# Select Bus Service Problems

I recently visited New York. I stayed in Kew Gardens Hills, a neighborhood located between Jamaica and Flushing, just close enough to the subway that it’s plausible to walk but just far enough that this walk is uncomfortable and I preferred to take a bus. The bus route, Main Street, is one of Queens’ busiest (see data here and here). I’ve been calling for investment in it for years, going back to a fantasy spite map I drew so long ago I don’t remember what year it was, and continuing more recently in my post on where New York should and shouldn’t build light rail. Last year, the route did get Select Bus Service, and I took it a few times. The result is not good.

Main Street maintains two bus corridors: the local Q20, and the Select Bus Service Q44. Almost every SBS route is an overlay of a local route and a rapid route; on the local route passengers must board from the front and pay within view of the driver, and on the rapid route passengers must validate a ticket at ticketing machines beforehand and can then board the bus from any stop, with the fare enforced via random checks for ticket receipts. This leads to the following problems, some preventable, some inherent to this setup:

1. Passengers who can take either the local or the SBS route need to decide in advance whether to validate their tickets at the machines or not, based on whether the next bus is SBS. The resulting last-minute validation delays boarding. After the mayhem caused by the introduction of SBS to the M15, on First and Second Avenues, bus drivers on local routes began to accept the receipts spitted out by the SBS ticketing machines. However, this practice is either inconsistent or not widely-known among occasional bus riders, such as the people I was staying with, who own cars.
2. The combination of local and limited buses on a medium-frequency route such as Main Street makes it impossible to maintain even headways. Even within each route (Q20 or Q44) I repeatedly saw bunching, but the different speeds of the Q20 and Q44 make bunching between a local and an express inevitable at some point on the route. Off-peak weekday frequency is 10 minutes on the Q20 and 8 on the Q44, which isn’t good enough to justify this split, especially given the bunching within each route; some stations will always be scheduled to have 8-minute service gaps, and in practice could see 15-minute gaps because of the bunching. See more on this problem of locals and rapids on infrequent routes on Human Transit.
3. The expense of the ticketing machines ($75,000 per stop for a pair of modified MetroCard vending machines and a machine that takes coins) limits how widely they can be installed. Everywhere else where proof-of-payment is used, holders of valid transfers and season passes can just board the train or bus and show their pass to an inspector. This would be especially useful in New York, because the biggest crunch at SBS stops occurs when many passengers arrive at the stop at once, which in turn is the most common where passengers transfer from the subway. The slow process of validating a ticket leads to queues at busy times, and adding more machines is difficult because of their cost. 4. Stop spacing is never what it should be. Most developed countries have converged on a standard of about 400-500 meters between successive bus stops. North America instead has converged on 200 meters, leading to slow buses that stop too often; see an old Human Transit post on the subject here. The stop spacing on the segment of the Q44 I was using was two stops in 1.7 km, leading to long walks between stops. 5. On the schedule, the Q44 makes 15 stops in 9.2 km between its origin in Jamaica and Flushing, and takes 42 minutes in the midday off-peak. This is an average speed of 13.1 km/h. In contrast, Vancouver’s limited-stop buses, which average about a stop per kilometer on Broadway and 4th Avenue, average 20 km/h and 30 km/h respectively; the 4th Avenue buses do not have off-board fare collection, but there’s less traffic than on Broadway, and the stoplights give priority to through-traffic, both private and public, over crossing traffic. The basic problem with New York’s approach to Select Bus Service is that all North American bus rapid transit ultimately descends from Jaime Lerner’s sales pitch of BRT as a cheap subway on tires, at grade. Lerner implemented BRT in Curitiba successfully, in the context of low wages: construction costs appear to only weakly depend on wealth (see e.g. my posts here, here, here, here, and here), but bus driver costs rise with average income, making replacing fifteen bus drivers with one subway driver a crucial money saver in rich cities and an unaffordable luxury in poor ones. North American BRT imitates Latin American BRT’s role as a cheap subway substitute, and ignores the superior usage of bus services in Europe, with which American transit planners do not dialog; there’s no systematic dialog with Latin American planners either, but Lerner has aggressively pitched his ideas to receptive audiences, whereas no comparable figure has pitched European-style reforms to the US. In cities that think of BRT as a subway substitute, the BRT network will tend to be small, consisting of a few lines only serving the most important corridors, and bundle various features of improved transit together (off-board fare collection, larger vehicles, bus lanes, signal priority). After all, a line can’t be partly a subway and partly a bus. In Bogota, whose BRT system has eclipsed Curitiba and is the world’s largest, the BRT lines run different vehicles from the local lines: local buses have doors opening on the right to the curb, BRT buses have doors opening on the left to a street median bus station, some hybrids have buses with doors on both sides (see photos on Spanish Wikipedia). ITDP, which promotes Latin American-style BRT around the world, has a BRT scoring guideline that awards points to systems that brand their BRT lines separately from the rest of the bus network, as New York does with SBS. In the European thinking, there’s already an improved quality urban transit service: the subway, or occasionally the tram. The bus is a bus. The biggest difference is that subway networks are smaller than bus networks. Paris and London, both with vast urban rail networks, have a number of subway lines measured in the teens, plus a handful of through-running commuter services; they have hundreds of bus routes. Instead of branding a few buses as special, they invest in the entire bus network, leading to systemwide proof-of-payment in many cities. Bus lanes and signal priority are installed based on demand on an individual segment basis. New York installs bus lanes without regard to local versus SBS status, but retains the special SBS brand, distinguished by off-board fare collection, and only installs it on a per-route basis rather than systemwide. The other issue, unique to New York, is the ticket receipts. Everywhere else that I know of, bus stops do not have large ticket machines as New York does. Vancouver, which otherwise suffers from the same problem of having just a few special routes (called B-Lines), has no ticket machines at B-Line stops at all: people who have valid transfers or monthly passes can board at their leisure from any door, while people who don’t pay at the front as on local buses. SBS in contrast does not give passengers the option of paying at the front. In New York, people justify the current system by complaining that the MetroCard is outdated and will be replaced by a smart card any decade now; in reality, systems based on paper tickets (including Vancouver, but also the entire German-speaking world) manage to have proof-of-payment inspections without smartcards. Small devices that can read the MetroCard magnetic stripe are ubiquitous at subway stops, where people can swipe to see how much money they have left. The right path for New York is to announce that every bus route will have off-board fare collection, regardless of stop spacing. It should also engage in stop consolidation to reduce the interstation to about 400-500 meters, but this is a separate issue from fare collection. Similarly, the question of bus lanes should be entirely divorced from fare collection. There should be no ticketing machines at bus stops of the kind currently used. At most, stops should have validators, similar to the MetroCard readers at subway turnstiles but without the fare barrier. Validators are not expensive: smartcard readers in Singapore are consumer items, available to people for recharging their cards at home via their credit cards for about$40, a far cry from the $75,000 cost in New York today. People with valid transfers or unlimited cards should be able to board without any action, and people without should be able to pay on the bus. Finally, the split between local and rapid routes should be restricted to the busiest routes, with the highest frequency in the off-peak. Conceivably it should be avoided entirely, in favor of stop consolidation, in order to increase effective frequency and reduce bunching. The city’s single busiest route, the M15, has 7-minute SBS and 8-minute local service in the midday off-peak, and given how slow the local is, it’s enough to tip the scales in favor of walking the entire way if I just miss the bus. # Quick Note: A Hypothesis About Airport Connectors It is a truth universally acknowledged that cities spend far more per rider on airport connectors than on other kinds of public transit. On this blog, see many posts from previous years on the subject. My assumption, and that of such other transit advocates as Charles Komanoff, was always that it came from an elite versus people distinction: members of the global elite fly far more than anyone else, and when they visit other cities, they’re unlikely to take public transit, preferring taxis for most intermediate-length trips and walking for trips around the small downtown area around their hotels. In this post, I would like to propose an alternative theory. Commuters who use public transit typically use their regular route on the order of 500 times a year. If they also take public transit for non-work trips around the city, the number goes even higher, perhaps 700. In contrast, people who fly only fly a handful of times per year. Frequent business travelers may fly a few tens of times per year, still an order of magnitude less than the number of trips a typical commuter takes on transit. What this means is that 2 billion annual trips on the New York-area rail network may not involve that many more unique users than 100 million annual trips between the region’s three airports. Someone who flies a few times per year and is probably middle class but not rich might still think that transportation to the airport is too inconvenient, and demand better. In the US, nearly half the population flies in any given year, about 20% fly at least three roundtrips, and 10% fly at least five. Usually, discussions of elite versus regular people do not define the elite as the top half; even the top 10% is rare, in these times of rhetoric about the top 1% and 0.1%. When Larry Summers called for infrastructure investment into airport transit, he said it would improve social equity because what he considered the elite had private jets. But what’s actually happening is not necessarily about the top 0.1% or 1% or even 5% directing government spending their way. It may be so; certainly politicians travel far more than the average person, and so do very rich donors. But broad segments of the middle class fly regularly. The average income of regular fliers is presumably considerably higher than that of people who do not fly, but not to the same extent as the picture drawn by political populists. None of this makes airport transit a great idea. Of course some projects are good, but the basic picture is still one in which per rider spending on airport connectors is persistently higher than on other projects, by a large factor. In New York, the JFK AirTrain cost about$2 billion in today’s money and carries 6.4 million riders a year, which would correspond to 21,000 weekday riders if it had the same annual-to-weekday passenger ratio as regular transit, 300 (it has a much higher ratio, since air travel does not dip on weekends the way commuter travel does). This is around $100,000 per rider, which contrasts with$20,000 for Second Avenue Subway Phase 1 if ridership projections hold. Earlier this year, the de Blasio administration proposed a developed-oriented waterfront light rail, projected to cost $1.7 billion and get 16 million riders a year, which corresponds to about$32,000 per daily rider; a subsequent estimate pegs it at $2.5 billion, or$47,000 per rider, still half as high as how much the AirTrain cost.

However, what I propose is that the high cost of airport connectors is not because the elite spends money on itself. Rather, it’s because many ordinary middle-class people fly a few times a year and wish for better airport transit, without thinking very hard about the costs and benefits. An airport connector appeals to a very wide section of the population, and may be very cheap if we divide the cost not by the number of daily users but by the number of unique annual users. Hence, it’s easier for politicians to support it, in a way they wouldn’t support an excessively costly subway line connecting a few residential neighborhoods to the city.

It’s a political failure, but not one that can be resolved by more democratic means. The conventional analysis that the root cause is excessive attention to elite concerns implies that if spending were decided in more democratic ways, it would be directed toward other causes. But if the hypothesis I’m putting forth is right, then democracy would not really resolve this, since the number of people who would benefit from an airport connector, if only shallowly, is large. A rigorous regime of cost-benefit analyses, including publicized estimates of cost per rider and the opportunity cost, would be required.

Following plans by the government of Norway to ban cars fueled by petrol or diesel by 2025, several other countries in Europe are formulating similar programs to phase out fuel-powered transportation. Moreover, sources close to the European Parliament say that once multiple member states pass such a ban as is expected later this year, the European Union will attempt to enforce these rules throughout its territory.

In Sweden, the office of Åsa Romson, minister for the environment and co-spokesperson for the Green Party, released a statement saying that a ban on the internal combustion engine is a necessary step to reduce pollution and carbon emissions. In Sweden, only about 3% of electricity production comes from fossil fuels, and plans made by the Persson cabinet in 2005, Making Sweden an Oil-Free Society, already call for a phaseout of the use of oil for heating. The Löfven cabinet has nowhere else to cut in its program to make Sweden a carbon-neutral society by 2050. The Social Democrats-Green minority government is expected to work with the more moderate parties in the opposition Alliance; the Centre Party has already endorsed the move, but the Liberals have yet to make a statement.

In France and Germany, the ban is expected to be far more contentious. Auto manufacturers in both countries have condemned the moves by their respective governments to ban the internal combustion engine, saying that it would make the economy less competitive. European automakers have lagged behind Japanese and American ones in both hybrid and all-electric car technology, as conventional European petrol and diesel cars already have high fuel economy. In response to so-called range anxiety, in which an electric car’s limited range may leave the driver stranded on the motorway, the Hollande administration is expected to pair the proposed phaseout with national investment into charging stations as well as additional investment into TGV lines, to make it easier to travel long distances in France without a car.

Demands by BMW and Volkswagen for Germany to commit to spending money on R&D for improved battery range and charging and battery swap stations on the highway network have run into budgetary problems. While Chancellor Angela Merkel is reported to be interested in implementing a phaseout, in order to attract Green support into a possible future grand coalition and reduce EU dependence on oil imports from Russia, Finance Minister Wolfgang Schäuble has openly rejected any package that would raise the budget deficit, and the allied Christian Social Union has rejected the proposed ban on principle. Opposition from far-right populist parties, including the Alliance for Germany (AfD) and France’s National Front (FN), is likely to be significant, and sources close to Hollande and Merkel say that both have ruled out tax increases to pay for the program.

In France the calls for a phaseout of the internal combustion engine are especially loud in the Paris region, where high levels of particulate pollution from diesel vehicles led to recent restrictions on car use. The mayor of Paris, the Socialist Anne Hidalgo, previously proposed to ban diesel vehicles from the city entirely, and has endorsed the state’s plans to phase out fuel-powered vehicles, adding that given Paris’s pollution crisis, a local ban on diesel vehicles should be implemented immediately. The president of the regional council, Valérie Pécresse of the Republicans (LR), is said to support the phaseout as well, and to push LR behind the scenes not to oppose it. Conversely, opposition from FN is especially acute. The party leader, Marine le Pen, quipped that France would not need any additional reductions in greenhouse gas emissions if it had not taken in non-European immigrants since the 1960s, and noted that the immigrants are especially likely to settle in Paris, where the problems are the most acute.

Elsewhere in Europe, Belgium, Switzerland, and the Netherlands are said to be considering a phaseout by 2030. Within Belgium, Saudi support of mosques preaching radical interpretations of Islam is said to have influenced the country’s liberal parties, the Francophone Reformist Movement (MR) and the Flemish Liberals and Democrats (VLD), to support a phaseout. However, the Flemish nationalist parties remain opposed, and the New Flemish Alliance (N-VA) issued a statement saying that this solution may work within Brussels but is inappropriate for Flanders. In contrast, the Netherlands is expected to pass the phaseout without any political problems. In Switzerland, a referendum is planned for next year, and early polling suggests that it is supported by 55-60% of the population.

Governments outside Europe are said to be watching the development closely, especially in France and Germany, which are perceived as more reliable bellwethers of European opinion than Sweden. In Japan, home to the world’s top-selling electric car, the Nissan Leaf, political support for a phaseout appears high. Prime Minister Shinzo Abe has called climate change a “defining issue of our time,” and is working on a national infrastructure plan. Sources close to Abe say it will pair subsidies for so-called city cars, short-range electric vehicles, with investments into the country’s rail network outside major metropolitan areas, to make it easier for people living outside the biggest cities to travel on public transport.

In the US, both the Obama administration and Hillary Clinton’s presidential campaign refused to comment, saying that it is an internal European affair. However, sources close to the administration say that it is already planning to use the Environmental Protection Agency’s executive power to restrict the sale of new fuel-powered cars to emergency needs. The sources speculate that an executive order is planned for shortly after the presidential election this November, provided Clinton wins, in order to avoid creating backlash among key swing constituencies, including the automakers and the exurban lower middle class. Donald Trump’s presidential campaign’s response is unprintable.

# Train Operator Labor Efficiency

Last summer, I brought up a metric of railroad labor efficiency: annual revenue hours per train driver. Higher numbers mean that train drivers spend a larger proportion of their work schedule driving a revenue train rather than deadheading, driving a non-revenue train, or waiting for their next assignment. As an example, I am told on social media that the LIRR schedules generous crew turnaround times, because the trains aren’t reliably punctual, and by union rules, train drivers get overtime if because their train is late they miss the next shift. Of note, all countries in this post have roughly the same average working hours (and the US has by a small margin the highest), except for France, which means that significant differences in revenue hours per driver are about efficiency rather than overall working hours.

I want to clarify that even when union work rules reduce productivity, low productivity does not equal laziness. Low-frequency lines require longer turnaround times, unless they’re extremely punctual. Peakier lines require more use of split shifts, which require giving workers more time to commute in and out.

The database is smaller than in my posts about construction costs, because it is much harder to find information about how many train operators a subway system or commuter railroad employs than to find information about construction costs. It is often also nontrivial to find information about revenue hours, but those can be estimated from schedules given enough grunt work.

In Helsinki, there is a single subway trunk splitting into two branches, each running one train every 10 minutes all day, every day: see schedules here and here. This works out to 65,000 train-hours a year. There are 75 train drivers according to a 2010 factsheet. 65,000/75 = 867 hours per driver. This is the highest number on this list, and of note, this is on a system without any supplemental peak service, allowing relatively painless scheduling.

In London, unlike in North America, the statistics are reported in train-km and not car-km. There are 76.2 million train-km a year, and average train speed is 33 km/h, according to a TfL factsheet; see also PDF-p. 7 of the 2013-4 annual report. In 2012, the last year for which there is actual rather than predicted data, there were 3,193 train drivers, and according to the annual report there were 76 million train-km. 76,000,000/33 = 2,300,000 revenue-hours; 2,300,000/3,193 = 721 hours per driver.

In Tokyo, there used to be publicly available information about the number of employees in each category, at least on Toei, the smaller and less efficient of the city’s two subway systems. As of about 2011, Toei had 700 hours per driver: from Hyperdia‘s schedules, I computed about 390,000 revenue train-hours per year, and as I recall there were 560 drivers, excluding conductors (half of Toei’s lines have conductors, half don’t).

In New York, we can get revenue car-hour statistics from the National Transit Database, which is current as of 2013; the subway is on PDF-p. 13, Metro-North is on PDF-p. 15, and the LIRR is on PDF-p. 18. We can also get payroll numbers from SeeThroughNY. The subway gets 19,000,000 revenue hours per year; most trains have ten cars, but a substantial minority have eight, and a smaller minority have eleven, so figure 2,000,000 train-hours. There were 3,221 train operators on revenue vehicles in 2013, and another 373 at yards. This is 556 hours per driver if the comparable international figure is all drivers, or 621 if it is just revenue vehicle drivers. The LIRR gets 2,100,000 annual revenue car-hours, and usually runs trains of 8 to 12 cars; figure around 210,000. There were 467 engineers on the LIRR in 2013; this is 450 hours per driver. Metro-North gets 1,950,000 annual revenue car-hours, and usually runs 8-car trains; figure about 240,000. It had 413 locomotive engineers in 2013; this is 591 hours per driver.

In Paris, the RER A has 523 train drivers (“conducteurs”). The linked article attacks the short working hours, on average just 2:50 per workday. The timetable is complex, but after adding the travel time for each train, I arrived at a figure of 230,000 train-hours a year. 230,000/523 = 440 hours per driver. There’s a fudge factor, in that the article is from 2009 whereas the timetable is current, but the RER A is at capacity, so it’s unlikely there have been large changes. Note also that in France, workers get six weeks of paid vacation a year, and a full-time workweek is 35 hours rather than 40; adjusting for national working hours makes this equivalent to 534 hours in the US, about the same as the New York subway.

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. # Why Costs Matter Stockholm is currently expanding its transit system, with about 19 kilometers of subway extension, and another 6 kilometers of a commuter rail tunnel taking regional traffic off the at-capacity mainline. The subway extension, excluding rolling stock acquisition, costs about2.1 billion, and the commuter rail extension $1.8 billion. The US is currently building five subways: Second Avenue Subway Phase 1 (2.8 km,$4.6 billion), East Side Access (2.2 km, $10 billion), the first phase of the Wilshire subway (6.3 km,$2.8 billion), the Regional Connector (3.1 km, $1.4 billion), U-Link (5 km,$1.8 billion). Two more projects are partially underground: the Crenshaw/LAX Line, a total of 13.7 km of which 4.7 are underground, at a total cost of $2.1 billion, and the Warm Springs BART extension, a total of 8.6 km of which 1.6 are underground, at a total cost of$900 million. (Update 2/1: the Central Subway is $1.6 billion for 2.8 km. Thanks to Joel for pointing out that I forgot about it.) The first observation is that Sweden has just 700 meters 3.5 km of subway under construction less than the US under construction, despite a vast gap in not only population but also current transit usage. Stockholm may have twice the per capita rail ridership of New York, but it’s still a small city, the size of Indianapolis, Baltimore, Portland, or Charlotte; 450 million annual rail trips is impressive for a city of its size, but the US combined has more than 3 billion. This relates to differences in costs: the amount of money Sweden is putting into heavy rail infrastructure is$3.9 billion, vs. $23.6 billion$25.2 billion among the seven eight US projects, which approaches the ratio of national subway and commuter rail ridership levels.

The second observation is that the US spending is not really proportional to current rail ridership. Two thirds of the spending is in New York, as is two thirds of US rail ridership, but nearly everything else is in Los Angeles, which takes in a majority of current subway construction route-length. Los Angeles is a progressive city and wants better public transit, but the same is true in many of the six major US transit cities – New York, Washington, San Francisco, Chicago, Boston, and Philadelphia. And yet, of those six, only New York and San Francisco are building urban subways (BART’s one mile of tunnel is in a suburb, under a park).

The difference is that Los Angeles builds subways at $400-450 million per km in the city core (less in future phases of the Wilshire subway), whereas in most of the US, lines are either more expensive or more peripheral. Boston, the Bay Area, and Washington are expanding their rapid transit networks, but largely above-ground or in a trench, and only outside the core. Boston’s Green Line Extension is in a trench, but has had major budget overruns and is currently on the high side for a full subway ($3 billion for 6.9 km), and the MBTA is even putting canceling the project on the table due to the cost. Washington’s Silver Line Phase 2 is 18.5 km and $2.7 billion, in a highway median through the Northern Virginia suburbs. BART’s Warm Springs extension is about$100 million per km, which is not outrageously high, but the next extension of the line south, to Berryessa, is $2.3 billion for 16 km, all above ground. Let us now stay on the North American West Coast, but go north, to Vancouver. Vancouver’s construction costs are reasonable: the cost projections for the Broadway subway (C$2.7 billion ex-vehicles, PDF-p. 95) are acceptable relative to route-length (12.4 km, PDF-p. 62) and very good relative to projected ridership (320,000 per weekday, PDF-p. 168). Judging by the costs of the Evergreen and Canada Lines, and the ridership evolution of the Canada Line, these projections seem realistic. And yet, in a May 2015 referendum about funding half the line as well as many other transit projects, 62% of the region’s voters, including a bare majority in Vancouver proper, voted no.

The referendum’s result was not a shock. In the few months before the vote, the polls predicted a large, growing no vote. Already in February, the Tyee was already comparing Vancouver negatively with Stockholm, and noting that TransLink’s regional governance structure was unusual, saying the referendum was designed to fail. This is not 100% accurate: in 2014, polls were giving the yes side a majority. The deterioration began around the end of 2014 or beginning of 2015: from 52-39 in December to 46-42 in January, to 27-61 in March. The top reason cited by no voters was that they didn’t trust TransLink to spend the money well.

This cannot be divorced from Vancouver’s Compass Card debacle: plans to replace paper tickets and SkyTrain’s proof-of-payment system with a regionwide smartcard, called Compass, and faregates on SkyTrain, were delayed and run over budget. The faregates aren’t even saving money, since TransLink has to pay an operating fee to vendor Cubic that’s higher than the estimated savings from reduced fare evasion. The height of the scandal was in 2014, but it exploded in early 2015, when TransLink replaced its manager amidst growing criticism. The referendum would probably have been a success a year earlier; it was scheduled in what turned out to be a bad period for TransLink.

The importance of the Vancouver example is that construction costs are not everything. Transit agencies need to get a lot of things right, and in some cases, the effects are quite random. (Los Angeles, too, had a difficult rollout of a Cubic-run faregate system.) The three key principles here are, then:

1. Absolute costs matter. They may not directly affect people’s perceptions of whether construction is too expensive. But when legislators have to find money for a new public transit project, they have some intuitive idea of its benefits, give or take a factor of perhaps 2. Gateway is being funded, even though with the latest cost overrun (to $23.9 billion) the benefit-cost ratio in my estimation is about 1/3, but this involved extensive lobbying by Amtrak, lying both to Congress and to itself that it is a necessary component of high-speed rail. Ordinary subways do not have the luxury of benefiting from agency imperialism the way the Gateway project did; if they’re too expensive, they’re at risk of cancellation. 2. Averaged across cities and a number of years of construction, cities and countries with lower construction costs will build more public transit. We see this in the US vs. Sweden. Of course, there are periods of more construction, such as now, and periods of less, such as around 2000, but this affects both countries right now. 3. Variations from the average are often about other issues of competence – in Vancouver’s case, the failure of the faregates and the delayed Compass rollout. Political causes are less important: Vancouver’s business community opposed the transit referendum and organized against it, but it’s telling that it did so and succeeded, whereas business communities in cities with more popular transit authorities support additional construction. In a post from 2011, Yonah Freemark argued that California HSR’s projected cost’s upper end was just 0.18% of the projected GDP of California over a 20-year construction period. The implication: the cost of high-speed rail (and public transit in general) is small relative to the ability of the economy to pay. This must be paired with the sobering observation that the benefits of public transit are similarly small, or at most of the same order of magnitude. New York’s survived decades without Second Avenue Subway. It’s a good project to have, provided the costs are commensurate with the benefits, but without cost containment, phase 2 is probably too expensive, and phases 3 and 4 almost certainly. What’s more, the people funding such projects – the politicians, the voters, even the community organizations – consider them nice-to-haves. The US has no formal mechanism of estimating benefit-cost ratios, and a lot of local political dysfunction, and this can distort the funding, to the point that Gateway is being funded even though at this cost it shouldn’t. But, first, even a factor of 3 distortion is unusual, and second, on average, these distortions cancel out. Democrats and Republicans shouldn’t plan on controlling either Congress or the White House more than about half the time, in the long run, and transit activists shouldn’t plan on political dysfunction persistently working in their favor. The only route forward is to improve the benefit-cost ratio. On the benefit side, this means aggressive upzoning around subway stations, probably the biggest lacuna in Los Angeles’s transit construction program. But in New York, and even in the next five transit cities in the US, this is not the main problem: population density on many corridors is sufficient by the standards of such European transit cities as Stockholm, Berlin, London, and Munich, none of which is extraordinarily dense like Paris. No: the main problem in most big US cities is costs, and almost only costs. Operating costs, to some extent, but mainly capital construction costs. Congress and the affected states apparently have enough political will to build a 5-km tunnel for$20 billion going on $24 billion; if this system could be built for$15 billion, they’d jump at the opportunity to take credit. The US already has the will to spend reasonable amounts of money on public transit. The difference is that its $24 billion$25 billion of spending on subways buys 26 km 28.5 km of subway and 16 km of a mix of light rail and el, where it could be buying 120 km 125 km of subway. Work out where you’d build the extra 94 km 96.5 km and ask yourself if ignoring costs is such a good idea for transit activists.

# Modeling Anchoring

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

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

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

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

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

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

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

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

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

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

Here are their graphs:

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

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

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

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

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

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

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

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

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

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

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

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

# Transfer Penalties and the Community Process

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

# Hyperloop Costs

Two years ago, when Elon Musk first proposed Hyperloop as a faster, cheaper, and more entrepreneurial alternative to California High-Speed Rail, I explained in depth what was wrong with the proposal. The curve radii were too tight for passenger comfort, and any attempt to fix them would require more expensive civil infrastructure. In general, the cost estimates in the plan were laughably low. Musk has moved on, but another team has been trying to build the system. It is planning to build a test track in the next three years, a distance of 8 km, for $150 million. Let us analyze these costs. The per-km cost of this scheme is about$19 million, which if costs don’t run over is reasonable for HSR flat terrain, if anything a bit low. California HSR’s Central Valley segments, in more urbanized areas, are about $24-27 million/km, ex-electrification and systems (which don’t add much). This, in principle, suggests the system could be built for about the same cost as conventional HSR. Of course, it’s already far more expensive than Musk’s original estimate of$6 billion for about 650 km (including tunnels), but it still sounds like a good deal – in theory.

In practice, I’d like to go back to my often-quoted sentence in my post from two years ago, that Hyperloop would be a barf ride. The plan is to run capsules at their full speed, but only when empty. Tests with passengers would be restricted to 160 mph, or about 260 km/h. If the picture in the article describing the test track is accurate, the turn looks like its radius is perhaps 800 meters. Passengers can’t ride through this at very high speed. Even at 260 km/h, it requires full canting, and will make passengers feel noticeable extra gravitational push, about 0.2 g.

The importance of this is that any attempt to build tracks at higher speed will run into problems with both horizontal and vertical curves very quickly. The picture depicts sleek viaducts in empty land; imagine much taller viaducts, to allow the track to curve more gently than the terrain. Once the terrain becomes problematic, as it does on the approaches to the mountain crossings from the Central Valley to both the Los Angeles Basin and the San Francisco Bay Area, costs go up. This is true for any mode of transportation, up to and including mountain roads with hairpin turns, but the higher the speed, the larger the cost differential. In this situation, 4 km horizontal curve radii and 20 km vertical curve radii (about absolute minimum for conventional HSR) are expensive; 20 km horizontal curves and 230 km vertical curves are far more so. And within the urban areas, the inability of the system to leverage legacy rail tracks forces expensive urban viaducts.