A draft of the MBTA’s “Focus 40” long-term plan was release on July 30, and I spent a little while reading it (it’s rather thin) and sending comments (both officially and on Twitter). If you’ve been reading this blog lately, you’ll know that I’m a strong supporter of Regional Rail, an initiative from the local advocacy group TransitMatters, and of course part of my comments concerned necessary investments in rail infrastructure:

One of the concerns about Regional Rail is how you replicate the existing peak capacity with electric multiple unit trainsets, given that current diesel-hauled commuter rail has quite long trains and bilevel commuter coaches. The Framingham/Worcester Line currently has peak loads of 1600 passengers, which is way more than a single-level, easy-boarding EMU can hold, but of course you can couple trains together, if the trains and platforms are long enough. The number of seats you can deliver on a Regional Rail line is ultimately determined by two factors: platform length and service pattern. The service pattern is profoundly influenced by storage capacity, since you’re not going to be able (or want) to run peak service all throughout the day. So I asked some people who would know what the current shortest high platform on the MBTA Commuter Rail system is — figuring that, if they built high platforms in the first place, there was probably a constructibility constraint that kept any one station from being as long as the rest. That would then influence my idea of how long a consist of EMU trainsets you could operate in peak service, which would then allow me to search for service patterns that would be able to meet that need.

I learned a few things: first, that the MBTA’s standard high-platform length is 800 feet (as compared to Amtrak’s 1050 feet). Second, that the shortest full-high platform in the system is 400 feet at Malden Center and at Oak Grove — these platforms were originally built for Orange Line service, and when the Orange Line extension to Reading was cancelled, they remained in use as commuter rail platforms. Finally, and more relevant for my particular inquiry, Yawkey Station has high platforms that are less than 650 feet long. Since the MBTA decided to have regular trains stop at Yawkey (it previously only served baseball games) it has become a popular stop, with bus transfers to Longwood and Cambridge, and the Green Line nearby in Kenmore Square; more than 400 people get off there during a typical weekday morning (and not all trains stop at Yawkey). That suggests that a Framingham-Worcester service requiring more than about 650 feet of platform is going to run into operational issues (either the trailing trainset[s] won’t be able to platform, or you’ll have to add short turns or local/express patterns to meet the demand in a shorter train). On a two-track main line like the Framingham-Worcester Line, expresses cause scheduling problems, because there are no passing tracks, but short-turns are OK so long as there’s a yard or siding where the train can reverse without fouling the main line — and this becomes more and more important as frequencies get higher.

In order to think about service patterns, I first had to come up with some reliable passenger counts for the existing commuter rail service. Unfortunately, that is quite tricky: the most recent data available was collected by CTPS in the winter of 2012, which predates, among other things, the opening of the popular new Boston Landing station, and the new super-express trains connecting Worcester (and making quite a mess of the schedule for everyone else). There are a lot of reasons to think that Regional Rail would not need any express services, at least on the Framingham-Worcester line, because it is already so much faster. Based on modeling done by Alon Levy in a study of the North-South Rail Link, with proper high-level platforms at all stations, electrification, and full electric multiple-unit trains — the Regional Rail program in a nutshell — a Boston-Worcester train would take only 61 minutes while making all local stops, including several new or restored infill stops that currently have no service at all (also part of the Regional Rail program). By contrast, the current inbound local trains, like P512, are scheduled to take 94 minutes from Worcester to Boston, the regular express takes 80 minutes, and the superexpress takes 66 minutes — so even a local Regional Rail train would beat the fastest current express train (while serving many more passengers).

For the rest of this post, I’m going to be using the 2012 CTPS data — but keep in mind that the peak 2012 loading on any Framingham-Worcester Line train was 1200 passengers, and now that number has increased to 1600; you may want to add 30% to all of the numbers below. (That said, one of the other numbers I don’t have is total boardings: it’s possible that the schedule clearing required to make the superexpress happen has simply concentrated existing demand in a smaller time window, because people still have to get to work at 9:00.)

The question then comes to how to model travel demand, given the passenger numbers. I’m no transportation planner, I haven’t studied this, I don’t know how they actually model these things, but I came up with a really simple way to do it. First, we assume that all travel demand is for people from outlying towns to get into the city. To a first approximation, this is true: in the current service, very few people get off at any of the intermediate stops in Newton, Wellesley, or Natick. One of the goals of Regional Rail is to change this, and encourage trips like Wellesley Square to West Newton to be made by rail instead of by car, but for service planning purposes we’ll start by looking at what people are actually doing today. We’ll model Boston as a point destination at South Station, the end of the line, although in reality about half the passengers get off at Back Bay and Yawkey; since all train schedules we will model will stop at all Boston stations (including the as-yet unbuilt West Station) we’ll treat these destinations as a unit. This allows us to consider only net boardings (which are nearly equal to boardings at all out-of-Boston stations) and makes the model especially simple.

So this is what I did: consider every boarding on the 2012 service as an indication of travel demand to arrive before the next train’s scheduled arrival at South Station (because otherwise they would take a later train). To be specific, for every boarding, we sample a uniform distribution of desired arrival times over [this train’s scheduled arrival, next train’s scheduled arrival). This model is clearly too simple: the distribution is probably not uniform (it should probably be something like a truncated exponential), and some passengers would undoubtedly choose to arrive earlier than the train they’re currently taking, but can’t because the next earlier train leaves too early. But at least this model, while simplistic, is not crazy stupid. So I wrote a bunch of really bad R code to take as input the CTPS data (manually rekeyed from the PDF into a spreadsheet which was then exported as a CSV file for R to ingest) and then, for each station, generate a vector of simulated desired arrival times. Then, for any given schedule (or at least, in the simple case I solved, for any schedule of 100% local trains with no crossing freights or other track fouling) we can compute the number of boardings to expect at each station, and thereby the cumulative loading at the Boston city line.

Once you know the cumulative load at each station, you can calculate the number of EMU trainsets required to serve that number of passengers, based on your preferred model of EMU. I used the JKOY class Sm5 EMU, used in Helsinki’s commuter network; it’s a broad-gauge version of the Stadler FLIRT, and in the middle of the size options Stadler offers for this product line. (The Sm5 is 75 meters or about 246 feet long, and carriers 232 fixed seats and 28 folding seats including wheelchair bays; I’m rounding up to 250 feet and 250 passengers since any Boston EMU will not be this exact configuration. The diesel FLIRT being constructed for TEXRail is 266 feet long but with a much higher seating density, rated capacity 488 passengers; with the same seating layout you could probably get the same capacity in a 250-foot EMU, but with slower boarding and less convenience for passengers with wheeled bags or mobility aids.) Given these numbers, you could carry 700 passengers in comfort on a three-trainset Sm5-equivalent, or over 900 passengers in less comfort on a two-trainset TEXRail-type train. I started doing this modeling before I found the capacity numbers for TEXRail’s FLIRT3 DMUs, so all of the rest of this analysis is based on the Sm5’s capacity. (That said, if you use my analysis but buy Fort Worth’s seating layout, then you’ve effectively accounted for a more than 50% increase in ridership over the 2012 numbers. My bias, however, would be towards boarding doors and bike/wheelchair/stroller space.)

Now finally to get to the point. I modeled three different scenarios, all with 100% local trains serving all stops between Worcester and Boston, with four, five, and six trains per hour. The 4-tph service pattern requires a minimum of five trains with 3 trainsets (peak loadings 541–643 passengers); the 5-tph service pattern requires a minimum of two 3-trainset trains (peak loadings 515 and 541), but for operational reasons you’d probably run five triples on that service as well. That causes a problem, because overnight storage at Worcester is limited to four 800-foot consists, so you end up having to make up three-trainset consists in Boston and send them out empty before the morning rush to be turned around in Worcester and used to make inbound peak service. The extra peak-load trainsets being used in non-peak (or worse, non-revenue) service significantly reduce the equipment utilization compared to a service pattern that uses no more than a two-trainset consist. For what it’s worth, the Helsinki service that the Sm5 was specified for uses to more than that — but they have sufficient passing tracks to run multiple express patterns in addition to their regular 2-tph local service. For my 6-tph scenario, with 30 trains arriving between 6 and 11 AM, the peak load is 464 passengers, for the 9:00 scheduled arrival, which makes sense — there’s another peak (450) that probably reflects people starting work at 8:30.

Having concluded that 6 tph was the best all-local, all-stops schedule, I went on to actually figure out the equipment and storage required to make this service operate. I assume a minimum 15-minute turnaround times (works out to 19 minutes at South Station), which requires at least two platform tracks (possibly you can make it work with as few as that, but the equipment plan does entail making and breaking consists on the platform, in addition to reversing direction, which means doing additional checks before boarding outbound passengers. Overall, the service requires 26 trainsets, of which 12 can be stored overnight in Worcester (more would be better) and 14 in Boston (at Southampton or Readville). At midday, 10 trainsets would be stored in Boston and 1 on the platform at Worcester, with the remaining 15 either in service or being turned at one of the terminals. (Note that the capacity at Worcester is for four 800-foot consists, and likewise 8 consists at Southampton and 12 consists at Readville. Three 250-foot trainsets of EMUs — or indeed three 266-foot trainsets of Fort Worth DMUs — will fit in 800 feet; whether the slack can be used for anything depends on the layout of the yard tracks being used for storage.)

If you look at the simulated boardings, there are no trains that leave Framingham with more than 270 passengers (one trainset’s worth). This suggests a different service pattern, which I haven’t written the code to model but which I suspect makes a lot of sense: instead of running 6 tph all the way from Worcester, run 3 tph from Worcester interspersed with 3 tph from Framingham. Then, you can store trainsets at one of the three Framingham yards (which would have to be wired to make this work), or even implement my idea to upgrade the Agricultural Branch as far as Crossing Blvd. and build a station there with a tail track to store Framingham-terminating trains. I think if you do this, you actually save a substantial number of trainsets (maybe as many as six), but of course the outer towns don’t get as much service in that scenario, which will cause higher loading on the interior segments of those runs. You’ll also notice that there are three early-morning runs in my schedule that have no boardings shown; there’s every reason to believe that people would use these early-morning trains, but 6:30 was the earliest arrival in the 2012 schedule that CTPS audited, so my model doesn’t predict any demand before then.

The crux of my argument to MassDOT and the MBTA is that, with looming procurement projects to replace the ancient and outdated commuter rail rolling stock, it makes sense to commit to building high platforms everywhere now, so that we can then purchase exclusively high-floor multiple-unit rolling stock like the FLIRT3 (which is assembled in Utah and thus eligible for “Buy America”-restricted funding) — specifically with the goal of acquiring a modular system that uses the same components for both electric and diesel-powered trainsets. We wouldn’t get the full benefits of electrification right away — for one thing, the prime mover in the diesel FLIRT only outputs half the power an EMU can draw from the overhead wire, so it accelerates much more slowly — but we would be ready to switch over as quickly as lines can be electrified, starting with the Providence Line which already is electrified aside from a few terminal and yard tracks. We should say “yes, we are going to do this, and we are not going to blow billions of dollars on obsolete unmotorized passenger cars and diesel locomotives.”

Code and data

All of the code and data used for this model is available in my commuter_rail_simulation repository on GitHub. A printable PDF version of a spreadsheet with the results is available at in the repo as well (direct download).

The contents of the spreadsheet are as follows:

1. The predicted schedule of a local train leaving Worcester, based on Alon Levy’s modeling but with most of Alon’s infill stations zeroed out. Note that he adds a 7% pad to the scheduled arrival time at each station, which adds up to just over four minutes pad in the arrival time at South Station.
2. Simulated passenger loading, 4 tph
3. Simulated passenger loading, 5 tph
4. Simulated passenger loading, 6 tph; I’ve added columns with terminal departure and arrival times as well as the number of trainsets required for peak loading on each run
5. An actual equipment schedule for the 6 tph service, based on the simulation
6. Predicted schedule of an express train leaving Worcester, again based on Alon’s numbers but with the stations the current P504 skips zeroed out; note that it gains 9 minutes over the local, which would cause problems for 6-tph operations.
7. Predicted schedule of a superexpress train leaving Worcester, adding stops at Framingham and Boston Landing over the current P552 schedule; it gains 15 minutes over the local, which would cause problems for any of the scenarios modeled, and is not worth emulating or even modeling, given that the local under Regional Rail is faster at any time of day than this twice-daily express is today
8. CTPS passenger loads, from the 2012 study, for Framingham/Worcester trains departing in the morning
9. Net passenger boarding, from the same study