# Modeling Anchoring

Jarrett Walker has repeatedly called transit agencies and city zoning commissions to engage in anchoring: this means designing the city so that transit routes connect two dense centers, with less intense activity between them. For example, he gives Vancouver’s core east-west buses, which connect UBC with dense transit-oriented development on the Expo Line, with some extra activity at the Canada Line and less intense development in between; Vancouver has adopted his ideas, as seen on PDF-page 15 of a network design primer by Translink. In 2013, I criticized this in two posts, making an empirical argument comparing Vancouver’s east-west buses with its north-south buses, which are not so anchored. Jarrett considers the idea that anchoring is more efficient to be a geometric fact, and compared my empirical argument to trying to empirically compute the decimal expansion pi to be something other than 3.1415629… I promised that I would explain my criticism in more formal mathematical terms. Somewhat belatedly, I would like to explain.

First, as a general note, mathematics proves theorems about mathematics, and not about the world. My papers, and those of the other people in the field, have proven results about mathematical structures. For example, we can prove that an equation has solutions, or does not have any solutions. As soon as we try to talk about the real world, we stop doing pure math, and begin doing modeling. In some cases, the models use advanced math, and not just experiments: for example, superstring theory involves research-level math, with theorems of similar complexity to those of pure math. In other cases, the models use simpler math, and the chief difficulty is in empirical calibration: for example, transit ridership models involve relatively simple formulas (for example, the transfer penalty is a pair of numbers, as I explain here), but figuring out the numbers takes a lot of work.

With that in mind, let us model anchoring. Let us also be completely explicit about all the assumptions in our model. The city we will build will be much simpler than a real city, but it will still contain residences, jobs, and commuters. We will not deal with transfers; neither does the mental model Jarrett and TransLink use in arguing for anchoring (see PDF-p. 15 in the primer above again to see the thinking). For us, the city consists of a single line, going from west to east. The west is labeled 0, the east is labeled 1, and everything in between is labeled by numbers between 0 and 1. The city’s total population density is 1: this means that when we graph population density on the y-axis in terms of location on the x-axis, the total area under the curve is 1. Don’t worry too much about scaling – the units are all relative anyway.

Let us now graph three possible distributions of population density: uniform (A), center-dominant (B), and anchored (C).

Let us make one further assumption, for now: the distributions of residences and jobs are the same, and independent. In city (A), this means that jobs are uniformly distributed from 0 to 1, like residences, and a person who lives at any point x is equally likely to work at any point from 0 to 1, and is no more likely to work near x than anyone else. In city (B), this means that people are most likely to work at point 0.5, both if they live there and if they live near 0 or 1; in city (C), this means that people are most likely to work at 0 or 1, and that people who live at 0 are equally likely to work near 0 and near 1.

Finally, let us assume that there is no modal splitting and no induced demand: every employed person in the city rides the bus, exactly once a day in each direction, once going to work and once going back home, regardless of where they live and work. Nor do people shift their choice of when to work based on the network: everyone goes to work in the morning peak and comes back in the afternoon peak.

With these assumptions in mind, let us compute how crowded the buses will be. Because all three cities are symmetric, I am only going to show morning peak buses, and only in the eastbound direction. I will derive an exact formula in city (A), and simply state what the formulas are in the other two cities.

In city (A), at point x, the number of people who ride the eastbound morning buses equals the number of people who live to the west of x and work to the right of x. Because the population and job distributions are uniform, the proportion of people who live west of x is x, and the proportion of people who work east of x is 1-x. The population and job distributions are assumed independent, so the total crowding is x(1-x). Don’t worry too much about scaling again – it’s in relative units, where 1 means every single person in the city is riding the bus in that direction at that time. The formula y = x(1-x) has a peak when x = 0.5, and then y = 0.25. In cities (B) and (C), the formulas are:

(B): $y = \begin{cases}2x^2(1 - 2x^2) & \mbox{ if } x \leq 1/2\\ 2(1-x)^2(1 - 2(1-x)^2) & \mbox{ if } x > 1/2\end{cases}$

(C): $y = \begin{cases}(2x-2x^2)(1 - 2x + 2x^2) & \mbox{ if } x \leq 1/2\\ (2(1-x)-2(1-x)^2)(1 - 2(1-x) + 2(1-x)^2) & \mbox{ if } x > 1/2\end{cases}$

Here are their graphs:

Now, city B’s buses are almost completely empty when x < 0.25 or x > 0.75, and city C’s buses fill up faster than city A’s, so in that sense, the anchored city has more uniform bus crowding. But the point is that at equal total population and equal total transit usage, all three cities produce the exact same peak crowding: at the midpoint of the population distribution, which in our three cases is always x = 0.5, exactly a quarter of the employed population lives to the west and works to the east, and will pass through this point on public transit. Anchoring just makes the peak last longer, since people work farther from where they live and travel longer to get there. In a limiting case, in which the population density at 0 and 1 is infinite, with half the population living at 0 and half at 1, we will still get the exact same peak crowding, but it will last the entire way from 0 to 1, rather than just in the middle.

Note that there is no way to play with the population distribution to produce any different peak. As soon as we assume that jobs and residences are distributed identically, and the mode share is 100%, we will get a quarter of the population taking transit through the midpoint of the distribution.

If anything, the most efficient of the three distributions is B. This is because there’s so little ridership at the ends that it’s possible to run transit at lower frequency at the ends, overlaying a route that runs the entire way from 0 to 1 to a short-turn route from 0.25 to 0.75. Of course, cutting frequency makes service worse, but at the peak, the base frequency is sufficient. Imagine a 10-minute bus going all the way, with short-turning overlays beefing frequency to 5 minutes in the middle half. Since the same resources can more easily be distributed to providing more service in the center, city B can provide more service through the peak crowding point at the same cost, so it will actually be less crowded. This is the exact opposite of what TransLink claims, which is that city B would be overcrowded in the middle whereas city C would have full but not overcrowded buses the entire way (again, PDF-p. 15 of the primer).

In my empirical critique of anchoring, I noted that the unanchored routes actually perform better than the anchored ones in Vancouver, in the sense that they cost less per rider but also are less crowded at the peak, thanks to higher turnover. This is not an observation of the model. I will note that the differences in cost per rider are not large. The concept of turnover is not really within the model’s scope – the empirical claim is that the land use on the unanchored routes lends itself to short trips throughout the day, whereas on the anchored ones it lends itself to peak-only work trips, which produce more crowding for the same total number of riders. In my model, I’m explicitly ignoring the effect of land use on trips: there are no induced trips, just work trips at set times, with 100% mode share.

Let us now drop the assumption that jobs and residences are identically distributed. Realistically, cities have residential and commercial areas, and the model should be able to account for this. As one might expect, separation of residential and commercial uses makes the system more crowded, because travel is no longer symmetric. In fact, whereas under the assumption the peak crowding is always exactly a quarter of the population, if we drop the assumption the peak crowding is at a minimum a quarter, but can grow up to the entire population.

Consider the following cities, (D), (E), and (F). I am going to choose units so that the total residential density is 1/2 and so is the total job density, so combined they equal 1. City (D) has a CBD on one side and residences on the other, city (E) has a CBD in the center and residences on both sides, and city (F) is partially mixed-use, with a CBD in the center and residences both in the center and outside of it. Residences are in white, jobs are in dark gray, and the overlap between residences and jobs in city (F) is in light gray.

We again measure crowding on eastbound morning transit. We need to do some rescaling here, again letting 1 represent all workers in the city passing through the same point in the same direction. Without computing, we can tell that in city (D), at the point where the residential area meets the commercial area, which in this case is x = 0.75, the crowding level is 1: everyone lives to the west of this point and works to its east and must commute past it. Westbound morning traffic, in contrast, is zero. City (E) is symmetric, with peak crowding at 0.5, at the entry to the CBD from the west, in this case x = 0.375. City (F) has crowding linearly growing to 0.375 at the entry to the CBD, and then decreasing as passengers start to get off. The formula for eastbound crowding is,

(F): $y = \begin{cases}x & \mbox{ if } x < 3/8\\ x(5/2 - 4x) & \mbox{ if } 3/8 \leq x \leq 5/8\\ 0 & \mbox{ if } x > 5/8\end{cases}$

In city (F), the quarter of the population that lives in the CBD simply does not count for transit crowding. The reason is that, with the CBD occupying the central quarter of the city, at any point from x = 0.375 east, there are more people who live to the west of the CBD getting off than people living within the CBD getting on. This observation remains true down to when (for a symmetric city) a third of the population lives inside the CBD.

In city (B), it’s possible to use the fact that transit runs empty near the edges to run less service near the edges than in the center. Unfortunately, it is not possible to use the same trick in cities (E) and (F), not with conventional urban transit. The eastbound morning service is empty east of the CBD, but the westbound morning service fills up; east of the CBD, the westbound service is empty and the eastbound service fills up. If service has to be symmetric, for example if buses and trains run back and forth and make many trips during a single peak period, then it is not possible to short-turn eastbound service at the eastern edge of the CBD. In contrast, if it is possible to park service in the center, then it is possible to short-turn service and economize: examples include highway capacity for cars, since bridges can have peak-direction lanes, but also some peaky commuter buses and trains, which make a single trip into the CBD per vehicle in the morning, park there, and then make a single trip back in the afternoon. Transit cities relies on services that go back and forth rather than parking in the CBD, so such economies do not work well for them.

A corollary of the last observation is that mixed uses are better for transit than for cars. Cars can park in the CBD, so for them, it’s fine if the travel demand graph looks like that of city (E). Roads and bridges are designed to be narrower in the outskirts of the region and wider near the CBD, and peak-direction lanes can ensure efficient utilization of capacity. In contrast, buses and rapid transit trains have to circulate; to achieve comparable peak crowding, city (E) requires twice as much service as perfect mixed-use cities.

The upshot of this model is that the land use that best supports efficient use of public transit is mixed use. Since all rich cities have CBDs, they should work on encouraging more residential land uses in the center and more commercial uses outside the center, and not worry about the underlying distribution of combined residential and job density. Since CBDs are usually almost exclusively commercial, any additional people living in the center will not add to transit crowding, even as they ride transit to work and pay fares. In contrast, anchoring does not have any effect on peak crowding, and on the margins makes it worse in the sense that the maximum crowding level lasts longer. This implies that the current planning strategy in Vancouver should be changed from encouraging anchoring to fill trains and buses for longer to encouraging more residential growth Downtown and in other commercial centers and more commercial growth at suitable nodes outside the center.

# Transfer Penalties and the Community Process

In Seattle, there is an ongoing controversy over a plan to redesign the bus network along the principles proposed by Jarrett Walker: fewer one-seat rides to the CBD, more frequent lines designed around transfers to Link, the city’s light rail system. For some background about the plans, see Capitol Hill Seattle, Seattle Transit Blog, and the transit agency on a restructure specific to an upcoming Link extension to the university (U-Link), and Seattle Transit Blog on general restructure, called RapidRide+. The U-Link restructure was controversial in the affected neighborhood, with many opposing changes to their particular bus route.

Since the core of the plan, as with many restructure plans in North America, is to get people to transfer between frequent core routes more and take infrequent one-seat rides less, this has led to discussion about the concept of transfers in general, and specifically the transfer penalty. I bring this up because of a new post by Jason Shindler  on Seattle Transit Blog, which misunderstands this concept. I would like to both correct the mistake and propose why transfers lead to so much controversy.

The transfer penalty is an empirical observation that passengers prefer trips with fewer transfers, even when the travel time is the same. Usually, the transfer penalty is expressed in terms of time: how much longer the one-seat ride has to be for passengers to be indifferent between the longer one-seat trip and the shorter trip with transfers. For some literature review on the subject, see Reinhard Clever’s thesis and a study by the Institute for Transportation Studies for the California Department of Transportation.

Briefly, when passengers take a transit trip with a transfer, making the transfer takes some time, which consists of walking between platforms or stops, and waiting for the connecting service. Passengers weight this time more heavily than they do in-vehicle travel time. According to New York’s MTA’s ridership model, passengers weight transfer time 1.75 times as much as they do in-vehicle time. In other words, per the MTA, passengers are on average indifferent between a one-seat ride that takes 37 minutes, and a two-seat ride that takes 34 minutes of which 4 are spent transferring. Observe that by the MTA’s model, timed cross-platform transfers are zero-penalty. Other models disagree – for example, the MBTA finds an 11-minute penalty on top of a 2.25 factor for transfer time.

The transfer penalty can be reduced with better scheduling. Timed transfers reduce the waiting penalty, first because there is less waiting on average, and second because the (short) waiting time is predictable. When transfers cannot be timed, I believe countdown clocks reduce the waiting penalty. Walking between platforms or bus stops can be made more pleasant, and bus stops can be moved closer to train station entrances.

However, regardless of what the transit agency does, the transfer penalty is an average. Even for the same origin and destination, different people may perceive transfers differently. Any of the following situations can result in a higher transfer penalty:

1. Heavy luggage. This also leads to bias against staircases, and often against transit in general and for cars and taxis. The waiting penalty does not grow, but there may be a significant penalty even for cross-platform transfers.
2. Travel in large groups, especially with children. As an example, in comments here and on Itinerant Urbanist, Shlomo notes that ultra-Orthodox Jews, who travel with their large families, prefer one-seat bus rides over much faster and more frequent train rides. Families of 3-5 are also much likelier to drive in a family car than to take an intercity train or bus.
3. Disability, including old age. This has similar effect to heavy luggage.
4. Lack of familiarity with the system. This is common for tourists but also for people who are used to taking a particular bus route who are facing significant route restructuring. This can also create a large bias in favor of trams or trolleybuses, since their routes are marked with overhead wires and (for trams) rails, whereas bus routes are not so obvious.
5. Reading, or getting other work done in transit. For longer intercity trips, sleeping is in this category, too. This tends to bias passengers against mid-trip transfers especially, more so than against start-of-trip and end-of-trip transfers.
6. Seat availability. Passengers who get on a bus or train when it still has seats available may prefer to keep their seat even if it means a longer trip, and this shows up as a transfer penalty. This does not usually affect start-of-trip transfers (buses and trains probably still have seats), but affects mid- and end-of-trip transfers.

In contrast, people who are not in any of the above situations often have very low transfer penalties. In New York, among regular users of the subway who do not expect to get a seat, zero-penalty transferring appears to be the norm, especially when it’s cross-platform between local and express trains on the same line.

Usually, people in groups 3 and 4 are the major political forces against bus service restructuring plans. They’re also less willing to walk longer distances to better service, which makes them oppose other reforms, including straightening bus routes and increasing the average interstations in order to make bus routes run faster. This is also true of people in groups 1 and 2, but usually those are not inherent to the passenger: most disabled people are always disabled, but most passengers with luggage usually travel without luggage. The one exception is airport travel, where luggage is the norm, and there we indeed see more advocacy for one-seat rides to the CBD.

The key observation here is that even a route change that is a net benefit to most people on a particular origin-destination pair is sometimes a net liability to some riders on that pair. While it’s a commonplace that reforms have winners and losers, for the most part people think of it in terms of different travel patterns. Replacing a CBD-focused system with a grid leads to some losers among CBD-bound riders and winners among riders who travel crosstown; boosting off-peak frequency creates winners among off-peak travelers; straightening one kink in a bus route leads to losers among people served by that kink and winners among people riding through. The different transfer penalties are a different matter: even on the same origin-destination pair, among people traveling at the same time, there are winners and losers.

Solutions to this issue are bound to be political. The transit agency can estimate the net benefit of a restructure, and sell it on those grounds, but it’s not completely a win-win; thus some political process of conflict resolution is required.

In this particular case, the community process is reasonable. The main flaw of the community process is that the people who come to meetings are not representative of the body of riders and potential riders, and are especially likely to be NIMBYs. For example, on Vancouver’s West Side, the community meetings for the Broadway subway were dominated by NIMBYs who didn’t want outsiders (especially students) to have an easier commute to UBC, and not by people who could use the subway, often traveling through the West Side without living or working in it.

But the conflict when it comes to transfers is between groups of people who live in the same area. Moreover, there is no clear bias in either direction. Older people, who are usually more averse to change, are especially likely to show up to meetings; but so are transit activists, who are more informed about the system and thus more willing to transfer. People with intense familiarity with their home bus line are balanced out by people with familiarity with the system writ large. There is also no opposition of a widely shared but small benefit to most against a narrow loss to the few: instead, such reforms produce a large array of changes, ranging from major gains to major losses. Finally, frequent bus grids do not generate much transit-oriented development, unlike rail, which produces NIMBY contingents who are against transit investment on the grounds that it would lead to upzoning and new development (as in the above example from Vancouver).

The result is that here, political control can lead to positive outcomes, as the transit agency is required to consider the effect of change on many subsets of riders. Frequent grids really do generate losers, who deserve to be heard. In this case, it appears that they are outnumbered by winners, but the winners have as much of a political voice as the losers; there is no large gap between good transit and what the community thinks good transit is.

# New York’s Subway Frequency Guidelines are the Wrong Approach

In New York, the MTA has consistent guidelines for how frequently to run each subway route, based on crowding levels. The standards are based on crowding levels at the point of maximum crowding on each numbered or lettered route. Each line is designed to have the same maximum crowding, with different systemwide levels for peak and off-peak crowding. While this approach is fair, and on the surface reasonable, it is a poor fit for New York’s highly branched system, and in my view contributes to some of the common failings of the subway.

Today, the off-peak guidelines call for matching frequency to demand, so that at the most crowded, the average train on each route has 25% more passengers than seats. Before the 2010 service cuts, the guidelines had the average train occupied to exact seating capacity. At the peak, the peak crowding guidelines are denser: 110 passengers on cars on the numbered lines, 145 on shorter (60’/18 m) cars on the lettered lines, 175 on longer (75’/23 m) cars on the lettered lines. There’s a minimum frequency of a train every 10 minutes during the day, and a maximum frequency at the peak depending on track capacity. When the MTA says certain lines, such as the 4/5/6, are operating above capacity, what it means is that at maximum track capacity, trains are still more crowded than the guideline.

In reality, guideline loads are frequently exceeded. Before the 2010 service cuts, many off-peak trains still had standees, often many standees. Today, some off-peak trains are considerably fuller than 25% above seated capacity. In this post, I’d like to give an explanation, and tie this into a common hazard of riding the subway in New York: trains sitting in the tunnels, as the conductor plays the announcement, “we are delayed because of train traffic ahead of us.”

The key takeaway from the system is that frequency at each time of day is calculated separately for each numbered or lettered route. Even when routes spend extensive distance interlined, as the 2/3 and 4/5 do, their frequencies are calculated separately. As of December 2014, we have the following headways, in minutes:

 Line AM peak Noon off-peak PM peak 1 3 6 4 2 6:30 7:30 6:45 3 6 8:30 6:45 4 4:30 7:30 4:24 5 5 8:30 5:45 6 2:30 4 3:18 7 2:30 5 2:30 A 4:45 10 4:45 B 8:45 10 9:15 C 9:15 10 10 D 6:15 10 6:45 E 4 7:30 4 F 4:45 7:30 5 G 6:30 10 10 J/Z 5 10 5 L 4:30 6 4 M 8:45 10 9:25 N 7:15 10 7:30 Q 7:15 10 7:45 R 7:30 10 7:30

Consider now the shared segments between the various lines. The 4 comes every 4.5 minutes in the morning peak, and the 5 every 5 minutes. There is no way to maintain even spacing on both lines with these headways: they share tracks for an extensive portion of their trip. Instead, the dispatchers move trains around to make sure that headways are as even as possible on both the shared trunk segments and the branches, but something has to give. In 45 minutes, there are ten 4s and nine 5s. Usually, on trunk lines with two branches, trains alternate, but here, it’s not possible to have a perfect alternation in which each 4 is followed by a 5 and each 5 is followed by a 4. There is bound to be a succession of two 4s: the second 4 is going to be less crowded than the guideline, and the following 5 is going to be more crowded.

It gets worse when we consider the extensive reverse-branching, especially on the lettered lines. For example, on its northbound journey, the Q initially does not share tracks with any line; then it shares tracks with the B, into Downtown Brooklyn; then it crosses into Manhattan sharing tracks with the N; then it again shares tracks with no other route, running express in Manhattan while the N runs local; then it shares tracks with the N and R into Queens; and then finally it shares tracks with the N in Queens. It is difficult to impossible to plan a schedule that ensures smooth operations like this, even off-peak, especially when the frequency is so variable.

Concretely, consider what happens when the Q enters Manhattan behind an N. Adequate separation between trains is usually 2 minutes – occasionally less, but the schedule is not robust to even slight changes then. To be able to go to Queens ahead of the N, the Q has to gain 4 minutes running express in Manhattan while the N runs local. Unfortunately, the Q’s express jaunt only skips 4 stations in Manhattan, and usually the off-peak stop penalty is only about 45 seconds, so the Q only gains 3 minutes on the N. Thus, the N has to be delayed at Herald Square for a minute, possibly delaying an R behind it, or the Q has to be delayed 3 minutes to stay behind the N.

In practice, it’s possible to schedule around this problem when schedules are robust. Off-peak, the N, Q, and R all come every 10 minutes, which makes it possible to schedule the northbound Q to always enter Manhattan ahead of the N rather than right behind it. Off-peak, the services they share tracks with – the B, D, and M – all come every 10 minutes as well. The extensive reverse branching still makes the schedule less robust than it can be, but it is at least possible to schedule non-conflicting moves. (That said, the M shares tracks with the much more frequent F.) At the peak, things are much harder: while the N, Q, and R have very similar headways, the D is considerably more frequent, and the B and M considerably less frequent.

I believe that this system is one of the factors contributing to uneven frequency in New York, with all of the problems it entails: crowding levels in excess of guidelines, trains held in the tunnel, unpredictable wait times at stations. Although the principle underlying the crowding guidelines is sound, and I would recommend it in cities without much subway branching, in New York it fails to maintain predictable crowding levels, and introduces unnecessary problems elsewhere.

Instead of planning schedules around consistent maximum crowding, the MTA should consider planning schedules around predictable alternation of services on shared trunk lines. This means that, as far as practical, all lettered lines except the J/Z and the L should have the same frequency, and in addition the 2/3/4/5 should also have the same frequency. The 7 and L, which do not share their track or route with anything else, would maintain the present system. The J/Z, which have limited track sharing with other lines (only the M), could do so as well. The 1 and 6 do not share tracks with other lines, but run local alongside the express 2/3 and 4/5. Potentially, they could run at exactly twice the frequency of the 2/3/4/5, with scheduled timed local/express transfers; however, while this may work for the 6, it would give the 1 too much service, as there is much more demand for express than local service on the line.

To deal with demand mismatches, for example between the E/F and the other lettered lines, there are several approaches, each with its own positives and negatives:

– When the mismatch in demand is not large, the frequencies could be made the same, without too much trouble. The N/Q/R could all run the same frequency. More controversially, so could the 2/3/4/5: there would be more peak crowding on the East Side than on the West Side, but, to be honest, at the peak the 4 and 5 are beyond capacity anyway, so they already are more crowded.

– Some services could run at exactly twice the frequency of other services. This leads to uneven headways on the trunks, but maintains even headways on branches. For example, the A’s peak frequency is very close to exactly twice that of the C, so as they share tracks through Lower Manhattan and Downtown Brooklyn, they could alternate A-C-A-empty slot.

– Services that share tracks extensively could have drastic changes in frequency to each route, preserving trunk frequency. This should be investigated for the E/F on Queens Boulevard: current off-peak frequency is 8 trains per hour each, so cutting the E to 6 and beefing the F to 12 is a possibility.

– Service patterns could be changed, starting from the assumption that every lettered service runs every 10 minutes off-peak and (say) 6-7 minutes at the peak. If some corridors are underserved with just two services with such frequency, then those corridors could be beefed with a third route: for example, the Queens Boulevard express tracks could be supplanted with a service that runs the F route in Jamaica but then enters Manhattan via 53rd Street, like the E, and then continues either via 8th Avenue like the E or 6th Avenue like the M. Already, some peak E trains originate at Jamaica-179th like the F, rather than the usual terminus of Jamaica Center, which is limited to a capacity of 12 trains per hour.

– The service patterns could be drastically redrawn to remove reverse branching. I worked this out with Threestationsquare in comments on this post, leading to a more elegant local/express pattern but eliminating or complicating several important transfers. In particular, the Broadway Line’s N/Q/R trains could be made independent of the Sixth Avenue trains in both Queens and Brooklyn, allowing their frequencies to be tailored to demand without holding trains in tunnels to make frequencies even.

For the lettered lines, I have some affinity for the fourth solution, which at least in principle is based on a service plan from start to finish, rather than on first drawing a map and then figuring out frequency. But it has two glaring drawbacks: it involves more branching than is practiced today, since busy lines would get three services rather than two, making the schedule less robust to delays; and it is so intertwined with crowding levels that every major service change is likely to lead to complete overhaul of the subway map, as entire routes are added and removed based on demand. The second drawback has a silver lining; the first one does not.

I emphasize that this is more a problem of reverse branching than of conventional branching. The peak crowding on all lines in New York, with the exception of the non-branched 7 and 1, occurs in the Manhattan core. Thus, if routes with different colors never shared tracks, it would not be hard to designate a frequency for each trunk route at each time of day, without leading to large mismatches between service and demand. In contrast, reverse branching imposes schedule dependencies between many routes, to the point that all lettered routes except the L have to have the same frequency, up to integer multiples, to avoid conflicts between trains.

The highly branched service pattern in New York leads to a situation in which there is no perfect solution to train scheduling. But the MTA’s current approach is the wrong one, certainly on the details but probably also in its core. It comes from a good place, but it does not work for the system New York has, and the planners should at least consider alternatives, and discuss them publicly. If the right way turns out to add or remove routes in a way that makes it easier to schedule trains, then this should involve extensive public discussion of proposed service maps and plans, with costs and benefits to each community openly acknowledged. It is not good transit to maintain the current scheduling system just because it’s how things have always worked.

# LIRR Scheduling

The Long Island Railroad’s timetable is a mess. There is too little off-peak service, especially at the urban stations. At the peak, there is more service, but the service pattern is inscrutable. The Babylon Branch runs a skip-stop pattern in which trains make three stops, skip the next three, and then make the three after them. The pattern of which branch east of Jamaica is sent to which city terminal (Penn Station, Flatbush/Atlantic, or occasionally Hunterspoint) is inconsistent; passengers generally get timed cross-platform transfers at Jamaica, but the frequent interlacing of trains introduces a lot of dependency between different branches in the schedule, reducing reliability. Worst, the Main Line runs trains one-way, so for an hour in the peak, there is no off-peak service. As expected, reverse-peak ridership is minimal, even though there’s a fair number of jobs within a comfortable walk of Mineola. In this post, I am going to discuss how to improve the schedules.

The main tool I will use is a map of LIRR line speed zones. This was made by Patrick O’Hara, of the invaluable but now taken-offline blog The LIRR Today. I emphasize that Patrick does not endorse my plan to eliminate one-way service, on the grounds that it would unacceptably add to the travel time for conventional peak trips from Hicksville and points east to Penn Station. However, using the map and some data about rolling stock performance, I am going to show that LIRR schedules are so padded that improvements to reliability via simpler scheduling can reduce trip times significantly, more than making up for additional trip times to the elimination of most express runs.

First, let us compute technical trip times. In Boston, I compute these by looking at the acceleration rate of the FLIRT, but New York has passable rolling stock already, which means that modernization does not require full replacement of the fleet. This means we should use the specs of the M7: 13.9 kilowatts per ton (FLIRT: 21.7 maximum, 16.7 continuous), and an initial acceleration rate of 0.9 m/s^2 (FLIRT: 1.2). Assuming no air resistance, this means the theoretical acceleration penalty to 130 km/h, the speed over most of the electrified LIRR main lines, is 23 seconds. Judging by the difference between theoretical and actual FLIRT acceleration performance, the actual penalty is about 26 seconds. The deceleration penalty is 19 seconds, for a total of 45. Up to a speed of 100 km/h, the acceleration penalty is 17 seconds and the deceleration penalty is 13 seconds, for a total of 30.

Let us take dwell times to be 30 seconds. With reasonably wide doors at the quarter points and level boarding, it should not be difficult for the LIRR to hold to this standard. Actual dwells appear to be about 40-50 seconds, but are in the context of considerable schedule padding, as we will see. I am going to round speeds up from mph to km/h, so 80 mph will be rounded to 130 km/h, and 60 mph to 100 km/h; the numbers are close, and when I compute curve speeds, the total equivalent cant seems very low, such that large speed increases are possible. However, I am going to stick to the speed map, only changing to km/h for ease of calculation. Including dwell time, the stop penalty in 130 km/h territory is 75 seconds, and the stop penalty in 100 km/h territory is 60 seconds.

Of note, the actual stop penalties we see on LIRR schedules are larger, on the order of 100 seconds. Part of it is the padding again, but part of it is that LIRR trains do not accelerate as fast as they can; the LIRR derated its trains, limiting their acceleration to about 0.45 m/s^2 to reduce the electric current. This can and should be reversed. If it is not, the acceleration penalty is 40 seconds to 130 km/h and 31 seconds to 100 km/h, while the deceleration penalty, unaffected by the change to maximum acceleration, remains the same; overall, this slows trains by about 15 seconds per stop.

East of Jamaica, there are almost no slow zones on either the Main Line or the Babylon Branch. Hicksville’s 65 km/h zone slows trains that stop at Hicksville by about 30 seconds (even a few hundred meters from the station, trains could go faster if the line speed were higher). The curve between Bethpage and Farmingdale is worth 15 seconds. The slowdown in the interlocking at the junction with the Hempstead Line adds 5 seconds. The slowdowns in Jamaica add 35 seconds east of Jamaica, and 55 west of Jamaica, both for stopping trains. On the Babylon Branch, there are a few restrictions in the 80-110 km/h range, worth in total about 70 seconds; Babylon itself is in 100 km/h territory, adding another 10 seconds.

It is 63.6 km from Jamaica to Ronkonkoma. An express train from Jamaica to Ronkonkoma stopping only at Hicksville would do the trip in 33 minutes. A limited-stop train that stopped at Floral Park, Mineola, Hicksville, and then all stops to Ronkonkoma would do the trip in 44.5 minutes. A train that made every LIRR stop, even ones that Ronkonkoma trains never stop at today, would do it in 53 minutes. Under the current schedule, limited-stop trains, not stopping at Floral Park (with technical travel time of 43.5 minutes), do the trip in an hour, for a pad factor of 38%. After accounting for the fact that LIRR trains don’t accelerate this quickly because of the derating, we obtain a technical travel time of around 45.5 minutes, for a pad factor of 32%, still immense.

In Zurich, schedules are padded 7%. Rerating the trains to allow faster acceleration, and reducing the pad to 7%, would cut the trip time under the current off-peak stopping pattern from an hour to 47 minutes, which can be taken as either a material speed boost or as an opportunity to make more local stops. As I will argue later, trains should make more local stops – specifically, all from Floral Park east. This is five more stops than trains currently make; taking the 7% pad into account, we get 54 minutes, still a noticeable improvement over the current situation.

It is 17.4 km from Penn Station to Jamaica. Rather than detail the slow zones, I will just give the technical travel time, for a full-acceleration M7 making no intermediate stops: 13 minutes, or 14 with a 7% pad; 1 of those 13 minutes comes from the Penn Station throat and its 25 km/h speed limit, which is one of the reasons I have emphasized the need for simpler interlockings in station reconstruction. The schedule has 19 minutes, which is a 45% pad relative to full-acceleration travel time, and around 40% relative to the derated travel time. This is even worse, which I believe comes from a combination of congestion in the Penn Station area and the timed transfer at Jamaica; these mean that delays on one branch propagate to the others, requiring more slack in the schedule to maintain reliability. However, I will note that Zurich’s 7% pad is in the context of an environment with even more branches sharing a trunk line, and a plethora of timed transfers and overtakes.

It is 44.4 km from Jamaica to Babylon. An all-stop train – counting Saint Albans but not Atlantic Branch-only Rosedale and Valley Stream – would do the trip in 41 minutes. As I’ve argued years ago, the Babylon Branch’s stations all have relatively equal ridership, unlike the Main Line, where a few stations dominate, and therefore, we shouldn’t plan around express trains. The current schedule‘s travel time on all-stop off-peak trains is 53 minutes, a pad of 29% relative to full-acceleration performance and 19% relative to the derated performance. I believe the reason there is much less padding here than on the Ronkonkoma Branch is that the service pattern is simpler: off-peak, all trains make all stops, whereas the Main Line mixes skip-stop and express trains between the Ronkonkoma and Port Jefferson Branches. If all trains make the same stops and there are no overtakes, it’s easier to recover from delays, so there is less need for padding. (A similar principle is that you need less padding on double-track lines than on single-track lines.)

As mentioned before, at Swiss 7% padding, making all Main Line trains all-local from Floral Park east allows 54-minute service from Ronkonkoma to Jamaica. It also allows 69-minute service from Ronkonkoma to Penn Station, with a minute-long dwell at Jamaica. This is two minutes less than the fastest daily train on the current schedule, a nonstop that runs once a day and arrives at Penn Station at 7:30 am, before the greatest rush. Even at the Babylon Branch’s 19% padding, we get 60-minute service from Ronkonkoma to Jamaica and 76-minute service to Penn Station, which compares with 75 minutes for two peak trains with a few intermediate stops, and 82 minutes for off-peak trains with the above-mentioned pattern.

As for the Babylon Branch, going down to 7% padding and rerating the trains at higher speed means all-stop trains, including the three current local stops between Jamaica and Penn Station, would do the trip in 62 minutes. This is competitive with most peak trains: one train stopping only at Jamaica does the trip in 53 minutes, arriving at 7:02 am, but the other morning express trains, with pads varying based on how close to the peak of peak it is, do the trip in 62-65 minutes.

I claim that the solution to the problems of the Main Line is to indeed abolish all express runs. At the peak, there is no excuse for them: current traffic between the Ronkonkoma, Port Jefferson, and Oyster Bay Branches is about 23 trains per hour at the peak, and this means that either all peak-direction trains run local, or trains run one way, with local trains on one track and express trains on the other. The LIRR chooses to sacrifice reverse-peak service, because frankly providing a coherent network is not a priority; the priority is connecting peak-hour suburban travelers to Manhattan, and saving them a few minutes at any cost. This is despite the fact that peak travelers are the most expensive to serve – the peak is what drives capital investment, to say nothing of the crew utilization problems. But in this case, the peak-focused service may be self-defeating, as the above computation of pad ratios shows.

In the morning peak, west of Hicksville, the service pattern should thus be the same for every Ronkonkoma or Port Jefferson Branch train: all stops to Floral Park (where passengers could transfer to the Hempstead Branch), then express to Jamaica and then Penn Station. All trains should be as identical as possible, which means cutting the diesels to shuttles and, in the medium term, electrifying the Port Jefferson Branch to the end, since there is high ridership the entire way, whereas the Oyster Bay Branch and the Main Line beyond Ronkonkoma have low ridership. The dispatching should emphasize headway management rather than the schedule. Since all trains are functionally identical from Hicksville west, it does not matter to passengers if their favorite train left early – the next one will show up in at most 3 minutes. For the same reason, the transfer at Jamaica should not be timed at the peak.

The highest rapid transit capacity in the world is on subway lines that use headway management rather than fixed schedules, including the Moscow Metro and many modern driverless lines, where the limit is 39 tph. I do not expect 39 tph on the LIRR, but there is no demand for that on the Main Line right now; the point is to maintain 24 tph without excessive schedule padding. Off-peak, trains should keep a schedule because the frequency is lower, but the lower frequency is precisely what makes delays not propagate so fast; similarly, off-peak, the Jamaica transfer should be timed. The greatest problem is in the afternoon off-peak, but there, the bulk of boardings are at Penn Station, where delays are less likely since it’s the start of the line.

This pattern also suggests which capital investments the LIRR needs to make: it needs to construct interlockings such that there are no conflicts between Main Line trains and other trains. This means two things. First, grade-separating Queens Interlocking, between the Main Line and the Hempstead Branch, which currently has an at-grade conflict between opposing trains (eastbound Hempstead Branch, westbound Main Line). And second, reconstructing Jamaica’s access tracks from the east in a way that allows the Main Line from the east to continue on the Main Line’s express tracks to the west without interference from other lines. Right now, there’s an at-grade conflict with the Babylon Branch, but only in the same direction, which is less problematic.

This means kicking other branches off the express tracks from Jamaica to Penn Station, the most desirable track pair heading west of Jamaica. This is fine. Passengers on branches that connect to Flatbush, or to the local tracks to Penn Station, could still transfer cross-platform at Jamaica, even if at the peak the connecting train does not wait for them. Besides, as noted above, 7%-padded local trains from Babylon to Penn Station would have the same trip time as all but the single fastest express Babylon Branch train today.

Jamaica’s current track layout is 8 platform tracks, numbered 1-8, north to south. There are platforms between tracks 1-2, 2-3, 4-5, 6-7, and 7-8. This platform configuration allows three-way timed transfers: when a train platforms on track 2, passengers can walk from track 1 to track 3 via the train. Right now, to the west, the Atlantic Branch connects to tracks 3-6, and the four tracks of the Main Line each connects to two Jamaica tracks. But track connections exist to persistently connect tracks 2 and 7 to the express Main Line tracks, making 1 and 8 the local tracks and 3 and 6 the tracks to Flatbush. To the east, the Far Rockaway and Long Beach Branches connect to the Atlantic Branch without conflicting with other trains. Local Main Line tracks connect to tracks 1 and 8 without conflict. The only conflict involves the Babylon Branch, which runs in the middle between the eastbound and westbound Main Line tracks before diverging, and points at tracks 2 and 7. The current service pattern is that most Babylon Branch trains run express from Jamaica to Penn Station, making this track layout desirable. However, if they are switched to the local, single-track flyovers to connect them to tracks 1 and 8 are required, or alternatively a connection to tracks 3 and 6, which can be done without flyovers. In either case, three-way timed transfers would be retained, except at the peak.

Under my through-running proposal, the Atlantic Branch would continue to Lower Manhattan, so its demand would be much greater than today, encouraging a layout in which the Babylon Branch connected to tracks 3 and 6 and went to Brooklyn and Lower Manhattan. The Main Line trains would express to East Side Access and Grand Central, with an additional stop at Sunnyside Junction. The Hempstead Branch, connected to Penn Station and the Empire Connection, would have service increased, with mode-neutral fares encouraging more travel from within New York and Hempstead. I would also propose a new branch of the Hempstead Branch, using the inner Central Branch, going to the East Garden City job cluster. The Oyster Bay Branch would be electrified and its junction with the Main Line grade-separated.

However, I emphasize that none of my proposed schedule changes requires the intensive capital investment associated with connecting Flatbush with Lower Manhattan. Even East Side Access is not required. Queens Interlocking would be grade-separated, and the Oyster Bay Branch would be reduced to a shuttle with an additional track at Mineola (unless electrifying the entire line and grade-separating the junction is cheaper in the short run, which I doubt). Initially, I am not sure the at-grade conflict with the Babylon Branch on the approach to Jamaica would be deadly. The subway has a same-direction at-grade conflict at Rogers Avenue Junction, between the 2, 3, and 5 trains, whose combined peak frequency is higher than that of the Main Line and Babylon Branch’s. Rogers Avenue Junction is a key bottleneck on the numbered lines in New York, which is why the LIRR should not replicate it in the long run, but in the short run, it is fine.

To conclude, here are proposed westbound timetables for Ronkonkoma, Babylon, and Hempstead trains. These assume no new stations and only the minimally required physical infrastructure (that is, grade-separating Queens Interlocking).

Main Line:

 Ronkonkoma 7:00 Central Islip 7:05 Brentwood 7:09 Deer Park 7:12 Wyandanch 7:16 Pinelawn 7:19 Farmingdale 7:23 Bethpage 7:27 Hicksville 7:31 Westbury 7:35 Carle Place 7:37 Mineola 7:40 Merillon Avenue 7:42 New Hyde Park 7:44 Floral Park 7:47 Jamaica 7:53 New York Penn 8:08

This is a total travel time of 68 minutes, and not 69 as advertised above. This is because of rounding artifacts.

 Hempstead 7:31 Country Life Press 7:33 Garden City 7:36 Nassau Boulevard 7:38 Stewart Manor 7:40 Floral Park 7:43 Bellerose 7:34 Queens Village 7:46 Hollis 7:49 Jamaica 7:53 Kew Gardens 7:57 Forest Hills 7:59 Woodside 8:04 New York Penn 8:12

The 4-minute difference between local and express travel time between Jamaica and Penn Station comes from the fact that the intermediate stations are for the most part in slower zones than 130 – only at Forest Hills is there enough of a distance to get up to 130, and only west of the station, not east. Erratum: although it is true the stations are in slow zones, I wrote this paragraph thinking there are four intermediate stations, where of course there are only three; 4/3 = 80 seconds per stop, which comes from rounding artifacts.

The Hempstead Branch has a 1.5-km single-track segment starting west of Hempstead and ending east of Garden City. It is quite slow; the 25 km/h curve just north (west) of Country Life Press has geometry good enough for 50 km/h without any superelevation (cant deficiency would be 150 mm), and with 150 mm superelevation would be good for 70. Replacing that entire 25-50 km/h segment with 70 km/h saves about a minute of travel time.

Babylon Branch:

 Babylon 7:04 Lindenhurst 7:08 Copiague 7:10 Amityville 7:12 Massapequa Park 7:15 Massapequa 7:17 Seaford 7:19 Wantagh 7:21 Bellmore 7:24 Merrick 7:26 Freeport 7:29 Baldwin 7:31 Rockville Centre 7:34 Lynbrook 7:37 St. Albans 7:43 Jamaica 7:48 Kew Gardens 7:52 Forest Hills 7:54 Woodside 7:59 New York Penn 8:07

I arbitrarily chose the Ronkonkoma departure time to be 7:00, and then chose the Hempstead Branch schedule to allow a timed transfer at Jamaica. The five-minute offset for the Babylon Branch should be suggestive of the proposed frequency: off-peak, every ten minutes on the Babylon Branch (possibly every twenty but also every twenty on the West Hempstead Branch), every ten minutes on the Hempstead Branch (possibly every twenty but also every twenty on the Central Branch to East Garden City), and every ten minutes on the Main Line, with each of the Ronkonkoma and Port Jefferson Branches getting a train every twenty minutes. The Atlantic Branch trains should run every twenty minutes per branch, with a three-way timed transfer with the Main Line and Hempstead Branch. Off-peak, the Babylon Branch doesn’t transfer to anything else, so there is no need to worry about its at-grade conflict at Jamaica.

# Why Labor Efficiency is Important

In North America, commuter trains run with conductors, often several per train. On most systems they walk the entire length of the train to check every passenger’s ticket, whereas on a few, namely in California, they do not do that anymore, but there are nonetheless multiple conductors per train. In addition, the scheduling is quite inefficient, in that train drivers do not work many revenue hours. I investigated what effect this has on operating costs, and it turns out that the effect on the marginal operating costs, which are important for off-peak service, is large: on the LIRR and Metro-North, nearly fivefold improvements in revenue train-hours per on-board employee (driver or conductor) are possible, which would halve the marginal operating cost per train-km. The bulk of this post is dedicated to explaining the following breakdown of variable operating costs:

The National Transit Database has figures for service in car-km and car-hours for a variety of US transit agencies. In New York State, the Empire Center has lists of every public employee’s position and pay, which we can use to figure out the average pay of a train driver and conductor and the productivity of their labor. The NTD numbers are as of 2011, so I will use the number of employees of 2011, but the pay per employee of 2014 (at any rate, there have been no major service changes since 2011, so numbers are similar). In 2011, the LIRR averaged 5,000 car-hours per driver-year, and Metro-North averaged 4,000; the LIRR runs longer trains than Metro-North, so the figure for both railroads appear to be about 500 train-hours per driver-year. Both railroads had a little bit more than 2 conductors per driver on average (2.14 Metro-North, 2.47 LIRR). The average pay of a driver, as of 2014, is $109,000 on the LIRR and$120,000 on Metro-North, whereas the average pay of a conductor is $112,000 on the LIRR and$96,000 on Metro-North.

From this, we can piece together the average operating cost of commuter rail derived from on-board labor, per train-hour: $771 on the LIRR,$714 on Metro-North. Assuming 8 cars per train (and again, the LIRR tends to run longer trains), this is around $90-95 per car-hour. According to the NTD, the average operating cost of both was about$550 per car-hour in 2011, but this includes fixed costs, such as management and rolling stock. As we will see, variable operating costs are much lower.

As a digression, I’d like to point out that the peaky schedule of commuter rail contributes to the low productivity of the drivers. Crew schedules include substantial gap time between trips, and occasionally, especially on low-frequency diesel branches, they deadhead. That said, the subway’s number of revenue train-hours per driver is not materially different. For higher figures, one must leave New York. Toei got about 700 revenue hours per driver when I last checked, but I can no longer find the reference. On the London Underground, I do have fresh references, pointing in the same range: 76.2 million train-km per year at 33 km/h average speed (from TfL’s facts and figures), and a bit more than 3,000 train operators. In 2012, the last year for which there’s actual rather than predicted data (see also PDF-p. 7 of the TfL Annual Report), there were 720 revenue hours per train driver. This is in tandem with a less peaky schedule than in New York: although the average speed is barely higher than that of the New York subway, as reported in the NTD, the trains travel about 180,000 km per year (see fact 149 here), twice as long as in New York. In Helsinki, metro trains run every 10 minutes all day on each branch, every day, without any extra peak service, contributing to even higher utilization: the schedules show 65,000 revenue-hours per year, whereas a factsheet from 2010 shows 75 metro drivers, for a total of 867 revenue hours per driver. In both the UK and Finland, average hours per employee are marginally shorter than in the US; London Underground drivers have 36-hour workweeks.

The importance of this computation is not just to highlight that 44-73% improvement in revenue-hours per employee is possible, but to point out that, on the margins, adding off-peak service would make crew schedules more efficient, since higher frequency would reduce the need to deadhead and to wait between trains. This means that, although the average operating cost may be about $750 per train-hour, the marginal cost is lower, even without changes to work rules. Suppose now that trains run without conductors, using proof-of-payment as on light rail lines, even ones in North America, and on countless commuter rail systems in Continental Europe. Suppose also that there are 720 revenue-hours per driver, and that a driver is paid$115,000 per year. This means that running extra trains would not cost $90-95 in on-board labor per car-hour, but only$20, a nearly fivefold improvement. At Helsinki’s level of productivity, a nearly sixfold improvement to $16.60 is possible. At the LIRR’s present average speed of 50 km/h (compared with 53 on New Jersey Transit and 59 on Metro-North), the fivefold improvement based on London Underground productivity would cut the average cost per car-km from$1.80-1.90 to $0.40; at a higher but still realistic 67 km/h, it’s a cut from$1.35 to $0.30. A large majority of this cut comes from eliminating conductors, which, by itself, would cut costs threefold, but raising driver productivity would allow an additional cut of 30-40%. I again stress that the marginal cost is lower than the average cost computed here, since less peaky schedules come with simpler crew scheduling; more off-peak service would by itself cut the average cost, which means its marginal cost would be quite low. Let us now look at other variable costs than on-board labor. Two years ago, I did this computation for high-speed rail, and found that, provided the schedules did not have extra rush hour service, operating expenses would be very low. We can do the same computation for commuter rail, and note that the lower speeds imply that operating and maintenance costs are spread across less passenger-km, raising costs. Let us consider train maintenance, cleaning, and energy. I do not have information about train maintenance costs on commuter rail. Instead, I will use those of high-speed rail, for which standards are higher. As I noted in my computation from two years ago, the reference here is California HSR’s 2012 Business Plan, which aggregates these figures from around the world on PDF-p. 136. Maintenance costs per train-km are$4.47 for the Tokaido Shinkansen (with 16-car trains) and $2.58 per the UIC (with what I assume are 8-car trains), both in 2009 dollars. These figures cluster around$0.30 per car-km in 2009 dollars, or $0.30-35 per car-km in 2014 dollars. With cleaning, there is some information about commuter rail: the Empire Center has lists of coach cleaners on Metro-North (there are 314) and their pay (on average, a little less than$50,000 a year). This seems high given the amount of service Metro-North runs – about $0.15 per car-km. Shinkansen trains are cleaned on a seven-minute turnaround in Tokyo, using one cleaner per standard-class car; this includes tasks that are not required on commuter rail, such as flipping seats to face forward. A cleaner making$30 per hour cleaning a single car per 15 minutes, with each train cleaned once per 150 km roundtrip, would cost $0.05 per car-km. I suspect that part of the low productivity of Metro-North cleaners is again a matter of low off-peak frequency – Shinkansen cleaners work almost continuously – but I don’t have comparative data to back this up; New York City Transit pays even more per cleaner per car- or bus-km, but this is on much lower average speed, and per car- or bus-hour, it pays about$6.40, vs. about $8.90 for Metro-North. I’m going to pencil in$0.10 per car-km as the cost of cleaning.

Energy costs we can compute from first principles. This is easier than for HSR, since commuter trains travel at such speed that a large majority of their energy consumption is in acceleration, rather than cruising. The explicit assumptions I am making is that the top speed is 130 km/h (the two main LIRR lines are mostly 80 mph territory), each car weighs 54 metric tons (the LIRR M7s weigh 57.5 and the Metro-North M8s even more, but this is very high by international EMU standards, thanks to FRA regulations), the average distance between stations is 4 km (the LIRR’s average is less than that if all trains make all stops and more if there are some express trains), and the track resistance per unit of train mass is the same as for the X 2000, for which data exists on PDF-p. 64 of a thesis on tilting trains. Regenerative braking is assumed to exactly cancel out with losses in transmission. Train acceleration performance is assumed to be like that of the FLIRT, which would take about a kilometer to accelerate to line speed and have about 2 km of cruising before slowing down for the stop; the M7 has inferior performance, but this would reduce energy consumption since trains would spend more time at lower speed.

With the above assumptions, each acceleration, cruise, and deceleration cycle between stations consumes about 13 kWh, of which 10 kWh is required to accelerate the train to top speed, and the other 3 are for overcoming track resistance. See rough computations in a subthread on California HSR Blog starting with this comment, and bear in mind the initial comment made a large computational error. As for April of this year, transportation electricity costs in the state are $0.1245 per kWh, giving us about$1.60 per 4-km interstation, or $0.40 per car-km. Overall, those three items are$0.80 per car-km. This means that going from paying train crew $1.35 per car-km to paying them$0.30 per car-km represents halving of direct marginal operating expenses: it means going from $2.15 to$1.10 per car-km. Finally, let us add management costs, which are not exactly marginal costs, but do grow as the workforce grows, since more employees require supervisors. At RENFE, we can extract 0.27 support and management employees per operations employee from the data on PDF-p. 46 of its 2010 executive summary. On the Helsinki urban rail network, the corresponding figure is 0.34 as per the factsheet referenced above. This affects train crew, cleaning, and maintenance staff, but not energy. If this means 30% extra costs, this means going from $2.675 to$1.31 per car-km – again, we see costs are halved.

The importance of the above calculation is that it is quite possible that Utica will turn out to have a lower projected cost per rider than the next phase of Second Avenue Subway, a project for which there is nearly universal consensus in New York. The original cost projection for Second Avenue Subway’s second phase was $3.3 billion, but will have run over since (the projection for the first phase was$3.7 billion, but actual cost is nearly $5 billion); the ridership projection is 100,000 for each phase beyond the first, which is projected at 200,000. In such a situation, the line would be a great success for New York, purely on the strength of existing demand. I put Utica at the top of my list of underrated transit projects for a reason: the line’s worth is several times its cost assuming world-average per-km cost, and remains higher than the cost even at elevated American prices. The de Blasio administration is doing well to propose such a line, and it is nearly certain that costs will be such that good transit activists should support it. # What is the MTA Reinventing, Anyway? In the last few years New York’s MTA has gone through multiple cycles in which a new head talks of far-reaching reform, while only small incremental steps are taken. The latest is the MTA Transportation Reinvention Commission, which has just released a report detailing all the way the MTA could move forward. Capital New York has covered it and hosts the report in three parts. Despite the florid rhetoric of reinvention, the proposals contained in the report are small-scale, such as reducing waste heat in the tunnels and at the stations on PDF-pp. 43-44 of the first part. At first glance they seem interesting; they are also very far from the reinvention the MTA both needs and claims to be engaging in. Construction costs are not addressed in the report. On PDF-p. 53 of the first part, it talks about the far-reaching suburban Grand Paris Express project for providing suburb-to-suburb rapid transit. It says nothing of the fact that this 200-km project is scheduled to cost about 27 billion euros in what appears to be today’s money, which is not much more than$150 million per km, about a tenth as much as New York’s subway construction. (Grand Paris Express is either mostly or fully underground, I am not sure.) The worst problem for transit in the New York area is that its construction costs are an order of magnitude too high, but this is not addressed in the report.

Instead of tackling this question, the report prefers to dwell on how to raise money. As is increasingly common in American cities, it proposes creative funding streams, on the last page of the first part and the first six pages of the second part: congestion pricing, cap-and-trade, parking fees, a development fund, value capture. With the exception of congestion pricing, an externality tax for which it makes sense for revenues to go to mitigation of congestion via alternative transportation, all of these suffer from the same problem: they are opaque and narrowly targeted, which turns them into slush funds for power brokers. It’s the same problem as the use of cap-and-trade in California.

One of the most fundamental inventions of modern government is the broad-based tax, on income or consumption. Premodern governments funded themselves out of tariffs and dedicated taxes on specific activities (as do third-world governments today), and this created a lot of economic distortion, since not all activities were equally taxed, and politically powerful actors could influence the system to not tax them. The transparent broad-based tax, deeded to general revenue through a democratic process, has to be spent efficiently, because there are many government departments that are looking for more money and have to argue why they should get it. Moreover, the tax affects nearly all voters, so that cutting the tax is another option the spending programs must compete with. The dedicated fund does neither. If the broad-based tax is the equivalent of market competition, a system of dedicated funds for various government programs is the equivalent of a cartel that divides the market into zones, with each cartel member enjoying a local monopoly. In this way there’s a difference between the hodgepodge of taxes the MTA levies and wants to levy and Ile-de-France’s dedicated 1.4-2.6% payroll tax: the payroll tax directly affects all Francilien workers and employers, and were it wasted, a right-wing liberal politician could win accolades by proposing to cut it, the way New York Republicans are attacking the smaller payroll tax used to fund the MTA.

The proposals of where to spend the money to be raised so opaquely are problematic as well. There is a set of reforms, based on best practices in Continental Europe and Japan, that every urban transit system in the first world should pursue, including in their original countries, where often only some of those aspects happen. These include proof-of-payment fare collection on buses, commuter trains, and all but the busiest subway systems; all-door boarding on buses; mode-neutral fares with free transfers; signal priority and bus lanes on all major bus routes, with physically separated lanes in the most congested parts; a coherent frequent bus network, and high off-peak frequency on all trains; and through-service on commuter rail lines that can be joined to create a coherent S-Bahn or RER system. As far as I can tell, the report ignores all of these, with the exception of the vague sentence, “outfitting local bus routes with SBS features,” which features are unspecified. Instead, new buzzwords like resiliency and redundancy appear throughout the report. Redundancy in particular is a substitute for reliability: the world’s busiest train lines are generally not redundant: if they have parallel alternatives those are relief lines or slower options, and a shutdown would result in a major disruption. Amtrak, too, looks for redundancy, even as the busiest intercity rail line in the world, the Tokaido Shinkansen, has no redundancy, and is only about to get some in the next few decades as JR Central builds the Chuo Shinkansen for relief and for higher speeds.

The only foreigners on the Commission are British, Canadian, and Colombian, which may have something to do with the indifference to best industry practices. Bogota is famous for its BRT system, leveraging its wide roads and low labor costs, and Canada and to a lesser extent the UK have the same problems as the US in terms of best industry practices. Swiss, French, German, Japanese, Spanish, and Korean members might have known better, and might also have been useful in understanding where exactly the cost problems of the US in general and New York in particular come from.

The final major problem with the report, in addition to the indifference to cost, the proposal for reactionary funding sources, and the ignorance of best industry practices, is the continued emphasis on a state of good repair. While a logical goal in the 1980s and 90s, when the MTA was coming off of decades of deferred maintenance, the continued pursuit of the maintenance backlog today raises questions of whether maintenance has been deferred more recently, and whether it is still deferred. More oversight of the MTA is needed, for which the best idea I can think of is changing the cycles of maintenance capital funding from five years, like the rest of the capital plan, to one year. Long-term investment should still be funded over the long term, but maintenance should be funded more regularly, and the backlog should be clarified each year, so that the public can see how each year the backlog is steadily filled while normal replacement continues. This makes it more difficult for MTA chiefs to propose a bold program, fund it by skimping on maintenance, and leave for their next job before the ruse is discovered.

I tag this post under both good categories (“good transit” and “good/interesting studies”) and bad ones (“incompetence” and “shoddy studies”) because there are a lot of good ideas in the report. But none of them rises to the level of reinvention, and even collectively, they represent incremental improvement, of the sort I’d expect of a city with a vigorous capital investment program and industry practices near the world’s cutting edge. New York has neither, and right now it needs to imitate the best performers first.

# Airport Connectors

The most interesting transit planner in the world:

This principle is true primarily for large international airports. As I will explain, this is less true of smaller airports. But before going on, I would like to clarify a distinction between bad and overrated. Airport connectors, as I have argued many times, are overrated: city elites tend to like them disproportionately to their transit usage, as do many urban boosters, who think a comfortable airport connector is a necessary feature of a great global city. The result of this thinking (and also the main evidence we have that this thinking exists) is that airport connectors are built at much higher costs per rider than other transit projects: the JFK and Newark AirTrains cost more than $100,000 per weekday rider, much more than other recent rail projects in New York; even the far over-budget East Side Access, at current estimates, is about$60,000.

However, overrated does not mean bad. There exist airport connector projects with reasonable cost per rider. They’re still overrated, which means they’ll be built concurrently with even more cost-effective non-airport projects, but they’re good enough by themselves. As an example, take the Canada Line. The total cost was about $2 billion, and the latest ridership figure I have, from 2011, is 136,000 per weekday, ahead of projections. At$15,000 per rider, this is reasonable by European standards and very good by North American ones. Let us now look at the two branches of the line, to Richmond and the airport. Lacking separate cost data for them, I am going to estimate them at about $300 million each, as they are entirely above-ground; the airport branch is 4 km and the Richmond branch is 3 km, but the Richmond branch has an urban el and the airport branch doesn’t. For ridership data, we have this set of figures per station (which results in a Canada Line total of only 113,000). Boardings and alightings sum to 19,000 on the airport branch and 34,000 on the Richmond branch; we’re double counting intra-branch trips, but there presumably are very few of these. As we see, the Richmond branch is more cost-effective, but the airport branch holds its own – since the per-station data has a lower overall Canada Line ridership, the airport branch’s presumed cost per extra rider generated is less than that of the entire line! (This sometimes happens, even with branches that generate less ridership than the trunk.) Clearly, despite the fact that airport connectors are overrated, this is an example of a good project. The importance of the overrated vs. bad distinction is then that good transit advocates need to be wary, since airport connectors that don’t work well might get funded anyway, ahead of more deserving projects. But there remain good airport connectors, and therefore we should discuss what features they might have. The answer given by city elites is typically “nonstop connection to the CBD,” often with a premium fare. But the good transit answer is more complicated, and the graphic at the top of the post is only a partial answer. There is a difference between short- and long-distance air travel. In many cities it doesn’t matter much because there’s a single dominant airport – Beijing, Frankfurt, Zurich, Atlanta, Toronto – but in others there are multiple airports, with different roles. Often there will be a smaller, closer-in, older airport, serving mostly domestic flights, and a larger, farther away, newer international airport. Paris has Orly and Charles-de-Gaulle, Chicago has Midway and O’Hare, New York has LaGuardia and JFK (Newark is intermediate in its role, even if it’s the oldest), Los Angeles has Burbank and LAX (the other airports are somewhat outside this division), Dallas has Love Field and DFW, Tokyo has Haneda and Narita, Seoul has Gimpo and Incheon. Because those airports have different functions, they require different kinds of transportation links. First, let us consider departing passengers. If they travel to another continent, their options are quite restricted: for example, if they live within driving distance of Atlanta, they’re flying out of Atlanta. Even if there are closer secondary airports (such as Greenville-Spartanburg and Chattanooga), they don’t offer such service – at most, they offer a connecting puddle jumper flight to the primary airport. In contrast, if they travel shorter distances, and live far from the primary airport, they could fly out of a secondary airport, or might just drive instead of flying: a 2-hour drive to the airport is comparatively more tolerable for an 8-hour intercontinental flight than for a 1.5-hour short-hop flight. For example, when I lived in Providence, my air trips were all to the West Coast or Europe, so I flew out of Boston or even New York; but when my sister visited, she chained trips and also visited her boyfriend, who at the time lived in North Carolina, and for the domestic leg of the trip she flew out of T. F. Green. The result is that primary international airports draw their departing passengers from a much wider shed than mainly domestic airports. In metro areas with such separation of airports, the international airports – Charles de Gaulle, JFK, DFW, Incheon, etc. – draw riders from faraway suburbs and even from adjacent small metro areas, whereas the domestic airports draw riders primarily from the city and its nearby suburbs. Now, let us consider arriving passengers. Destinations are more centralized than origins, but this is especially true for international trips than for domestic ones. Tourism trips are heavily centralized around a few attractions, which in most cities are in the CBD, or in specific locations: if you’re flying to the Paris region for tourism, your destination is either Paris proper or Eurodisney, rather than an average suburb. Business trips are also heavily centralized around the CBD and a few edge cities. Personal visits have no such concentration, and these are much more common for short-distance domestic flights than for long-distance international flights. I am unusual in that I live on a different continent from my parents; usually, people live within ground transportation or short-distance flying distance from family and friends, depending on the country they live in (short-distance flying distance is more common in the US). The result here is that arriving passengers at domestic airports are typically interested in visiting the CBD but often also the rest of the metro area, whereas arriving passengers at international airports are much more CBD- or tourist attraction-centric. Some evidence for this difference can be found in looking at the Consumer Airfare Report, which has domestic O&D traffic counts between airport pairs. The primary international airport usually has a smaller percentage of its domestic O&D traffic going to shorter-distance cities. For example, at LAX, 13% of traffic is within California, and another 6% is to Las Vegas, Phoenix, and Tucson, within a 3-hour high-speed rail range. At Burbank, the corresponding figures are 42% and 21% respectively. The same pattern can be observed for O’Hare (8.6% of traffic is internal to the Midwest) and Midway (14.6%), and DFW (3% of traffic is internal to the Texas Triangle) and Love Field (27%). The mode of transportation that best suits the needs of international airports is then mainline rail. On the one hand, it tends to be better than urban transit at serving trips that are dedicated to CBD service, since commuter rail is more radial than urban transit, and the stop spacing is typically also longer (although dedicated premium connectors are still often wastes of money). On the other hand, it can extend deep into the suburbs and to adjacent metro areas, and expand the airport’s draw. People can ride intercity (often high-speed) trains direct to the terminal at Frankfurt, Zurich, and Charles-de-Gaulle, and this allows those airports to be the primary international airports for metro areas in a wide radius: SNCF code-shares with airlines to connect people from Charles-de-Gaulle to Lyon, 400 km and 2 hours away by TGV. This is not true of small domestic airports. A TGV connection to Orly would’ve been much less beneficial than the current connection to Charles-de-Gaulle: most of Orly’s traffic is short-distance, often competing with the TGV rather than complementing it. With this distinction in mind, we should look at the situation at the major American airports. In California, the current plan is to have California High-Speed Rail serve both SFO (at Millbrae) and Burbank Airport; the original plan served Downtown Burbank instead of the airport, but the HSR Authority seems to have shifted its focus, and wants Burbank to be the southern terminus of the line, pending construction to LA Union Station. This is bad planning. Nearly two-thirds of Burbank’s traffic competes either with California HSR or with future tie-ins. People from Bakersfield and Fresno are unlikely to take a train to the airport to connect to a flight, since they can take a train the whole way, or drive directly to Las Vegas or Phoenix. People in Bakersfield and Fresno would be more interested in a connection to LAX, whose traffic complements rather than competes with intercity rail. Los Angeles could build a connection to LAX, running both frequent electric commuter trains and high-speed trains on it. The Harbor Subdivision has existing tracks from Union Station almost the entire way to the airport, although the route is at-grade, with a large portion of it running next to Slauson Avenue, and most likely a major project like this would require viaducts. Only a short greenfield segment, elevated over Century, is required to reach the proposed Terminal 0 location, and that is only necessary if, as in Zurich and Frankfurt, LAX wishes to avoid a landside people mover. It is both bad transit and bad politics to build this only for nonstop trains: the route passes through reasonably dense urban neighborhoods, and should have 10-12 stops along the way, with some trains running local and others making only 1-3 stops, at major nodes such as Inglewood or the intersection with the Blue Line. There is room for passing sidings at the line’s midpoint, but the low top speed and the short length of the line is such that overtakes are only necessary if there are nonstop and local trains every 10 minutes. Such an airport connector would serve many different trips at once: HSR trips from Central Valley cities to LAX, arriving trips from LAX to Downtown LA (and, via transfers at intermediate stops, to the Westside), and local trips on the Slauson corridor. It’s a flexibility that modernized regional rail has, and that other modes of transportation, which can’t mix local and intercity traffic as well, lack. Leaving California, let us look at New York. There are perennial proposals for a new connection to LaGuardia (via an extension of the N) and an additional connection to JFK (usually using the Rockaway Cutoff). There is also a new proposal for a Newark connection via PATH. With the distinction between short-distance domestic and long-distance international airports (Newark is intermediate between the two), we can analyze these proposals. Newark is the easiest to dispose of: the cost is extreme,$1.5 billion for 4 km above ground. It also has several design flaws: unlike the LAX connector I outlined above, this proposal is nonstop from Newark Penn, skipping the former South Street railroad station; the lack of intercity service improvement and the poor service to the Midtown hotel clusters doom it as a CBD connector.

The JFK proposals are problematic as well. The AirTrain connection to Jamaica is quite useful, since it lets people from all over Long Island connect to the airport. Improving JFK access hinges on improving service to Jamaica, then: through-service from New Jersey, higher off-peak LIRR frequencies, reelectrification with catenary to permit Amtrak send Northeast Corridor trains that aren’t needed for Boston service to Jamaica. East Side Access improves JFK access as well, since it allows LIRR trains to serve Grand Central, which is closer to the Midtown hotel clusters than Penn Station. Ideally there wouldn’t be an AirTrain connection, but it’s the best that can be done given existing infrastructure and given Jamaica’s importance. A Rockaway Cutoff connection, which branches from the LIRR Main Line west of Jamaica, would not help Long Islanders go to JFK; it would also not be able to carry intercity trains, since Amtrak trains to Jamaica can serve both airport riders and Long Island riders, each of which groups alone is too small to justify intercity trains on its own.

In contrast, LaGuardia proposals are better, since for a close-in, domestic airport, service to the entire city is more important. I remain somewhat skeptical – airport connectors are still overrated – but less dismissive than of Newark and JFK proposals. LaGuardia travelers from the Upper East Side, which as far as I remember supplies a majority of its departing traffic, would have to transfer at 59th Street; but they have to detour through 59th or 125th via taxi already, and the subway would not get stuck in Manhattan traffic. Conversely, there is much less need to connect the airport with the suburbs and with neighboring metro areas than there is with JFK, which means that there is no point in constructing people movers to the LIRR.

Finally, let us look at Chicago. O’Hare has the airport connection of a domestic airport rather than that of an international airport. There are plans for an express link to the Loop, but these do nothing for departing passengers from neighboring areas. While airport connectors tend to be overrated, express premium-fare links are especially overrated, since they give business travelers dedicated trains, on which they always find seats, without needing to commingle with lower-income riders.

However, some of the Midwestern high-speed rail proposals include a connection to O’Hare from the outlying metro areas, and this is good planning, assuming the cost is not excessive. SNCF’s proposal includes a bypass of Chicago that serves O’Hare, similar to the Interconnexion Est. A second step, if such a connection is built, is to attempt to connect regional lines to it, if they are electrified. This includes both inward connections, i.e. a frequent commuter rail connection to the Loop or West Loop with good connections (ideally, through-service) to other commuter lines, and outward connections, i.e. low-speed short-distance intercity lines, such as to Rockford.

In all of these cases, the common thread is that the connection to the airport does not need to be a premium service, marketed only to the business traveler. These services are never the majority of airport transit ridership: see Hong Kong, Tokyo, and London numbers on PDF-p. 28 here. However, it does need to provide service to both departing and arriving passengers, and for a major international airport, this requires good service to the suburbs and to adjoining metro areas. The optimal technologies are often bundled together with premium fares – high-speed rail is in many countries, mainline rail is in North America – but the benefits come from features of the technology and service pattern, rather than of the branding. Good transit projects connecting to airports will make sure to have the correct service reach, while at the same time not excluding local riders.

# Underrated Transit Projects

In between the airport connectors and mixed-traffic streetcars are some public transit proposals that would be potentially high-performing. This is a list of potential lines in the US that don’t get nearly the exposure that they deserve.

The basic rule of this post is that if it’s being built, or is on an official urban wishlist pending finding the budget for it, then it’s not underrated. Some of the most important transit projects in North America are in this category: Second Avenue Subway’s current and future phases, the Regional Connector, the UBC SkyTrain extension. What I’m interested in is lines that are only vaguely on any official wishlist, if at all, but could still get very high ridership compared to their length. It is possible that these underrated lines would turn out to be worse-performing if a study were undertaken and the costs turned out to be very high, but in no case was there an honest study. Sometimes there has been no recent study; other times there is one but it sandbags the project.

Finally, I am not including commuter rail projects on this list. Under current regulations and operating practices, nearly all North American commuter rail projects are wastes of money. Conversely, nearly all projects that assume modernization of practices are underrated. This swing, based almost entirely on organizational question, is why I’m excluding these projects from this list. The subway and light rail projects below are less sensitive to organizational questions.

Utica Avenue Subway

Location: New York

Concept: an extension of the 4 from Crown Heights along Utica Avenue to Kings Plaza, about 7 km. If Second Avenue Subway’s Phases 3 and 4 are built, then a branch can be built from Second Avenue to Williamsburg and thence under Bushwick, Malcolm X, and Utica, taking over the entirety of the line, with the 4 cut back to its current terminus; this is an additional 9 km to Second and Houston.

Why it’s underrated: the second busiest bus route in New York, the B46, follows Utica: see here for New York bus route rankings. The busiest follows First and Second, which are getting a subway. Two additional routes in the top ten, the B44 and the B41, follow Nostrand and Flatbush respectively, fairly close to Utica. The B46 has 48,000 weekday riders and the B41 and B44 have another 70,000 between them. Since subways are much faster than city buses, the expected ridership is much higher than 120,000, measured in multiples rather than in a percentage increase. In addition, the 2, 3, 4, and 5 are all busier coming to the Manhattan core from Uptown than from Brooklyn, so adding to their ridership from the Brooklyn end balances the loads better, and avoids the required increase in operating costs for the new riders.

What is being done right now: nothing.

Geary Subway

Location: San Francisco

Concept: a full subway from Market Street to the Outer Richmond District, about 9 km. This can connect to the BART subway, the Muni Metro tunnel, or a second Transbay Tube if one is built.

Why it’s underrated: the 38-Geary is the busiest bus route in San Francisco, with 57,000 weekday riders between the local, the limited, and the express buses: see here for San Francisco bus ridership. Parallel corridors are also busy: the 1-California has 29,000, the 31-Balboa has 10,000, and the 5-Fulton has 17,000. Some of the census tracts along the middle of the route, in Little Osaka Japantown, rank together with Los Angeles’s Koreatown as the densest in the US outside New York. BART’s current limiting factor is not the Transbay Tube, but the grades farther south in San Francisco, which lengthen the braking distance and make it impossible to run a full 30 trains per hour through the core segments; a Geary branch leaving south of Montgomery Street would reduce service to points farther south, but improve capacity for riders heading from Oakland to the San Francisco CBD.

What is being done right now: there were never subway plans, but there were light rail plans, which due to local merchants’ opposition to loss of space for cars were downgraded to a rapid bus. The city’s FAQ on the subject even has the cheek to portray the Boston Silver Line and the Los Angeles Orange Line as successes.

Downtown Relief Line

Location: Toronto

Concept: there are several different alignments, but all feature an east-west line somewhere between Queen Street and Union Station, with one or two bends to the north to intersect the Bloor-Danforth Line. The latter two alignments (using option 4B for the second one) feature about 12 km of tunnel; I do not know how much the first one has.

Why it’s underrated: only one subway line serves Downtown Toronto, the Yonge-University-Spadina Line. Bloor-Danforth is too far from the CBD, and requires a transfer. The transfer points are very crowded: as far as I can tell from this list, the central one, Bloor-Yonge, has 200,000 weekday boardings, apparently including transfers. Without figures that include transfers in other cities I can’t make comparisons, but I doubt any two-line, four-track station in New York has this many riders. Union Station is quite crowded as well, and DRL proposals include transfers to outlying commuter rail stations. Ridership on parallel streetcars is very high: there are 53,000 on King Street, 44,000 on Queen, and, if a more northern alignment for the DRL is chosen, 32,000 on Dundas.

What is being done right now: more studies; construction will almost certainly begin any decade now. Neither David Miller’s Transit City light rail proposal nor Rob Ford’s replacement of Transit City with subways included the DRL.

125th Street Subway

Location: New York

Concept: either Phase 5 or Phase 2.5 of Second Avenue Subway, going west along 125th to Broadway, with a station at each intersection with an existing north-south subway.

Why it’s underrated: east-west transportation in Manhattan is slow, even by the standards of Manhattan buses. The 125th Street buses in my experience are slower than walking; despite this, the various routes have about 90,000 weekday boardings between them, of which about 30,000 come from 125th Street itself. Second Avenue Subway Phase 1 is going to substantially improve east-west transportation, by serving Times Square and offering a two-seat ride from the Upper East Side to the Upper West Side and Central and West Harlem; however, passengers from East Harlem will still have to take a major detour to avoid the crosstown buses. While SAS offers a relief to the 4/5 and 6 lines, the 2/3 and A/D express lines are overcrowded as well, and a connection at 125th Street would divert some East Side-bound commuters.

What is being done right now: nothing, although (some) railfans who work at the MTA privately want to see such a line built.

Silver Line Light Rail

Location: Boston

Concept: replacement of the Silver Line buses along Washington Street with light rail, feeding into an existing Green Line portal, about 4 km of light rail.

Why it’s underrated: the Silver Line buses are the busiest in Boston, with 15,000 weekday riders on the buses to Dudley Square: see PDF-pp. 47-48 of the MBTA Blue Book. The ridership doesn’t justify a subway, but does justify dedicated lanes and rail. The Green Line tunnel has some spare capacity, has a portal pointing in the correct direction, and could take an additional train every 6 or 7 minutes, which would give riders in Roxbury faster trips through Downtown Boston.

What is being done right now: nothing – a study sandbagged the rail bias factor and assumed only 130 new transit riders on a Silver Line light rail service, making the project appear cost-ineffective.

Triboro RX

Location: New York

Concept: a circumferential subway line, with about 1 km of new tunnel and 35 km of route on preexisting rights-of-way, abandoned or lightly used by freight trains today.

Why it’s underrated: the biggest cost driver, right-of-way formation, is already present. The right-of-way in question has a few daily freight trains, but the most critical link, the Hell Gate Bridge, is four-tracked, and freight trains can be kicked out from their segment of the bridge and moved to the Amtrak tracks. The work done by Michael Frumin and Jeff Zupan in the late 1990s estimated about 150,000 commute trips per weekday (76,000 commuters each making a roundtrip per day), which is low for a greenfield line of this length but reasonable for a line on existing rights-of-way.

What is being done right now: nothing, although ever since Lee Sander mentioned the line in 2008, politicians have paid lip service to the concept, without committing funding.

Boston Circumferential Line

Location: Boston

Concept: a circumferential subway, from Harvard Square to Dudley Square or the JFK-UMass subway stop, roughly following the 66 bus route where it runs and intersecting the busiest stops of the Green Line branches and some commuter rail stops. This is about 12 km.

Why it’s underrated: although the busiest Boston bus is the Silver Line to Dudley Square, the next few are circumferential, particularly the 1 and 66, and secondarily the 23 and 28; together this is about 50,000 riders. Boston’s street network is hostile to surface transit except on a few major streets such as Washington, which is why there is no hope of making such a line light rail, which would fit the projected ridership better. A route that parallels the 66, at least until it hits the E branch of the Green Line, would intersect the B, C, and D branches at their busiest respective surface stops, and improve connectivity to Cambridge, which is increasingly a major business district of the Boston region in its own right.

What is being done right now: BRT, on convoluted alignments that don’t exactly follow either the 66 or the 1 where they are parallel but instead make detours.

Nostrand Avenue Subway

Location: New York

Concept: an extension of the 2/5 from Flatbush to the southern end of Nostrand Avenue, about 5 km.

Why it’s underrated: all the reasons that make Utica so strong apply to Nostrand secondarily; the present bus ridership may be high enough to support two subway lines rather than one. The present terminus was built as a temporary one, which is why it has side platforms rather than an island platform.

What is being done right now: nothing.

# The Metro-North Accident and Train Control

Early in the morning on Sunday, a Metro-North train derailed on the Hudson Line, immediately south of the junction with Amtrak’s Empire Connection: maps of the derailment area can be found on the BBC, while The LIRR Today has a map and a diagram with speed limits. Four cars overturned, and four people died while more than 70 others were injured. The train was going at 82 mph (132 km/h) through a tight curve at Spuyten Duyvil with a 30 mph limit; the speed limit on the straight segment before the curve is 75 mph according to Rich E. Green’s map, which may be a few years out of date, and 70 mph according to the first New York Times article about the derailment. The curve radius appears to be 230 meters on Google Earth, putting the lateral acceleration rate at 5.8 m/s^2, minus a small amount of superelevation (at most 0.8 m/s^2, or 125 mm, to perfectly match the centrifugal force at the curve’s speed limit, and likely lower); the cutting edge of tilting trains allows about 2 m/s^2 lateral acceleration (see PDF-p. 2 of this article about the Pendolino), or 300 mm cant deficiency.

Initial reports of a mechanical brake failure seem unfounded: a National Transportation Safety Board briefing mentions that the brakes had functioned properly on brake tests and at previous stops on the journey (starting at 00:40 in the video). The focus is now on human error: the NTSB refused to say this outright, but beginning at 03:00 in its briefing video it trumpets positive train control as something that “could have” prevented the accident. Rick Gallant, who led California’s rail regulatory agency at the time of the 2005 Glendale crash, is also quoted as saying positive train control “probably could have” prevented the accident on NBC. Moreover, the train driver is quoted as having told investigators “he had become dazed before the accident, suffering what his lawyer referred to as ‘highway hypnosis.'” Metro-North’s spokeswoman made the strongest statement: “if the accident was caused by speeding, positive train control would have stopped it.”

It is extremely likely that a robust train control system would have prevented the accident, as it is capable of slowing the train sufficiently before it reaches a speed restriction. The bulk of this post will be dedicated to talking about what train control systems can do. There’s a large array of acronyms, some of which mean different things in different countries, and one of which has two different meanings.

Broadly speaking, train control can prevent two types of dangerous driving: crashing into another train on the same track, and excessive speeding. If the system detects dangerous behavior, it will automatically stop or slow down the train. Driverless trains are based on robust enough systems that are so automated they no longer need the driver. The hard part is having an on-board system figure out whether the train is traveling too close to another train or too fast, which requires communication with the signaling system; automatically slowing the train down is comparatively easy. In nearly all cases, the signals are static and embedded in the track systems, but in a few, usually high-frequency subways rather than mainline rail, the system directly communicates with the train ahead on the same track (this is moving block signaling, or communication-based train control).

It is century-old technology to stop a train that is about to enter a segment of track too close to another train (“signal passed at danger,” or SPAD). A train’s steel wheels close an electric circuit that detects whether there is a train on a block of track, and this communicates to the signals entering this block of track to prohibit trains from proceeding; see diagrams in the moving-block signaling link, which also show how it works in the more common fixed-block setup. A situation that electrically insulates the train from the track is therefore extremely dangerous and may lead to line shutdowns for safety. Any system with the capability to stop a train in such a situation is called automatic train stop, or ATS. The 79 mph speed limit on nearly all passenger train lines in the US comes from a 1947 regulation by the Interstate Commerce Commission (which has since morphed into the FRA) requiring ATS or in-cab signaling at higher speed; the intention was to force the railroads to install ATS by threatening a crippling speed limit, not to actually reduce train speed.

It is much harder to enforce speed limits. ATS systems do not have to enforce speed limits: at Amagasaki, there was an ATS system that would have stopped a train running a stop signal (as it had earlier on the trip), but no protection from excessive speeding, which is what led to the crash. The signaling system needs to be able to communicate both permanent and temporary speed restrictions. It is nontrivial to maintain an up-to-date database of all speed restrictions on an on-board computer, or alternatively communicate many different speeds from wayside track signals to the train’s computer.

In 2008, the FRA mandated positive train control (PTC) as a result of the Chatsworth crash; PTC is a term that doesn’t exist outside North America, and refers to an automatic train control system capable of not just ATS but also enforcement of all speed restrictions. In Europe it is called automatic train protection, or ATP, and in Japan it is called automatic train control, or ATC. It is common in the US to do trackwork on one track of a multiple-track railroad and slap a temporary speed restriction on adjacent track, and enforcing such limits to protect wayside workers is specifically part of PTC.

Because the ATC system requires trainside equipment, a train that travels between different systems will need more equipment, raising its cost. In Europe, with its hodgepodge of national standards, some international trains require 7 different systems, raising locomotive costs by up to 60%. This led to the development of a unified Europe-wide standard, European Train Control System (ETCS), which combined with GSM radio for communication between lineside signals and the train is called European Rail Traffic Management System (ERTMS). The obligatory cost and schedule overruns of any IT project have plagued this system, and led to delays in installing train protection on some lines, which led to a fatal accident in Belgium. However, the agony of the ERTMS project has for the most part already passed, and now there is a wide variety of vendors manufacturing equipment to the specified standards, leading to widespread installations on new and upgraded lines outside Europe. As of September of 2013, ETCS is installed on 68,000 track-km and 9,000 vehicles worldwide.

Although ETCS is an emerging global standard (outside Japan, which has a vast system of domestic ATC with multiple domestic vendors), American agencies forced to install PTC have not used it. California HSR is planning to use ETCS, and Amtrak’s signaling system on much of the Northeast Corridor, Advanced Civil Speed Enforcement System (ACSES), with full implementation on the Northeast Corridor expected by this year, is similar to ETCS but not the same. Elsewhere in the US, systems have been bespoke (e.g. on Caltrain), or based on the lower-capacity systems used by the freight operators.

Metro-North does not have PTC. It has an ATS system that protects against SPAD, but can only enforce one speed limit, the maximum speed on the line (MAS). As the maximum speed on the outer Hudson Line is 90 mph, the system cannot enforce any lower speed, and so the train could travel at 82 mph even in 70 or 75 mph territory, let alone 30 mph territory. More modern systems can enforce several speed limits (e.g. the TGV’s TVM), and the most modern can enforce any speed limit, in 1 km/h or 1 mph increments.

Metro-North and the LIRR have been trying to wrangle their way out of the PTC mandate, saying it offers “marginal benefits”; a year and a half ago, the New York Post used the word “outrageous” to describe the PTC mandate, saying it would cost over a billion dollars and that the money could go to capacity improvements instead, such as station parking. Lobbying on behalf of Metro-North and the LIRR, Senator Charles Schumer made sure to amend a proposed Senate transportation bill to give the railroads waivers until 2018, so that they could devote resources to more rush hour capacity from the outer suburbs (such as Ronkonkoma) to Manhattan and fewer to safety. According to Siemens, the work will actually take until 2019, and Siemens says it “has developed PTC specifically for the North American market,” in other words built a bespoke system instead of ETCS. (ACSES was developed by Alstom.)

Because the systems developed for the US are based on the needs of American freight railroads and perhaps Amtrak, which do not need as much capacity in terms of trains per hour as the busiest commuter lines, they are much lower-capacity than those used in Europe. The LIRR and Metro-North have far busier mainline tracks than any other US commuter rail system with the exception of the inner part of New Jersey Transit, which is equipped with ACSES as part of the Northeast Corridor; to modify the system to their needs raises costs, as per the New York Post article. The MTA released the following statement (see also mirrors on Fox and CBS):

The MTA began work to install Positive Train Control on the Long Island Rail Road and Metro-North Railroad in 2009. To date, the MTA has budgeted nearly $600 million for elements of PTC installation, including a$428 million procurement last month for a system integrator. Full implementation is estimated to cost $900 million, and the MTA will make sure the appropriate funding is made to implement PTC on the most aggressive schedule possible. However, implementing PTC by the 2015 deadline will be very difficult for the MTA as well as for other commuter railroads, as the Federal Railroad Administration (FRA) and the Government Accountability Office (GAO) have both concluded. Much of the technology is still under development and is untested and unproven for commuter railroads the size and complexity of Metro-North and LIRR, and all of the radio spectrum necessary to operate PTC has not been made available. The MTA will continue its efforts to install PTC as quickly as possible, and will continue to make all prudent and necessary investments to keep its network safe. Of course, the technology is no longer under development or untested. Just ask the Belgians, the Swiss, the Chinese, the Saudi, or the Taiwanese. Older technologies meeting the definition of PTC exist practically everywhere on mainline trains in the European and Asian first world. Urban commuter lines in Tokyo such as the Tokaido Main Line and the Yamanote Line, each with more ridership than all North American commuter lines combined, are equipped with ATC. The RER A, with slightly less ridership than all North American commuter lines combined, has a train control system providing moving-block signaling capability on the central trunk. A Swiss mainline with 242 passenger and freight trains per day and minimum train spacing of 110 seconds at 200 km/h has ERTMS as its only ATP system, and Switzerland expects to fully equip its network with ERTMS by 2017. Although the US mainline rail system is freight-primary, with different needs from those of Europe south of Scandinavia (e.g. critical trunk lines are thousands of kilometers long and lie in sparsely-populated territory), the same can’t be said of the Northeastern commuter rail lines, most of which only see a few daily freight trains and are dominated by tidal flows of commuter trains with high traffic density at rush hour. Rush hour traffic levels approaching 20 tph per track are routine, with 24-26 on the Northeast Corridor entering Penn Station from New Jersey. It is incompetent to try to adapt a system developed for long-distance low-cost freight railroads and ignore one developed for busy commuter lines just because it has an E for European in its name. While most European countries have long implementation timelines coming from a large installed base of good but not top-line legacy signaling, countries with inferior systems sometimes choose to replace their entire signaling systems, as the passenger-primary parts of the US should. Denmark, whose intercity rail far lags that of most peer European countries, decided to replace its signaling system entirely with ERTMS. The projected cost is €3.2 billion, of which €2 billion is for ERTMS on the network, €400 million is for equipping the Copenhagen S-Bahn with CBTC, and €800 million is contingency; the total length of the system is 2,132 route-km and 3,240 track-km. At a million euros per route-km, exclusive of contingency, Metro-North could install the system on all east-of-Hudson lines, except the New Haven Line, where Amtrak plans to install ACSES, for about$450 million, and the LIRR could install the system on its entire system (including parts currently without any signaling) for about $650 million. Denmark has about 700 trainsets and locomotives to install the system on, in addition to tracks; on the LIRR and Metro-North, those figures are about 150 each, although this assumes that trainsets would be permanently coupled, whereas today they run in married pairs, so that in an eight-car unit there are four cabs where only two are needed. If the LIRR and Metro-North agreed to treat trains as permanently-coupled sets, then the scope of the order would be about 40% of the size of the Danish fleet, consistent with a total cost of about a billion dollars. This would also allow higher capacity than the current systems, which could squeeze more trains onto busy lines, so it wouldn’t be at the expense of capacity improvements. In particular, the LIRR could keep postponing the$1.5 billion Main Line third track to Hicksville project, and instead run trains on the currently double-track bidirectionally (today they run one-way at rush hour, to accommodate local and express service) using the very high frequency that ETCS permits. Another project, which Sen. Schumer thinks is more important than PTC, a $400 million plan to double-tracking the outer part of the Main Line from Farmingdale to Ronkonkoma, could also be postponed while still providing the necessary capacity. Although both of the LIRR multi-tracking projects’ cost figures are enormous – the third track is about$100 million per kilometer, almost what a subway in suburbia should cost, and the outer second track is $15 million per km, more reasonable but still very high – adding tracks is in general more expensive than adding signals. IT procurement is expensive and prone to cost overruns, but once the initial system has been developed, the marginal cost of implementing it in new but similar environments is relatively low; ETCS would cost about the same on the LIRR and Metro-North as the MTA plans to spend on signaling, but provides better functionality as it’s compatible with their high traffic density. Organisation vor Elektronik vor Beton. Of course the first step in the organization before electronics before concrete slogan is improving the state of the organization. In terms of safety, there may be scope for better training, but the train driver according to the NTSB has 10 years’ experience (start at 02:20 in the video) and based on his work schedule would have had enough time to get a full night’s sleep before his shift started (start at 07:25). Since there is no obvious organizational way to further improve safety, electronics is the next step, and this means installing a good PTC system in a timely manner. However, in terms of cost, there is something to be done. While the MTA claims PTC is too expensive and provides little benefit, Metro-North spent$80 million a year on conductors’ salaries in 2010 (although it’s been going down, to about $65 million by 2012) and the LIRR spent another$95 million (in either 2010 or 2012), both numbers coming from the Empire Center’s SeeThroughNY. About six years’ worth of conductor salaries would pay for full PTC; future savings are free. The NTSB briefing said there were 4 conductors on the train (start at 09:15). The main duty of conductors is to sell, check, and punch tickets, an old-time rail practice that has been abolished in modern commuter railroads throughout the first world.

A commuter train needs between 0 and 1 conductor. Stephen Smith quotes Vukan Vuchic, a professor of transportation engineering at Penn who was involved in the implementation of SEPTA’s through-running in the 1980s, as saying that ticket-punching is “extremely obsolete” and “very 19th century.” A tour of any of the major urban commuter rail systems of Europe will reveal that a few, such as the Paris RER and the London systems, use turnstile, while most use proof-of-payment, in which roving teams of ticket inspectors only check a small proportion of the trains, slapping fines on people caught without a valid ticket. On American light rail lines, which are often similar in role to German commuter rail lines (especially tram-trains) except that they run on dedicated greenfield tracks, this is routine; this can and should extend to commuter mainlines. While the electronics is needed to handle safety, this organizational improvement would pay for the electronics.

Although the investigation seems to be going in a competent manner, the MTA’s position on the relevant issues in general does not come from a position of competence. It is not competent to have this many redundant employees but then cry poverty when it comes to avoiding crashes and derailments. And it is not competent to pretend that there is nothing in Europe or Japan worth using for American signaling systems. The US did not invent PTC – at most, it invented the term for what’s called ATP or ATC elsewhere. It shouldn’t act like it’s the only place in the world that uses it.