Category: Good Transit

When Buses are a Poor Guide to Corridor Demand

Vancouver is going to open the Evergreen Line at the end of the year, an 11-km SkyTrain branch to Coquitlam with a projected ridership of 70,000 per weekday; current ridership on the B-line bus paralleling the route, the 97, is 11,000, the 20th busiest citywide (see data here).

New York is going to open the first phase of Second Avenue Subway at the end of the year or early next year, a total of 4 km of new route with projected ridership of 200,000 per day (see pp. 2-3). The bus running down First and Second Avenues, the M15, has 46,000 weekday riders, trading places with two other routes for first citywide, but first phase only covers a quarter of the route, and the ridership projection in case the entire Second Avenue Subway is built is 560,000; nobody expects the other two top bus routes in New York, the B46 on Utica and the Bx12 on Fordham, to support such ridership if they’re ever replaced with subways.

In Boston, the Green Line Extension northwest in Somerville is projected to have 52,000 weekday riders by 2030. There is no single parallel bus, but a few buses serve the same area: the 101 with 4,800 weekday riders, the 89 with 4,200, the 88 with 4,100, and the 87 with 3,800 (all bus ridership data is from the Bluebook, PDF-pp. 48-54); the busiest of these ranks 28th regionwide.

In all three cases, I think the ridership estimates are reasonable. Vancouver especially has a good track record, with Canada Line ridership meeting projections; it’s harder to tell in New York and Boston, which have not opened a rail line recently (New York’s 7 extension was just one stop, and its predicted ridership explicitly depends on future development). Since in general I do think cities should plan their rail extensions around where the busiest buses are, I want to talk about the situations that create a disjunction.

I mentioned in two past posts that rapid transit that surface transit and rapid transit alignments obey different rules, with respect to street geometry. In the more recent post, I used it to argue that tramway corridors should follow buses. In the older post, I argued that subways can take minor detours or go under narrower, slower streets to reach major destinations, for example Century City in Los Angeles, which is near the Wilshire corridor but not on it. However, the latter case isn’t quite what’s happening in any of the three examples here: Second Avenue Subway follows Second Avenue (though phases 1-2 diverge west to serve Times Square, which is important), and the Green Line Extension and Evergreen Line’s routes are both straighter than any bus in the area.

The situation in Boston and Vancouver is not that there’s an arterial bus that misses key destinations. Rather, it’s that the street network is inhospitable to buses. Boston is infamous for its cowpaths: only a few streets, such as Massachusetts Avenue, are wide and long enough to be reasonable corridors for arterial buses, and as a result, the bus network only really works as a subway feeder, with very high rail to bus ridership ratio by US standards. The corridors that do support busier buses – in the Greater Cambridge sector, those are the 77, 71, and 73 buses – are defined by the presence of continuous arterials more than by high latent travel demand.

Vancouver, of course, is nothing like Boston. Its bus grid is Jarrett Walker‘s standard example of an efficient, frequent bus grid. But this is only true in Vancouver proper, and in parts of Burnaby. In the other suburbs, either there’s an arterial street grid but not enough density for a good bus grid (Richmond, Surrey), or there’s no grid at all (Coquitlam). There’s a bus map of the Port Moody-Coquitlam area, with the 97-B line in bright orange and the 5-roundtrips-per-day West Coast Express commuter rail line in purple; the Evergreen Line will run straight from Port Moody to Coquitlam along an alignment parallel to the railroad, whereas the 97-B has to take a detour. Overall, I would class Coquitlam and Somerville together, as places where the street network is so bad for buses that rail extensions can plausibly get a large multiple of the ridership of existing buses.

Second Avenue Subway phase 1 partly belongs in this category, due to the difficulty of going from Second Avenue to Times Square by road, but high projected ridership on phase 3 suggests something else is at play as well. While First and Second Avenues are wide, straight throughfares, functioning as a consistent one-way pair, two factors serve to suppress bus ridership. First, Manhattan traffic is exceedingly slow. The MTA is proud of its select bus service treatments, which boosted speed on the M15 between 125th and Houston Streets to an average of about 10 km/h; in contrast, the Bx12 averages 13-14 km/h west of Pelham Bay Parkway. And second, the Lexington Avenue Line is 360 meters, so riders can walk a few minutes and get on the 6 train, which averages 22 km/h. The Lexington trains are overcrowded, but they’re still preferable to slow buses.

Now, the closeness to the Lexington trains can be waved away for the purposes of the principle of this post: I am interested in where preexisting transit ridership is not a good guide to future transit ridership, and in this example, we see the demand via high ridership on the 4, 5, and 6 trains. However, the issue of slow Manhattan traffic can be folded generally into the issue of circuitous street networks in Boston and Coquitlam.

It makes intuitive sense that the higher the bus-to-rail trip time ratio is, the higher the rail line’s ridership is relative to that of the bus it replaces. But what I’m saying here goes further: the two mechanisms at hand – a street network that lacks continuous arterials in the desired direction, and extensive traffic congestion – reduce the effectiveness of any surface solution. Is it possible to build tramways in the Vancouver suburbs? Yes. But in Coquitlam (and in Richmond and Surrey, for different reasons), they would be circuitous just like the buses. This also limits the ability of bus upgrades to solve transportation problems in such areas.

Now, what of New York? In theory, a bus or tram with absolute signal priority could run down the Manhattan avenues or the major outer-borough throughfares at high speed. But in practice, there is no such thing as absolute signal priority on city streets. It’s possible to speed up surface vehicles via signal priority, but they’ll still have to stop if cross-traffic blocks the intersection. In Paris, the tramways are not fast, averaging around 17-18 km/h, even though they have dedicated lanes and run on wide boulevards in the outer parts of the city and in the inner suburbs; in contrast, Metro Line 14, passing through city center, averages almost 40 km/h.

The implication here is that when a city develops its subway network, it should pay attention not just to where its busiest surface lines are, but also to which areas have intense activity but have suppressed surface ridership because the roads are slow or circuitous. These are often old city centers, built up before there were cars and even before there was heavy horse wagon traffic. Other times, they are general areas where the road network is not geared toward the desired direction of travel.

In cities without subways at all, there is a danger of overrelying on surface traffic, because such cities often have old cores with narrow streets, with intense pressure for auto-oriented urban renewal as they get richer. This is less common in the developed world, but nearly every developed-world city of note either has a rapid transit network already or is completely auto-oriented and has no areas where the road network is weak. Israel supplies several exceptions, since its transportation network is underdeveloped for how rich it is; in past posts I have already voiced my criticism of the decision to center the Tel Aviv Subway around wide roads rather than the older, often denser parts of the city.

In cities with subways, it’s rarely a systemic problem. That is, there’s rarely a specific type of neighborhood that can support higher rapid transit ridership than preexisting transit ridership would indicate. It depends on local factors – for example, in Somerville, the railroads are oriented toward Downtown Boston, but the streets are not, nor are they oriented toward good transfer points to the subway. This means transit planners need to carefully look at the road network for gaps in the web of fast arterials, and consider whether those gaps justify transit investment, as the GLX and Evergreen Line do.

Train Weight and Safety

A recent New Jersey Transit train accident, in which one person was killed and more than a hundred was injured, has gotten people thinking about US rail safety again. New Jersey has the second lowest fuel tax in the US, and to avoid raising it, Governor Chris Christie cut the New Jersey Transit budget (see PDF-pp. 4-5 here); perhaps in reaction to the accident, Christie is announcing a long-in-the-making deal that would raise the state’s fuel tax. But while the political system has been discussing funding levels, transit advocates have been talking about regulations. The National Transportation Safety Board is investigating whether positive train control could have prevented the accident, which was caused by overspeed. And on Twitter, people are asking whether Federal Railroad Administration regulations helped protect the train from greater damage, or instead made the problem worse. It’s the last question that I want to address in this post.

FRA regulations mandate that US passenger trains be able to withstand considerable force without deformation, much more so than regulations outside North America. This has made American (and Canadian) passenger trains heavier than their counterparts in the rest of the world. This was a major topic of discussion on this blog in 2011-2: see posts here and here for an explanation of FRA regulations, and tables of comparative train weights here and here. As I discussed back then, FRA regulations do not prevent crumpling of passenger-occupied space better than European (UIC) regulations do in a collision between two trains, except at a narrow range of relative speeds, about 20-25 mph (30-40 km/h); see PDF-pp. 60-63 of a study by Caltrain, as part of its successful application for waivers from the most constraining FRA regulations. To the extent people think FRA regulations have any safety benefits, it is purely a stereotype that regulations are good, and that heavier vehicles are safer in crashes.

All of this is old discussions. I bring this up to talk about the issue of systemwide safety. Jacob Anbinder, accepting the wrong premise that FRA regulations have real safety benefits, suggested on Twitter that rail activists should perhaps accept lower levels of rail safety in order to encourage mode shift from much more dangerous cars toward transit. This is emphatically not what I mean: as I said on Twitter, the same policies and practices that lead to good train safety also lead to other good outcomes, such as punctuality. They may seem like a tradeoff locally within each country or region, but globally the correlation goes the other way.

In 2011, I compiled comparative rail safety statistics for the US (1 dead per 3.4 billion passenger-km), India (1 per 6.6 billion), China (1 per 55 billion), Japan (1 per 51 billion), South Korea (1 per 6.7 billion), and the EU (1 per 13 billion), based on Wikipedia’s lists of train accidents. The number for India is an underestimate, based on general reports of Mumbai rail passenger deaths, and I thought the same was true of China. Certainly after the Wenzhou accident, the rail activists in the developed world that I had been talking to stereotyped China as dangerous, opaque, uninterested in passengers’ welfare. Since then, China has had a multi-year track record without such accidents, at least not on its high-speed rail network. Through the end of 2015, China had 4.3 billion high-speed rail passengers, and by 2015 its ridership grew to be larger than the rest of the world combined. I do not have statistics for high-speed passenger-km, but overall, the average rail trip in China, where there’s almost no commuter rail, is about 500 km long. If this is also true of its high-speed rail network, then it’s had 2.15 trillion high-speed passenger-km, and 1 fatality per 54 billion. This is worse than the Shinkansen and TGV average of zero fatalities, but much better than the German average, which is weighed down by Eschede. (While people stereotype China as shoddy, nobody so stereotypes Germany despite the maintenance problems that led to the Eschede accident.)

I bring up China’s positive record for two reasons. First, because it is an example of how reality does not conform to popular stereotypes. Both within China and in the developed world, people believe China makes defective products, cheap in every sense of the term, and compromises safety; the reality is that, while that is true of China’s general environmental policy, it is not true of its rail network. And second, China does not have buff strength requirements for trains at all; like Japan, it focuses on collision avoidance, rather than on survivability.

The importance of the approaches used in Japan and on China’s high-speed rail network is that it provides safety on a systemwide level. By this I do not mean that it encourages a mode shift away from cars, where fatality rates are measured in 1 per hundreds of millions of passenger-km and not per tens of billions. Rather, I mean that the entire rail network is easier to run safely when the trains are lighter.

It is difficult to find exact formulas for the dependence of maintenance costs on train weight. A discussion on Skyscraper City, sourced to Bombardier, claims track wear grows as the cube of axle load. One experiment on the subject, at low speeds and low-to-moderate axle loads, finds a linear relationship in both axle load and speed. A larger study finds a relationship with exponents of 3-5 in both dynamic axle load and speed. The upshot is that at equal maintenance cost, lighter trains can be run faster, or, at equal speed, lighter trains make it easier to maintain the tracks.

The other issue is reliability. As I explained on Twitter, the same policies that promote greater safety also make the system more reliable, with fewer equipment failures, derailments, and slowdowns. On the LIRR, the heavy diesel locomotives have a mean distance between failures of 20,000-30,000 km, and the medium-weight EMUs 450,000 (see PDF-pp. 21-22 here). The EMUs that run on the LIRR (and on Metro-North), while heavier than they should be because of FRA requirements, are nonetheless pretty good rolling stock. But in Tokyo, one rolling stock manufacturer claims a mean distance between failures of 1.5 million km. While within Japan, the media responds to fatal accidents by questioning whether the railroads prioritize the timetable over safety, the reality is that the overarching focus on reliability that leads to low maintenance costs and high punctuality also provides safety.

In the US, especially outside the EMUs on the LIRR and Metro-North, the situation is the exact opposite. The mean distance between failures for the LIRR’s diesel locomotives is not unusually low: on the MBTA, the average is about 5,000 km, and even on the newest locomotives it’s only about 20,000 (State of the Commuter Rail System, PDF-pp. 8-9). The MBTA commuter rail system interacts with freight trains that hit high platforms if the boxcars’ doors are left open, which can happen if vandals or train hoppers open the doors; as far as I can tell, the oversize freight on the MBTA that prevents easy installation of high platforms systemwide is not actually oversize, but instead veers from the usual loading gauge due to such sloppiness.

Of course, given a fixed state of the infrastructure and the rolling stock, spending more money leads to more safety. This is why Christie’s budget cuts are important to publicize. Within each system, there are real tradeoffs between cost control and safety; to Christie, keeping taxes low is more important than smooth rail operations, and insofar as it is possible to attribute political blame for such low-probability events as fatal train accidents, Christie’s policies may be a contributing factor. My contention here is different: when choosing a regulatory regime and an overarching set of operating practices, any choice that centers high performance and high reliability at the expense of tradition will necessarily be safer. The US rail community has a collective choice between keeping doing what it’s doing and getting the same result, and transitioning operating practices to be closer to the positive results obtained in Japan; on safety, there is no tradeoff.

When Through-Running Is Inappropriate

I support through-running of regional trains: as far as possible, trains should not terminate in major city centers, but instead run through to urban neighborhoods and suburbs on the other side of the CBD. My first blog posts made this point about New York, and over the years I’ve written about this in the contexts of New York, Boston, Washington, Chicago, and Tel Aviv. However, in secondary cities, through-running is not always appropriate policy. If a city is near the edge and not at the center of its metro area, then quite often it’s preferable to run a separate service, which may overlap the primary city’s regional rail system. In some cases, through-running is actively harmful; unfortunately, this is currently done in San Jose and Providence.

Theory

Consider the following example city:

throughrunexample

The metro area lies on an east-west rail line, and consists of a central city several suburbs; higher-density areas are denoted by darker shades, with the primary CBD in the darkest shade. The city proper also has five secondary CBDs, two of which are on the rail line. On the west, one suburb, really a secondary city, is larger than the rest, and has its own CBD, as job-dense as one of the primary city’s secondary CBDs. With rough symmetry of suburban demand west and east, there is no good reason why trains should not through the primary CBD, and good reasons why they should:

  • People in the eastern suburbs may work in the secondary CBD just west of the primary one, and people in the western suburbs may work in the secondary CBD just east of the primary one.
  • The primary CBD may not have room to park trains at rush hour without a costly railyard expansion.
  • People within the central city may use the line as a rapid transit trunk, to get to either the primary CBD or the two secondary CBDs on the line, as well as to residential neighborhoods not depicted in the diagram.

This is relatively uncontroversial – urban transit is designed along the same guidelines. Also uncontroversial is the question of how far east the commuter line should run: the diagram shows a string of medium-size suburbs, so the line should run as far as the easternmost one, potentially with short-turn runs if the trains at the end are too empty.

The real controversy is how far west to run the service. On the one hand, the secondary city provides a natural outer anchor, with some reverse-peak ridership potential, so there’s an argument for terminating service there. I have criticized the Human Transit model of anchoring as a matter of urban planning, but as a matter of transit planning with fixed urban layout, it is sound; see explanations here and here. On the other hand, there are two smaller suburbs farther west, where people might want to commute to either the primary city or the secondary one, so perhaps service should run farther, with many trains short-turning at the secondary city to avoid running too many empty trains at the western end.

Which of the two options is better – terminating services at the secondary city or continuing onward – depends on the frequency the trunk rail line can support. The reason is that continuing onward requires a very large drop in capacity to avoid empty trains. In the depicted diagram, in relative units, 10% of the western suburbs’ built-up residential area is west of the secondary city; maybe another 10% is the western areas of the secondary city, which could host a station in addition to that at the city’s center. This means that nearly all trains should short-turn; only perhaps one in three or four should continue. If the demand is so intense that a quarter of the base frequency is enough, then trains should continue. But most likely, it isn’t. An individual commuter line with a train every 10 minutes off-peak would be stepped down to every half an hour at the western end, which is borderline; a train every 10 minutes off-peak almost never happens outside Paris, Tokyo, and other enormous systems, except when multiple branches interline to a single trunk.

The alternative is to terminate commuter trains at the secondary city, but then run supplemental service, centered at the secondary city. This supplemental service is not supposed to serve demand into the primary city, handling supercommuters from the western end via a timed transfer (with possible peak through-service), so it can run shorter trains at higher frequency. Sometimes, the secondary city’s CBD must be judged too auto-oriented to be served with commuter rail, and then the correct service pattern is no trains at all west of the secondary city.

Examples

In both Providence and San Jose, a situation akin to the above diagram occurs, except without any through-service beyond the primary CBD (respectively, Boston and San Francisco). Of course, San Jose has more residents than San Francisco, 1.03 million compared with 870,000, but it has only 360,000 jobs to San Francisco’s 610,000. Moreover, San Jose’s employment is more dispersed; according to OnTheMap, its CBD’s job density is about comparable to that of Providence’s CBD. Evidently, Caltrain ridership is 13,600 per weekday at San Francisco and 4,200 at San Jose Diridon (PDF-p. 6 here), with both stations located somewhat away from their respective cities’ CBDs. A proper comparison of Providence to Boston is harder to make, since South Station has multiple line and not just the Providence Line, but Providence’s secondary role within New England is well-understood.

In both cities, service runs beyond the secondary city, at reduced frequency. Between San Francisco and San Jose, Caltrain runs 5 trains per hour at the peak, and a train every hour off-peak; but Caltrain also runs three trains per day in each direction south to Gilroy, 47 km to the south (San Francisco-San Jose is 77 km). Between Boston and Providence, a distance of 70 km, the MBTA runs 3-4 trains per hour at the peak and a train every 1.5-2 hours off-peak, but one train per hour at the peak and one train every four hours off-peak continues another 31 km south to Wickford Junction.

Both tails, to Gilroy and to Wickford Junction, are significant drags on the ability of their respective cores to modernize. Ridership is very low: Tamien, just south of San Jose Diridon, has 1,100 weekday riders, but the sum total of all the stations to its south is 559; the two stations south of Providence have between them 454 weekday riders, compared with about 2,300 at Providence and 20,000 on the Providence Line overall (see PDF-pp. 74 and 77 of the 2014 MBTA Bluebook). In both cases, low ridership is a cause of poor service rather than a consequence: Clem Tillier tallied the population and job densities near each Caltrain station and found that, except in the southern neighborhoods of San Jose, there is no real ridership potential on the Gilroy extension; a similar analysis of the Providence Line’s tail has not been carried out, but one of its two stations is in a low-density suburb without many Boston-bound commuters, while Wickford Junction is surrounded by undeveloped land. Caltrain is currently planning to electrify south to Tamien, but there is no justification for continuing electrification further, which means that maintaining Gilroy service would require mixing diesel locomotive-hauled trains with lightweight EMUs; moreover, south of Tamien, the tracks are owned by Union Pacific rather than by Caltrain, and UP has little interest in allowing modern passenger trains on its tracks. In Rhode Island, an additional complication is that the line from Providence down to Wickford Junction is prime high-speed rail territory, and commuter rail ridership is frankly too low to justify complex scheduling with multiple overtakes, unlike the situation farther north in Massachusetts.

In the Bay Area, there is little that can be done, due to the low potential ridership south of Tamien, San Jose’s suburban layout and the distance of Diridon from the CBD, and UP ownership of the tracks. Perhaps a few diesel trains could run to San Jose Diridon with timed transfers to the electrified line from Tamien to San Francisco, but quite likely service could just be canceled. In Rhode Island, Wickford Junction should probably be closed due to low ridership, but Peter Brassard proposed an alternative, a Providence-focused line running short trains at medium frequency (perhaps once every 15 minutes), with very short interstations in order to serve Providence neighborhoods and not just the CBD. Such a line, running at the same average speed as a freight train due to the frequent stops, would interfere heavily with intercity trains, which means that four-tracking the line is a necessary precondition, as discussed here, but this may be worth it given potential local ridership. The most constrained part of the right-of-way is alongside the Route 10 expressway, which requires considerable repairs and is currently being overhauled at high cost.

Mixing Circumferential and Radial Transit in the Other Direction

Two years ago, I wrote a post criticizing subway lines that mix radial and circumferential elements. These lines, for examples Shanghai Metro Lines 3 and 6 and New York’s G train before 2001, contain long radial segments, going from an outlying neighborhood toward city center, but then switch to circumferential mode, avoiding city center and instead serving secondary nodes. Such lines do not get high ridership, because they fail at either radial or circumferential transit. Recently, I was challenged in comments about my support for a mixed line that goes in the other direction: circumferential on the outside, radial on the inside. I would like to talk more about such lines.

Consider the following diagram of a subway system:

subwaydiagram

The city is shown in light gray, with its center in dark gray. There are five subway lines: the red and blue lines are straightforward radials, the green line is a straightforward circumferential, the yellow line mixes radial and circumferential as criticized in my previous post, the pink line mixes radial and circumferential in the other manner, which I will describe in this post.

The reason the yellow line is going to underperform in this system is that it fails as a radial: it does not go to city center, which has the largest concentration of destinations for transit users. People who have equal access to the red and yellow lines, north and south of city center, are much likelier to choose the red line, which takes them where they want to go. The green line fails as a radial too, but has the positive features of a circumferential: it only serves relatively nearby neighborhoods, which are likely to be denser and produce more riders per unit length; it connects to every line in the system; it allows people to connect between two radial lines without going through the congested city center; it has no dominant direction at the peak, so trains are unlikely to be full in the peak direction and empty in the reverse-peak direction. The yellow line has none of these features, unless one wants to connect between the western legs of the blue and pink lines.

The pink line still works as a radial. Its northeastern leg is a straightforward radial, but even its southwestern leg  works as a radial for people who live west of the yellow line and wish to commute to city center. In this way, it is not truly a mixture of radial and circumferential elements the way the yellow line is, but is simply a radial with a circumferential element tacked on at the end.

Whether the pink line’s circumferential tail works must be evaluated against two alternatives: build nothing, and build a radial leg. This is because in an incrementally-built transit system, the radial parts of the line are typically built first, and the circumferential tail is tacked on as a later extension. In the no-build case, the pink line’s southwestern leg would simply be shorter than the other radial legs in this system. In the radial case, the pink line’s southwestern leg would look symmetric with the northeastern leg. This depends on the following factors:

  1. The strength of the radial alternative. If the radial alternative is strong, then this discourages building the circumferential extension, and vice versa. The radial alternative can be weak in several ways: the southwestern quadrant of the city depicted above may be already replete with radial transit and not need more; the population density in the neighborhoods that would be served by the radial option may be low; and the city’s layout may not be the above-depicted perfect circle, so that there is nowhere for the line to turn except sideways.
  2. The strength of the corridor that would be served by the circumferential leg. The leg can never be a complete circle, so it must be evaluated as a rapid transit line on an individual street or corridor. This far out of city center, transit demand on each route is unlikely to be high, but there may well be exceptions, for example if there is a linear secondary CBD. For example, while Seoul Metro Line 2 is fully circumferential, one of its segments follows a Tehran Avenue, a major street in Gangnam with high transit demand, which would justify a subway even if it weren’t part of a large circle.
  3. The strength of the circumferential transit demand from the end of the potential circumferential extension to the radial segment. In the depicted city, there may be strong demand for east-west transit south of the CBD, and the circumferential pink line is then better at serving it than connecting between the red and yellow lines via the blue line.

The original impetus for this post, as noted at the beginning, is a comment challenging me for my support of an extension of Second Avenue Subway Phase 2, going under 125th Street from the planned terminus at Lexington Avenue to Broadway, with stations at the intersection with each preexisting subway line. I contend that in this case, all three factors above point to a very strong circumferential extension. In order:

  1. The radial alternative is to extend Second Avenue Subway to the north, to the Bronx, presumably under Third Avenue, but according to some railfans also under University Avenue. This is problematic, for three reasons. First, the Bronx already has many north-south lines feeding into Manhattan trunk lines, with mediocre ridership. The Manhattan trunk lines are overloaded, but mostly with traffic coming from the Upper East and West Sides, Harlem, and Washington Heights. Second, Third Avenue is close to the Harlem Line, which could be used for local transit if fares and schedules are integrated with the subways and buses. And third, the plan for Second Avenue Subway is for the line to turn west at 125th toward Lexington, since 125th and Second is not as compelling a destination, and this makes it easier to extend the line to the west than to the north.
  2. 125th Street is a very busy street, and acts as the main street of Harlem. Transit demand is high: four bus routes use the street, with a total of 32,630 boardings per weekday on 125th Street, exclusive of other segments of those routes. This count misses people who board elsewhere and get off on 125th, but conversely assigns people who board on 125th and get off elsewhere to this street and not the other segment. But with this caveat in mind, this points to about 11,000 weekday riders per route-km, ahead of New York’s busiest bus per unit length (the M86, with about 7,000), and not far behind the subway average (15,000). This is despite the fact that, in my experience going between Columbia and the Metro-North station at Park Avenue, those buses are not faster than walking.
  3. East-west transit in Uptown Manhattan consists of Pokey-winning crosstown buses; the 125th Street buses are as slow on 125th. An underrated feature of Second Avenue Subway Phase 1 is that it will soon enable a two-seat subway ride from the Upper East Side to the Upper West Side, West Harlem, and Washington Heights. However, this option will require connecting at Times Square, and is useful mainly for people in the southern areas of the Upper East Side connecting to the 1/2/3 rather than to the A/B/C/D. A two-seat ride based on going up Second Avenue to 125th Street and thence connecting to the 2/3, A/B/C/D, or 1 would enable more connections, many without any backtracking. This could have a potential cascading effect on all Uptown east-west buses, and not just those using 125th Street.

Of course, a Second Avenue Subway extension on 125th Street cannot be exactly like the pink line in the diagram above, because a key feature of it is that the circumferential part is not in fact near the outer end of the city. It’s barely 5 km north of the northern edge of Midtown, not even halfway from Midtown to the northern ends of most preexisting north-south subway lines. This is how it can have such high residential and commercial density and strong transit demand. Much farther north, Fordham Road is a very strong bus corridor, with about 4,500 weekday riders per route-km on the Bx12, but this is at much higher speed than in Manhattan, about 13 km/h rather than 5 km/h. An extension of the A east toward the Bronx under Fordham would underperform, because Fordham just doesn’t have that much demand; but 125th does.

The result of this discrepancy is that in a small city, one whose subway system is only about as large as in the diagram, it’s unlikely that such circumferential extensions would work. A radial line built all the way out is going to have as its terminus either a relatively low-density area or an anchor point, such as a commercial center or big housing project, neither of which lends itself to a strong continuous circumferential corridor. A radial line built part of the way to the edge of the city could potentially find a Tehran Avenue or a 125th Street, but if the system is small, with many key outlying neighborhoods still unserved, then it is usually best to keep extending lines outward.

The factors that conspire to make a 125th Street subway extension work are in place precisely because New York already has a large, mature subway network, in which Second Avenue Subway is a relief line. Certainly the projected demand on Second Avenue is very high, but the East Side is already served by a north-south subway 500-600 meters to the west of this line; it’s being built because this subway is overcrowded, not because the East Side has no access. This means that there’s more leeway with choosing what to do with the line once it reaches Harlem – after all, the Bronx subways are not overcrowded, and do not need relief.

Whereas mixed lines like the above-depicted yellow line are always bad transit, mixed lines like the pink line, in which the circumferential part is farther out than the radial part, are potentially an option for large cities that already have many rapid transit lines. They are especially useful for providing connections between closely parallel radial lines when other crosstown transit options are slow, and should be considered as extensions for relief lines, provided the radial lines farther out do not need relief as well.

De Blasio Versus Good Transit

In New York, the de Blasio administration has been spending considerable political capital pushing for a $2.5 billion light rail line connecting Astoria and the Brooklyn waterfront south to Sunset Park. There has been a lot of criticism from good transit advocates about implementation – namely, it’s unclear there will be free transfers to the subway and buses, in order to avoid having to share turf with the state-owned MTA – but also of the basic concept, which is not the biggest transit priority in the region, or for matter the twentieth. In comments and on social media, I’ve seen a few wrong arguments made in support of waterfront light rail and similar bad investments over and over, and I’d like to go in some detail into where cities should and should not build such lines.

The principles below are based on various oppositions: first world versus third world, fast versus slow growth, subway versus no subway. I think a good meta-principle is that if the presence of a certain factor is an argument in favor of a specific solution, then its absence should be an argument against that solution. For instance, if high wages are an argument in favor of rail and against bus rapid transit, then low wages should be an argument in favor of bus rapid transit; this principle makes me wonder what Addis Ababa was thinking when it built light rail instead of BRT, while at the same time thinking very little of American cities that make the decision that Addis Ababa should have made. The upshot of the meta-principle is that many of the guidelines that work in New York could work in very different cities, in reverse.

1. New York is a mature first-world city with low population growth; it should build transit exclusively or almost exclusively based on current population and transportation patterns, and not attempt to engage in development-oriented transit. The upzoning the city engages in is too small compared to current population, and cannot justify anything of the magnitude of Vancouver’s Expo Line, which was built simultaneously with Metrotown and the New Westminster offices around the train stations. And even Vancouver cannot reasonably expect the growth rates of various third-world cities with annual population growth rates in the vicinity of 5% and even higher per capita income growth rates.

2. Rail bias is approximately the same on all routes. Routes with many turns and narrow roads have unusually slow buses, but they’ll also have unusually slow surface rail. Rapid transit does have the ability to avoid the extra traffic jams coming from such alignments, and this is especially important in cities where the main street is not the same as the nearby wide boulevard, but this is not what’s under discussion in New York. Yes, de Blasio’s proposed light rail line would get more riders than the buses on segments of the route in question are getting now; the same would be true of any number of light rail routes paralleling the busiest buses in the city.

3. In a city with a subway, the best light rail routes are the ones that don’t make sense as subway extensions. Of the three busiest buses in New York, two make sense as subway lines, so there’s no point building light rail and only later a subway: the M15, on First and Second Avenues, and the B46, on Utica. In contrast, the third route, the Bx12 on Fordham, is crosstown, and cannot reasonably be an extension of any subway line, so it would be a strong light rail corridor. The same can be said of Main Street in Queens, between Flushing and Jamaica; and 14th and 86th Streets in Manhattan, where the M14 and M86 are the busiest surface routes in the US in terms of riders per kilometer, well ahead of the Boston Green Line (they both have about 8,000, and the Green Line 6,000). Of note, 14th Street already hosts the L, but a branch going on Avenue D is far from the subway, and the street is so well-trafficked that despite slower-than-walking bus speeds, that arguably light rail makes sense there even with the subway.

4. As soon as a project is judged as not a top priority, it’s best to think of how useful it is once the top priorities are built. In the case of New York, let us zoom in on Brooklyn’s top two circumferential buses, the B4 B6 and B35. Triboro RX is a higher priority than turning these routes into light rail, and once it’s in place, how much demand is there really going to be for them? It would be faster to take the subway and connect to Triboro, except at very short distances, where speeding up surface traffic is less useful.

In New York, excluding the somewhat special cases of 14th and 86th Streets, I’d say there are three light rail networks that make sense: one in the Bronx, one in Brooklyn, and one in Queens. The Bronx network involves taking the borough’s most frequent buses and turning them into light rail routes: the Bx12 on Fordham as noted above, but also the Bx1/2 on Grand Concourse (like 14th Street, hosting both a subway and a very busy bus route), the Bx19 on Southern and 145th, the Bx15 on Third, and a route on Tremont combining the Bx36 and the Bx40/42. These routes roughly form a grid, each has at least 30,000 weekday riders, and none is SBS except the Bx12. In this case, light rail should really be thought of as the next step after publishing a frequent grid map based on these routes and equipping the entire city bus fleet with off-board fare collection.

In Queens, there’s less room for a grid – the borough has street grids, but it really is based on several old centers, with major roads connecting them. The strongest routes are the ones that cannot reasonably be subway extensions, because they’re too circumferential; in turn, the strongest subway extension, i.e. Northern, is not a major bus route, because it’s close enough to the Queens Boulevard subway that people instead take the subway, which is overcrowded. Of the strong surface transit routes, the corridor with the highest ridership takes in several bus routes between Flushing and Jamaica; Main Street is the most important route, but potentially there’s room both there and on the second route, Kissena-Parsons. Other potential light rail routes radiate from Flushing and Jamaica, in directions not well-served by the subway and the LIRR, or even west on Queens Boulevard to help serve the gap in subway coverage between the 7 and the Queens Boulevard Line and relieve the subway lines.

Brooklyn is the most interesting. The main missing pieces in subway coverage in Brooklyn are good subway extensions: Triboro, Utica, Nostrand. With those in place, the only real gaps are Flatbush, and some route serving Red Hook. Possibly service to the Navy Yard may be desirable, but the area is not very well-developed right now, and the buses serving it have low ridership. Those are two or three routes radiating out of the same center in Downtown Brooklyn, which makes it tempting to not only build light rail on them, but also send it over the Brooklyn Bridge to City Hall. This would be like the subway-surface lines in Boston and San Francisco, where one underground trunk splits into several at-grade branches, except that in this case the trunk would be elevated rather than underground. It’s not worth building by itself, but the possibility of leveraging Brooklyn Bridge lanes for several light rail lines may make the ridership per unit of cost pencil out.

The common factor to all of these possibilities is that they are not meant for signature development areas that the city is targeting. Maybe there’s some new development there, but the focus is on improving public transit services to existing residents, who either are riding very slow buses or have given up on public transit because of the inconvenience. It can be marketed as an improvement in transit, but cannot really be sold as part of a plan to revitalize the Brooklyn waterfront. It’s about day-to-day governing, whereas the administration is interested in urban renewal schemes, which are rarely good transit.

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).

cityA cityBcityC

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:

cityAcrowd cityBcrowd cityCcrowd

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.

cityD cityE cityF

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}

cityDcrowd cityEcrowd cityFcrowd

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 Branch:

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:

train 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 off-peak LIRR fare is 15 cents per kilometer at long distances (14 to Ronkonkoma, but much more at shorter distances, for example 21 to Hicksville). If the marginal cost of running off-peak service is $1.31 per car-km, it means a car needs to have 9 passengers without season passes on it paying 15 cents per km for the trip to break even. If it’s $2.675, it needs 18. Passengers who commute off-peak and get season passes for those commutes also contribute, but less – a monthly pass for Ronkonkoma is $377, which at 46 trips a month is 10 cents per kilometer. It is not hard to have 9 passengers even on a long train, or even 13 (at the lower rate of season passes); Ronkonkoma itself is a park-and-ride, where this is less likely, but high enough passenger volumes as far as Mineola and Hicksville and all over the Babylon Branch are quite likely. If the required minimum is 18, let alone 26, this is substantially harder.

I harp on North American mainline rail operations for a variety of antiquated practices, but the on-board overstaffing is by far the worst. While improvement in train driver productivity can occur as a natural byproduct of improvement in off-peak frequency, getting rid of conductors is not so easy. It means a fight with the unions over job losses. Some of the required layoffs can be mitigated by retraining conductors as train drivers and running more service, but this would not boost service hours by a factor of 5; on the Ronkonkoma Branch, the peakiest of the three long LIRR lines, boosting off- and reverse-peak frequency to half the peak frequency would only increase train service by a factor of about 1.8.

I am not an expert on labor relations, so I do not know if any solution barring a prolonged SEPTA-style strike could work, alone or in combination. One possibility would be to commit to reducing working hours in the next five or ten years instead of hiking pay; working hours would be gradually reduced to core Western European levels, with 35-hour workweeks and 6 weeks of paid vacation, and hourly pay would rise as scheduled while annual pay would be frozen. Another possibility is that the MTA would help laid off employees find private-sector work, as happened in the 1980s with Japan National Railways (see PDF-pp. 103-4 of a handbook on rail privatization). This possibility requires implementing the reform at a time of wage growth and low unemployment, when private-sector work is easier to find, but the US is posting strong job growth numbers nowadays and is projected to keep doing so for at least another year.

But whatever happens, the most important reform from the point of view of reducing marginal off-peak service provision costs is letting go of redundant train crew. Halving the variable operating costs is exactly what is required to convert the nearly empty off-peak trains from financial drains to an extra source of revenues, balancing low ridership with even lower expenses. This would of course compound with other operating efficiencies, limiting the losses of branch lines and turning the busier main line trains into profit centers. But nowhere else is there the possibility of cutting costs so much with one single policy change as with removing conductors and changing the fare enforcement system to proof-of-payment.

Update 7/31: first, check comments below about maintenance costs: as far as I can tell from poorly presented Empire Center data, they are about 2.5 times higher, for both trains and the infrastructure, than the maintenance costs of high-speed rail. Although the effect of reducing those costs to conventional HSR level is larger than the effect of eliminating conductors, the details of reducing maintenance costs are far more delicate than those of eliminating conductors and running trains more often so that train drivers have less downtime.

Second, there is a small error in the above calculations: the figure of $90-95 in crew salary per car-hour is based on two conflicting assumptions. To get to $771 per train-hour on the LIRR, I assumed the LIRR ran 10-car trains. To get down to the $90-95 range, I assumed 8-car trains; 10-car trains would make this $77/hour. If we redo the entire calculation with 10-car trains, still with HSR maintenance costs, then instead of a cut from $2.675/car-km to $1.31/car-km, improved labor efficiency would cut costs from $2.415/car-km to $1.21/car-km. This is based on exact LIRR salaries, whereas the original calculation assumes hybrid LIRR/Metro-North salaries, and Metro-North pays drivers better than the LIRR.

Now, trains are somewhat longer at the peak than off-peak. If off-peak service is already with 8-car trains, and the average number of conductors is constant, then the original calculation (a cut from $2.675 to $1.31) still holds. After all, the salaries of train drivers and conductors are the same no matter how long the train is. But the number of conductors is not constant – let’s say it is proportional to train length, so 8-car LIRR trains have 2 conductors instead of 2.47, just as Metro-North’s average number of conductors per train is shorter than the LIRR’s, in tandem with its shorter consists. This changes the calculation to a cut from $2.535 (reflecting fewer conductors than in the original calculation) to $1.31. Observe that no matter what assumption we use, the operating cost cut coming from removing conductors and using drivers more efficiently is about 50%, give or take 1-2%.