents of the stations served by M, neutral to slightly bad for everyone else, and costly. The issue is that on the section where M trains run, the operating costs are those of eight local trains per hour, but the maximum gap is not 7.5 but 10 minutes. Moreover, the trains arriving after the longer gap are L trains and not M trains. Thus, the L trains would end up considerably more crowded than the M trains – all passengers traveling beyond the short-turn would be on L and so would two-thirds of the passengers traveling on the short-turn section. Ideally, if there are programmed irregular gaps on a line with short-turn trains, the short-turns should arrive after the longer gap and not after the shorter gap; if L departs :02 and M departs :12, then L takes just one-third of the passengers on the shared section and M takes two-thirds, which manages capacity better. But the presence of X and Y makes this impossible, because X and Y have to run behind M and ahead of L and still have a fairly long gap from M to avoid having to overtake.

Irregular express patterns

Okay, so short-turn trains are not a good way to add capacity to a line with a mix of local and express trains. This leads to the next step: slowing down some express trains, reducing the speed difference between locals and expresses, and compensating by running more express trains serving different stations.

On the Worcester Line, this means running trains in the pattern Y-X-L, with X making more stops to slow it down a little. But this then raises the question of which intermediate stops get to run express.

The New York City Subway standard of having express stops at regular intervals every three to six stations doesn’t work on commuter rail. The subway is designed around four-track trunk lines with cross-platform transfers at express stations, and those work because the trains are very frequent (or, off-peak, used to be). What works for a four-track system that runs local trains every five minutes doesn’t work for a two-track one that runs them every 15. On a commuter rail network, if a station only gets local trains, there is not going to be an opportunity to transfer, not at the scale we’re talking about.

The simplest answer to who gets the express stations is “the busiest stations.” This is a valid answer. Here is the RER B, between Massy-Palaiseau and Cité-Universitaire, the last station within Paris, where all trains make all stops. Off-peak, the southbound stopping patterns include S trains to Robinson on a branch, K trains making all stops to Massy, and P trains running express to Massy and local beyond, each every 15 minutes; at peak, the S is as before, the K skips one stop, there’s an L pattern skipping stops and running local from Massy to Orsay, and the P runs the fastest and is express to Orsay and only local past that, each every 12 minutes.

Station	Ridership	S	P (base)	K (rush)	L (rush)	P (rush)
Cité-U	7,531,642	*	*	*	*	*
Gentilly	2,415,990	*		*	*	*
Laplace	3,707,718	*		*	*	*
Arcueil-Cachan	3,634,116	*		*	*	*
Bagneux	2,241,461	*		*	*	*
Bourg-la-Reine	4,446,499	*	*	*	*	*
Parc de Sceaux	574,699			*
La Croix de Berny	3,161,602		*	*	*	*
Antony	6,304,424		*	*	*	*
Fontaine-Michalon	731,635				*
Les Baconnets	1,860,108			*	*
Massy-Verrières	607,314			*
Massy-Palaiseau	9,141,486		*	*	*	*

There are no overtake locations on the RER B; because of this, the shared trunk to Bourg-la-Reine has to run local at rush hour. The express patterns still run on a regular clockface schedule every 12 minutes at rush hour and every 15 off-peak, but they aren’t neat, due to the density of traffic. The stations that always get served are the busiest ones – Bourg-la-Reine, La Croix de Berny, Antony, Massy – and are an order of magnitude busier than the stations that get skipped the most. This is not an artifact of service – at the distance of those stations from Paris, a train every 12 or 15 minutes is enough for ridership not to depend too much on frequency. There really is much higher demand at Bourg-la-Reine and Massy than at the minor stations.

In contrast, here is ridership per station between Boston Landing and Framingham, on weekdays:

Boston Landing: 479
Newtonville: 429
West Newton: 243
Auburndale: 203
Wellesley Farms: 285
Wellesley Hills: 322
Wellesley Square: 591
Natick: 697
West Natick: 914
Framingham: 995

So, the first thing to notice is that Framingham, the busiest station, has 995 weekday boardings, which is maybe 290,000 per year, which would be by far the least busy on the RER B (the least busy on the entire RATP-run part of the RER is La Hacquinière, on the outer tail of the RER B, with 419,294/year). But also, the spread is much smaller than on the RER B, a factor of about 5 rather than 16. The spread in potential demand is actually larger, since Auburndale and West Newton are close enough to Boston that the hourly frequencies hurt a lot, whereas Framingham and West Natick both are farther away and get much more rush-hour frequency at any case.

A line like the Worcester Line should only even be running express trains in the first place to speed up some outer-zone trips, and with the expectation that Framingham could develop to something bigger. But that brings in the issue of land use in American suburbs.

Land use and commuter rail ridership

I encourage people to compare land use near American and Parisian commuter rail stations. Here is Bourg-la-Reine:

And here is Massy:

These are town centers. Massy is a postwar suburb developed around the train station, with town center development near the station and plenty of later urban renewal as the area got a TGV station. There’s visibly more stuff near Massy or Bourg-la-Reine than near the minor stations on the RER B, in the same way there is more stuff near a major transfer point on most subways than near a station on one line on a tail. They anchor express service.

The land use near American commuter rail stations works differently. It is lower-density, of course, but more importantly, it is uniformly low-density. Density isn’t especially oriented near the train stations. Occasionally there is walkable retail from the train, but it’s not consistent, and there are no clusters of mid-rise buildings with retail and some local office jobs. American suburbanization of residences may follow the train, with gray near the lines and green between them, but suburbanization of jobs never does, instead following highways.

In this context, there’s no real distinguishing feature that allows some stations to get more express service than others. Riders get to the station by car; the fares and schedules don’t allow for integration with suburban buses, and there is no reason for anyone in these suburbs to rely on bikes when all local destinations are auto-centric. The car has a fairly long range within suburbia, and thus riders drive to a better park-and-ride or kiss-and-ride; the busiest suburban American train station, Ronkonkoma, with around 10,000 weekday riders pre-corona, is a parking lot with practically nothing else near it.

What this means is that express trains often generate their own demand, as passengers start driving to them, neglecting other stations. It creates a fiction of lopsided demand with similar ratios between busier and less busy stations as on the RER B, with no underlying reason for it; the Worcester Line has no such ratio, but the LIRR Main Line does, largely due to the park-and-ride effect. Once planners accept that everyone needs an express trains, schedules evolve to be ever more irregular and less reliable, in the search of the perfect express. Caltrain even came up with the push model, in which the scheduler’s job is to push passengers to park-and-rides with open spots, and otherwise there would be no reason to run trains other than the fastest express trains.

This, in turn, guarantees bad service – these irregular patterns repel riders who are not city-bound commuters, and the frequency is never good enough to sustain such patterns off-peak. In the most extreme cases, it can even backfire: the LIRR’s split between Grand Central and Penn Station frequencies has made it so that so far, the East Side Access project has generated zero new ridership. It’s sometimes possible to salvage something: in the case of Framingham and Worcester, both cities have skeletons of bus networks, and coordinated planning could ensure that the buses would be timed with the train and have free transfers. But at most stations, it’s pointless to try to turn them into distinguished nodes beyond the usual for a local train station.

The upshot is that the only way to run coherent timetables is to focus on local trains. Express trains are for express stops, and few places in the suburban United States are worth the effort; Framingham and Worcester are two of those few because of their town center development, but nothing else on the line is.

In that sense, when I harp on the need for high platforms and electrification, it’s not just because these are good practices in and of themselves, but also because they’re necessary for making local service work. Otherwise, the stop penalty kills you: Boston-Worcester is 1:38 on all-local off-peak trains today, which is an average speed of 43 km/h. And nothing except local stretches works in the context of continuous, isotropic suburban density.