For the most part, the optimal average spacing between bus stops is 400-500 meters. North American transit agencies have standardized on a bus stop every 200-250 meters, so stop consolidation is usually a very good idea. But this is based on a model with specific inputs regarding travel behavior. In some circumstances, travel behavior is different, leading to different inputs, and then the model’s output will suggest a different optimum. In contrast with my and Eric’s proposal for harsh stop consolidation in Brooklyn, I would not recommend stop consolidation on the crosstown buses in Manhattan, and am skeptical of the utility of stop consolidation in Paris. In Vancouver I would recommend stop consolidation, but not on every route, not do we recommend equally sweeping changes on every single Brooklyn route.
The model for the optimal stop spacing
If demand along a line is isotropic, and the benefits of running buses more frequently due to higher in-vehicle speed are negligible, then the following formula holds:
The most important complicating assumption is that if demand is not isotropic, but instead every trip begins or ends at a distinguished location where there is certainly a stop, such as a subway connection, then the formula changes to,
The choice of which factor to use, 2 or 4, is not exogenous to the bus network. If the network encourages transferring, then connection points will become more prominent, making the higher factor more appropriate. Whether the network encourages interchanges depends on separate policies such as fare integration but also on the shape of the network, including bus frequency. Higher average bus speed permits higher frequency, which makes transferring easier. The model does not take the granularity of transfer ease into account, which would require a factor somewhere between 2 and 4 (and, really, additional factors for the impact of higher bus speed on frequency).
After the choice of factor, the most contentious variable is the walk speed and penalty. Models vary on both, and often they vary in directions that reinforce each other rather than canceling out (for example, certain disabilities reduce both walk speed and willingness to walk a minute longer to save a minute on a bus). In Carlos Daganzo’s textbook, the walk speed net of penalty is 1 m/s. For an able-bodied adult, the walk speed can exceed 1.5 m/s; penalties in models range from 1.75 (MTA) to 2 (a Dutch study) to 2.25 (MBTA). The lower end is probably more appropriate, since the penalty includes a wait penalty, and stop consolidation reduces waits even as it lengthens walk time.
Update 10/31: alert reader Colin Parker notes on social media that you can shoehorn the impact of walk time into the model relatively easily. The formula remains the same with one modification: the average trip distance is replaced with
The factor of 2 in the formula comes from computing average wait time; for worst-case wait time, remove the 2 (but then the wait penalty would need to be adjusted, since the wait penalty is partly an uncertainty penalty).
The average distance between buses is proportional to the number of service-hours, or fleet size: it obeys the formula
The factor of 2 in the formula comes from the fact that route-length is measured one-way whereas revenue hours are for a roundtrip.
If we incorporate wait time into the model this way, then the walk and wait penalties used should be higher, since we’re taking them into account; the Dutch study’s factor of 2 is more reasonable. The conclusions below are not really changed – the optima barely increase, and are unchanged even in the cases where stop consolidation is not recommended.
The situation in New York
The average unlinked New York City Transit bus trip is 3.35 km: compare passenger-miles and passenger trips as of 2016. In theory this number is endogenous to the transit network – longer interstations encourage passengers to take the bus more for long trips than for short trips – but in practice the SBS routes, denoted as bus rapid transit in the link, actually have slightly shorter average trip length than the rest. For all intents and purposes, this figure can be regarded as exogenous to stop spacing.
The stop penalty, judging by the difference between local and limited routes, is different for different routes. The range among the routes I have checked looks like 20-40 seconds. However, Eric tells me that in practice the B41, which on paper has a fairly large stop penalty, has little difference in trip times between the local and limited versions. The local-SBS schedule difference is consistent with a stop penalty of about 25 seconds, at least on the B44 and B46.
As a sanity check, in Vancouver the scheduled stop penalty on 4th Avenue is 22 seconds – the 84 makes 19 fewer stops than the 4 between Burrard and UBC and is 7 minutes faster – and the buses generally run on schedule. The actual penalty is a little higher, since the 4 has a lot of pro forma stops on the University Endowment Lands that almost never get any riders (and thus the bus doesn’t stop there). This is consistent with 25 seconds at a stop that the bus actually makes, or even a little more.
Plugging the numbers into the formula yields
if we assume everyone connects to the subway (or otherwise takes the bus to a distinguished stop), or
if we assume perfectly isotropic travel demand. In reality, a large share of bus riders are connecting to the subway, which can be seen in fare revenue, just $1.16 per unlinked bus trip compared with $1.91 per subway trip (linked or unlinked, only one swipe is needed). In Brooklyn, it appears that passengers not connecting to the subway disproportionately go to specific distinguished destinations, such as the hospitals, universities, and shopping centers, or Downtown Brooklyn, making the higher figure more justified. Thus, our proposed stop spacing, excluding the long nonstop segments across the Brooklyn-Battery Tunnel and between borough line and JFK, is 490 meters.
Update 10/31: if we incorporate wait time, then we need to figure out the average distance between buses. This, in turn, depends on network shape. Brooklyn today has 550 km of bus route in each direction, which we propose to cut to 350. With around 600 service hours per hour – more at the peak, less off-peak – we get an average distance between buses of 1,830 meters today or 1,180 under our proposal. Using our proposed network, and a wait and walk penalty of 2, we get
Short bus routes imply short stop spacing
Our analysis recommending 490 meter interstations in Brooklyn depends on the average features of New York’s bus network. The same analysis ports to most of the city. But in Manhattan, the situation is different in a key way: the crosstown buses are so short that the average trip length cannot possibly match city average.
Manhattan is not much wider than 3 km. Between First and West End Avenues the distance is 2.8 km. The likely average trip length is more than half the maximum, since the typical use case for the crosstown buses is travel between the Upper East Side and Upper West Side, but the dominant destinations are not at the ends of the line, but close to the middle. With Second Avenue Subway offering an attractive two-seat ride, there is less reason to take the crosstown buses to connect to the 1/2/3 (and indeed, the opening of the new line led to prominent drops in ridership on the M66, M72, M79, M86, and M96); the best subway connection point is now at Lexington Avenue, followed by Central Park West. On a long route, the location of the dominant stop is not too relevant, but on a short one, the average trip length is bounded by the distance between the dominant stop and the end of the line.
If we take the average trip length to be 1.6 km and plug it into the formula, we get
A crosstown bus stopping at First, Second, Third, Lex, Madison, Fifth, Central Park West, Columbus, Amsterdam, Broadway, and West End makes 10 stops in 2.8 km, for an average of 280 meters. There isn’t much room for stop consolidation. If the bus continues to Riverside, lengthening the trip to 3 km at the latitude of 96th Street, then it’s possible to drop West End. If the buses running up Third and down Lex are converted to two-way running, presumably on Lex for the subway connections, then Third could be dropped, but this would still leave the interstation at 330 meters, much tighter than anything we’re proposing in Brooklyn.
The only other places where avenues are too closely spaced are poor locations for stop removal. Amsterdam and Broadway are very close, but Amsterdam carries a northbound bus, and if the Columbus/Amsterdam one-way pair is turned into two two-way avenues, then Amsterdam is a better location for the bus than Columbus because it provides better service to the Far West Side. Fifth and Madison are very close as well, but the buses using them, the M1 through M4, are so busy (a total of 32 buses per hour at the peak) that if the two avenues are converted to two-way running then both should host frequent bus trunks. It’s not possible to skip either.
Within Brooklyn, there is one location in which the same issue of short bus routes applies: Coney Island. The B74 and B36 act as short-hop connectors from Coney Island the neighborhood to Coney Island the subway station. The routes we propose replacing them have 7 stops each from the subway connection west, over distances of 2.5 and 2.7 km respectively, for interstations of 360 and 390 meters.
Vancouver supplies two more examples of routes similar to the B74 and B36: the 5 and 6 buses, both connecting the West End with Downtown. The 6 is only 2 km between its western end and the Yaletown SkyTrain station, and the 5 is 2.3 km from the end to the Burrard station and 2.8 km to city center at Granville Street. The average trip length on these buses is necessarily short, which means that stop consolidation is not beneficial, unlike on the main grid routes outside Downtown.
Update 10/31: incorporating wait time into this calculation leads to the same general conclusion. The short routes in question – the Manhattan crosstowns, the B36 and B74, and the 5 and 6 in Vancouver – have high frequency, or in other words short distance between buses. For example, the M96 runs every 4 minutes peak, 6 off-peak, and takes 22-24 minutes one-way, for a total of 6 circulating buses per direction peak (which is 500 meters), or 4 off-peak (which is 750 meters). This yields
A network that discourages transferring should have more stops as well
In Paris the average interstation on buses in the city looks like 300 meters; this is not based on a citywide average but on looking at the few buses for which Wikipedia has data plus a few trunks on the map, which range from 250 to 370 meters between stations.
The short stop spacing in Paris is justified. First of all, the average bus trip in Paris is short: 2.33 km as of 2009 (source, PDF-p. 24). Parisian Metro coverage is so complete that the buses are not useful for long trips – Metro station access time is short enough that the trains overtake the buses on total trip time very quickly.
Second, there is little reason to transfer between buses here, or to transfer between buses and the Metro. The completeness of Metro coverage is such that buses are just not competitive unless they offer a one-seat ride where the Metro doesn’t. Another advantage of buses is that they are wheelchair-accessible, whereas the Metro is the single least accessible major urban rail network in the world, with nothing accessible to wheelchair users except Line 14 and the RER A and B. It goes without saying that people in wheelchairs are not transferring between the bus and the Metro (and even if they could, they’d have hefty transfer penalties). The New York City Subway has poor accessibility, but nearly all of the major stations are accessible, including the main bus transfer points, such as Brooklyn College and the Utica Avenue stop on the 3/4.
With little interchange and a mostly isotropic city density, the correct formula for the optimal bus stop spacing within Paris is
which is close to the midpoint of the range of interstations I have found looking at various routes.
The half-kilometer (or quarter-to-a-third-of-a-mile) rule for bus stop spacing is an empirical guideline. It is meant to describe average behavior in the average city. It is scale-invariant – the density of the city does not matter, only relative density does, and the size of the city only matters insofar as it may affect the average trip length. However, while scale itself does not lead to major changes from the guideline, special circumstances might.
If the geography of the city is such that bus trips are very short, then it’s correct to have closer stop spacing. This is the case for east-west travel in Manhattan. It is also common on buses that offer short-hop connections to the subway from a neighborhood just outside walking range, such as the B36 and B74 in Coney Island and the 5 and 6 in Vancouver’s West End.
Note that even in New York, with its 3.3 km average trip length, stop consolidation is still beneficial and necessary on most routes. North American transit agencies should not use this article as an excuse not to remove extraneous stops. But nor should they stick to a rigid stop spacing come what may; on some routes, encouraging very short trips (often 1.5 km or even less), closely spaced stations are correct, since passengers wouldn’t be riding for long enough for the gains from stop consolidation to accumulate.
There’s en emerging concept within North American urbanism and planning called missing middle. This refers to housing density that’s higher than suburban single-family housing but lower than urban mid- and high-rise buildings. The context is that in some cities with rapid housing construction, especially Toronto, the zoning code is either single-family or high-density, with nothing in between. The idea of allowing more missing middle housing has become a mainstay of New Urbanism as well as most North American YIMBY movements, underpinning demands such as the abolition of single-family zoning in California and Seattle.
Unfortunately, it’s an overrated concept. It applies to Toronto, but not Vancouver or the most expensive American cities, which are replete with missing middle density. The most in-demand neighborhoods have far too many people who want to move in to make do with this density level. Moreover, missing middle density in its New Urbanist form is not even really transit-oriented: low-rise construction spread over a large area is unlikely to lead middle-class workers to take transit when cars are available. The density required to encourage transit ridership and reduce housing costs is much higher, including mid- and high-rise residences.
What’s missing middle density?
A website created by Opticos Design, an architecture firm specializing in this kind of housing, has a helpful graphical definition:
Many of the missing middle housing forms are part of the vernacular architecture of American cities. In New England, this is the triple-decker, a three-story building with an apartment per floor. In Chicago, this is the fourplex, a two-story building with two apartments per floor. In Los Angeles this is the dingbat, with two or three inhabited floors on top of ground floor parking. In Baltimore and Philadelphia (and in London) this is the rowhouse. This history makes it easier to accept such buildings as both part of the local culture and as affordable to the lower middle class.
The triple-deckers in the parts of Providence and Cambridge I am most familiar with have a floor area ratio of about 1-1.5: they have 2.5 to 3 floors (counting sloped roofs as half a floor) and build on one third to one half the lot. A quick look at some Philadelphia rowhouses suggests they, too, have a floor area ratio in that range. Somerville has a population density just short of 7,000 people per km^2, with little non-residential land and some mid-rise and single-family areas canceling out to missing middle density. Kew Gardens Hills has about 12,000 people per km^2, and has a mixture of missing middle and mid-rise housing.
In Continental Europe, the vernacular architecture is instead mid-rise. In Scandinavia and Central Europe the euroblock has 4-7 floors and a floor area ratio of 2.5-4; Urban Kchoze shows many examples with photos, mostly from Prague, and Old Urbanist finds a euroblock in Berlin with a floor area ratio of 4.3. Central Stockholm’s residential buildings are almost entirely euroblocks, and residential density is 17,000/km^2 in Södermalm, 21,000/km^2 in Vasastan, and 28,000/km^2 in Östermalm. Parisian density is even higher – the floor area ratio of the traditional buildings looks like 4-5, with about 30,000-40,000 people per km^2.
Is missing middle really missing?
In Europe the answer is obviously no: lower-density cities like London are largely missing middle in their inner areas, and higher-density ones like Paris have missing middle density in their outer areas. But even in North America, where the term is popular, the expensive cities where people call for abolishing single-family zoning have missing middle housing. In addition to the above-listed vernacular examples, New York has brownstones all over Brooklyn (the term Brownstone Brooklyn refers to the gentrified inner neighborhoods, but this density is also seen in outer neighborhoods like Bay Ridge and Sheepshead Bay).
Vancouver is an especially instructive example. English Canada’s big cities are fast-growing, and a zoning regime that’s historically been friendlier to developers than to local NIMBYs has encouraged high-rise growth. Moreover, the high-rises are built in the modern boxy style (earning the ire of people who hate modern architecture) and tend to target middle-class and high-skill immigrant buyers (earning the ire of people who blame high housing costs on new construction). In contrast, vast swaths of Toronto and Vancouver are zoned for single-family housing.
And yet, Vancouver has considerable missing middle housing, too. The population density in Mount Pleasant, Fairview, Kitsilano, and West Point Grey is similar to that of Somerville and Eastern Queens. Buildings there are in modern style, but the housing typologies are not modernist towers in a park, but rather mostly buildings with 2-4 floors with the medium lot coverage typical of missing middle. I lived in an eight-unit, three-story building. Across from me there was a high-rise, but it was atypical; for the most part, that part of Vancouver is low-rise.
Shaughnessy offends people in its extravagance and wealth. In one Twitter conversation, an interlocutor who blamed absent landlords and foreigners (read: Chinese people) for Vancouver’s high housing costs still agreed with me that Shaughnessy, a white Canadian-born single-family area, shares the blame with its low-density zoning and very high residential space per person. Legalizing accessory dwelling units (“granny flats”) and townhouses in such a neighborhood faces local political headwind from the neighbors (who are still nowhere near as empowered to block rezoning as they would south of the border), but not from citywide social movements.
And yet, the density in the inner Westside neighborhoods near Broadway and Fourth Avenue is insufficient, too. It’s of course much higher than in Shaughnessy – I never really missed not owning a car living in Kitsilano – but the price signal screams “build more housing in Kits and Point Grey.”
Is missing middle transit-oriented?
Not really. In Providence the answer is absolutely not: car ownership is expected of every person who can afford it. The nearby supermarket, East Side Market, has an enormous parking lot; I’d walk, but it was obvious to me that my mode choice was not the intended use case. Even some Brown grad students owned cars (though most didn’t); at Columbia, car ownership among people below tenure-track faculty rank approaches zero. Once they own cars, people use them to take trips they wouldn’t otherwise have made, reorienting their travel patterns accordingly.
In Cambridge, car use is lower, but still substantial. The same is true of Vancouver (where outside Downtown and the West End the entire region’s density is at most missing middle, even if the typology is towers in a park and not uniformly low-rise). In Kew Gardens Hills, people seem to mostly drive as well.
This is not a universal feature of the urban middle class. In Stockholm, my postdoc advisor as far as I can tell does not own a car, and commutes to work by bike. Both there and in Basel, biking and using transit are normal and expected even among people who earn tenured academic salaries. At 7,000 people per km^2, people can forgo driving if they really want to, but most people will not do so. Only at the higher mid-rise density will they do so.
Last year, I saw a tip by the Metropolitan Police: if you witness any crime on a London bus and wish to report it later, you should tell the police the number on your Oyster card and then they’ll already be able to use the number to track which bus you rode and then get the names and bank accounts of all other passengers on that bus. Londoners seem to accept this surveillance as a fact of life; closed-circuit TV cameras are everywhere, even in front of the house where Orwell lived and wrote. Across the Pond, transit agencies salivate over the ability to track passenger movements through smartcards and contactless credit cards, which is framed either as the need for data or as a nebulous anti-crime measure. Fortunately, free countries have some alternative models.
In Germany, the population is more concerned about privacy. Despite being targeted by a string of communist terrorist attacks in the 1970s and 80s, it maintained an open system, without any faregates at any train station (including subways); fare enforcement in German cities relies on proof of payment with roving inspectors. Ultimately, this indicates the first step in a transit fare payment system that ensures people pay their fares without turning the payment cards into tracking devices. While Germany resists contactless payment, there are ways to achieve its positive features even with the use of more modern technology than paper tickets.
The desired features
A transit fare payment system should have all of the following features:
- Integration: free transfers between different transit vehicles and different modes should be built into the system, including buses, urban rail, and regional rail.
- Scalability: the system should scale to large metro areas with variable fares, and not just to compact cities with flat fares, which are easier to implement. It should also permit peak surcharges if the transit agency wishes to implement them.
- No vendor lock: switching to a different equipment manufacturer should be easy, without locking to favored contractors.
- Security: it should be difficult to forge a ticket.
- Privacy: it should not be possible to use the tickets to track passengers in most circumstances.
- Hospitality: visitors and occasional riders should be able to use the system with ease, with flexible options for stored value (including easy top-up options) and daily, weekly, and monthly passes, and no excessive surcharges.
Smartcard and magnetic card systems are very easy to integrate across operators; all that it takes is political will, or else there may be integrated fare media without integrated fares themselves, as in the Bay Area (Clipper can store value but there are no free transfers between agencies). Scalability is easy on the level of software; the hardest part about it is that if there are faregates then every station must have entry and exit gates, and those may be hard to retrofit. Existing smartcard technologies vary in vendor lock, but the system the US and Britain are standardizing on, contactless credit cards, is open. The real problem is in protecting privacy, which is simply not a goal in tracking-obsessed Anglo-American agencies.
The need for hospitality
Hospitality may seem like a trivial concern, but it is important in places with many visitors, which large transit cities are. Moreover, universal design for hospitality, such as easily recognizable locations for topping up stored value, is also of use to regular riders who run out of money and need to top up. Making it easy to buy tickets without a local bank account is of use to both visitors and low-income locals without full-service bank accounts. In the US, 7% of households are unbanked and another 20% are underbanked; I have no statistics for other countries, but in Sweden banks will not even give debit cards to people with outstanding debts, which suggests to me that some low-income Swedes may not have active banking cards.
New York’s MetroCard has many faults, but it succeeds on hospitality better than any other farecard system I know of: it is easy to get the cards from machines, there is only a $1 surcharge per card, and season tickets are for 7 or 30 days from activation rather than a calendar week or month. At the other end of the hospitality scale, Navigo requires users to bring a passport photo and can only load weekly and monthly passes (both on the calendar); flexible 5-day passes cost more than a calendar weekly pass.
In fact, the main reason not to use paper tickets is that hospitality is difficult with monthly passes printed on paper. Before the Compass Card debacle, Vancouver had paper tickets with calendar monthly passes, each in a different color to make it easy for the driver to see if a passenger was flashing a current or expired pass. The tickets could be purchased at pharmacies and convenience stores but not at SkyTrain stations, which only sold single-ride tickets.
ID cards and privacy
The Anglosphere resists ID cards. The Blair cabinet’s attempt to introduce national ID cards was a flop, and the Britons I was reading at the time (such as the Yorkshire Ranter) were livid. And yet, ID cards provide security and privacy. Passports are extremely difficult to forge. Israel’s internal ID cards are quite difficult to forge as well; there are occasional concerns about voter fraud, but nothing like the routine use of fake drivers’ licenses to buy drinks so common in American college culture.
At the same time, in countries that are not ruled by people who think 1984 was an uplifting look at the future, ID cards protect privacy. The Yorkshire Ranter is talking about the evils of biometric databases, and Israeli civil liberties advocates have mounted the same attack against the government’s attempt at a database. But German passports, while biometric, store data exclusively on the passport, not in any centralized database. ID cards designed around proving that you paid your fare don’t even have to use biometrics; the security level is lower than with biometrics, but the failure mode is that the occasional forger can ride without paying $100 a month (which is much less than the cost of the forgery), not that a ring of terrorists can enter the country.
Navigo’s ID cards are not hospitable, but allowing passengers to ride with any valid state-issued ID would be. Visitors either came in from another country and therefore have passports, drove in and therefore have drivers’ licenses, or flew in domestically and therefore still have ID cards. Traveling between cities without ID is still possible here and in other free European countries, but everyone has national ID cards anyway; the ID problem is mainly in the US with its low passport penetration (and secondarily Canada and Australia), and the US has no intercity public transit network to speak of outside the Northeast Corridor.
What this means is that the best way to prevent duplication of transit passes is to require ID cards. Any ID card must be acceptable, including a passport (best option), a national ID card (second best), or an American driver’s license (worst).
Getting rid of the faregates
There are approximately three first-world Western cities that have any business having faregates on their urban rail networks: London, Paris, New York. Even there, I am skeptical that the faregates are truly necessary. The Metro’s crowd control during the World Cup victory celebration was not great. New York’s faregates sometimes cause backups to the point that passengers just push the emergency doors open to exit, and then rely on an informal honor system so that passengers don’t use the open emergency doors to sneak in without payment.
Evidently, the Munich S-Bahn funnels all traffic through a single two-track city center tunnel and has 840,000 weekday users, without faregates. Only one or two trunk lines are busier in Paris, the RER A with about a million, and possibly the RER B and D if one considers them part of the same trunk (they share a tunnel but no platforms); in London, only the Central, Victoria, and Jubilee lines are busier, none by very much; in New York, none of the two-track trunks is as busy. Only the overcrowded lines in Tokyo (and a handful in Osaka, Beijing, and Shanghai) are clearly so busy that barrier-free proof-of-payment fare enforcement is infeasible.
The main reason not to use faregates is that they are maintenance-intensive and interfere with free passenger flow. But they also require passengers to insert fare media, such as a paper ticket or a contactless card, at every station. With contactless cards the system goes well beyond exact numbers of users by station, which can be obtained with good accuracy even on barrier-free systems like Transilien using occasional counts, and can track individual users’ movements. This is especially bad on systems that do not have flat fares (because then passengers tag on and off) and on systems that involve transferring with buses or regional trains and not just the subway (because then passengers have to tag on and off at the transfer points too).
Best industry practice here is then barrier-free systems. To discourage fare evasion, the agency should set up regular inspections (on moving vehicles, with unarmed civilian inspectors), but at the same time incentivize season passes. Season passes are also good for individual privacy, since all the system registers is that the passenger loaded up a monthly pass at a certain point, but beyond that can’t track where the passenger goes. All cities that have faregates except for the largest few should get rid of them and institute POP, no matter the politics.
Tickets and ID cards
In theory, the ID card can literally be the ticket. The system can store in a central database that Alon Levy, passport number [redacted], loaded a monthly pass valid for all of Ile-de-France on 2018-08-16, and the inspector can verify it by swiping my machine-readable passport. But in practice, this requires making sure the ticket machine or validator can instantly communicate this to all roving fare inspectors.
An alternative approach is to combine paper tickets with ID cards. The paper ticket would just say “I am Alon Levy, passport number [redacted], and I have a pass valid for all of Ile-de-France until 2018-09-14,” digitally signed with the code of the machine where I validated the ticket. This machine could even be a home printer, via online purchase, or a QR code displayed on a phone. Designing such a system to be cryptographically secure is easy; the real problem is preventing duplication, which is where the ID card comes into play. Without an ID card, it’s still possible to prevent duplication, but only via a cumbersome system requiring the passenger to validate the ticket again on every vehicle (perhaps even every rail car) when getting on or off.
The same system could handle stored value. However, without printing a new ticket every time a passenger validates, which would be cumbersome, it would have to fall back on communication between the validator and the handheld readers used by the inspectors. But fortunately, such communication need not be instant. Since passengers prepay with stored value, the ticket itself, saying “I am Alon Levy, passport number [redacted], and I loaded 10 trips,” is already valid, and the only communication required is when passengers run out of money; moreover, single-use tickets have a validity period of 1-2 hours, so any validator-to-inspector communication lag time of less than the validity period will be enough to ensure not to validate expired tickets. The same system can also be used to have a daily cap as in Oyster, peak surcharges, and even generally-undesirable station-to-station rather than zonal fares.
It’s even possible to design a system without single-use tickets at all. Zurich comes close, in that a 24-hour pass costs twice as much as a single-use ticket (valid for just an hour), so passengers never have any reason to get a single-use ticket. In this system there would not be any stored value, just passes for a day or more, valid in prescribed zones, with printable tickets if regular riders in one zone occasionally travel elsewhere.
The upshot here is that advanced technology is only required for printing and reading QR codes. The machines do not need to be any more complicated than ATMs or Bitcoin ATMs (insert money, receive a Bitcoin slip of paper); I don’t know how much Bitcoin ATMs cost, but regular ATMs are typically $2,000-3,000, and the most expensive are $8,000, unlike the $75,000 ticket machines used at New York SBS stations. The moving parts are software and not hardware, and can use multi-vendor cryptographic protocols. In effect, the difficult part of verifying that there is no duplication or forgery is offloaded to the state ID system.
When I lived in Vancouver, I was enthusiastic about SkyTrain, which combined high service levels with relatively low construction costs. At the time, the budget for the 12-kilometer Broadway subway from VCC-Clark to UBC was $3 billion (all figures are in Canadian dollars, so subtract 20% for US PPP equivalents). The cost per km was average for a non-English-speaking country, and very low for an English-speaking one, and the corridor has high population and job density. With a ridership projection of 350,000, it was by a large margin North America’s most cost-effective rail extension.
Since then, costs have sharply risen. TransLink lost its referendum and had to scramble for funding, which it got from the new Trudeau administration – but the money was only sufficient to build half the line, between VCC-Clark and Arbutus. With the latest cost overrun, the budget is now $2.83 billion for 5.6 km: C$500 million per kilometer. This is barely below average for a North American subway, and very high for a Continental European one. I tried reaching out to TransLink before the overrun was announced, trying to understand how it was building subways for less money than the rest of North America, but while the agency knew who I am and what I was querying, it didn’t respond; now I know why.
Outside Vancouver, costs are high as well. In Toronto, there are several subway projects recently built or proposed, all expensive.
The least expensive is the Vaughan extension of the Yonge-University-Spadina Line. It opened last year, after a two-year delay, at the cost of $3.2 billion for 8.6 km, or C$370 million per kilometer. Andy Byford, then the chair of the Toronto Transit Commission, now New York City Transit chief, was credited with limiting the cost overruns after problems began. The line is an outward extension into low-density suburbia, and construction has no reason to be difficult. The source also cites the expected ridership: 24 million per year by 2020, or about 80,000 per weekday, for a total of $40,000 per rider, a high though not outrageous figure.
More expensive is the Scarborough subway. Toronto has an above-ground rapid transit line connecting Scarborough with Kennedy on the Bloor-Danforth Line, using the same technology as SkyTrain but with a driver. But unlike Vancouver, Toronto is unhappy with the technology and has wanted to replace the entire line. Originally the plan was to replace it with light rail, but subsequently the plans have changed to a subway. The current plan is to build a 6.4-km nonstop extension of the Bloor-Danforth Line, which would cost $3.35 billion, or C$520 million per kilometer. While this is still slightly below average by American standards, the dominant factor for construction costs in New York is the stations, which means a long subway tunnel with just one new station should be cheap. At the per-item costs of Paris, the line should cost US$1.07 billion, or about C$1.35 billion. At those of Second Avenue Subway, it should cost US$3.3 billion, or about C$4.1 billion. In other words, Toronto is building a subway for almost the same costs as New York, taking station spacing into account, through much lower-density areas than the Upper East Side.
Finally, Toronto has long-term plans for a Downtown Relief Line, providing service to the CBD without using the Yonge-University-Spadina Line. The estimated cost in 2016 dollars is $4-4.4 billion (source, PDF-p. 31), but this assumes faster-than-inflation cost escalation already, and adjusted only for inflation this is higher, about $5-5.5 billion. Per PDF-p. 15 the line would have 6.25-6.7 km of tunnel, for a total cost of about C$800 million per kilometer. The DRL is planned to go under older subways and serve Downtown Toronto, contributing to its higher cost, but the stations are to be constructed cut-and-cover. Despite using cheap construction methods, Toronto is thus about to build an extremely expensive subway.
While I’ve drawn a distinction between costs in English- and non-English-speaking countries, or between common and civil law countries Montreal’s costs are solidly common law Anglophone even though Quebec is Francophone and uses civil law. A 5.8 km extension of the Blue Line is budgeted at $3.9 billion, a total of C$670 million per kilometer. The Blue Line is circumferential, and the extension would extend it further out, but the residential areas served are fairly dense, around 10,000 people per square kilometer on adjacent census tracts.
The last case is Ottawa, where costs are less clear. Ottawa is replacing its BRT line with light rail, which includes a short city center tunnel, called the Confederation Line. The cost is $2.1 billion and the length of the line is 12.5 km, of which 2.5 is in tunnel and the rest is on the surface. The overall project is more expensive, at $3.6 billion, but that includes related works on other lines. I don’t know the portion of the Confederation Line’s cost that’s attributed to the tunnel, so any estimate for tunneling cost has to rely on estimates for the underground premium over surface transit. In Vancouver the original estimate for Broadway rail had a 2.5:1 premium, which would make the cost of the tunnel $320 million per km; however, a more common premium is 6:1, which would raise the cost of the tunnel to $500 million per km.
I don’t know why Canada is so expensive; I’m less familiar with the details of its subway extensions than I am with those of either the US or the UK. The fact that Toronto manages to have very high construction costs even while using cheap methods (cut-and-cover stations, or long nonstop segments) is worrying, since it casts doubt on the ability of high-cost cities to rein in expenses by using cut-and-cover stations rather than mining.
Moreover, the social reasons leading to degradation of civil service in the US are less relevant to Canada. There is less hyperlocal empowerment than in the US and stronger provinces relative to both the federal government and municipalities. Anecdotally I have also found Canadians less geographically solipsistic than Americans. If I had to guess I would say that Canadians look to the US as a best practices model, just as Americans in various cities do to other American (and sometimes Canadian) cities, and if they look at foreign models they look at the UK. Montreal used Paris as a model when it first built its Metro, but more recently its ideas about using France as a model have devolved into no-bid contracts.
The American discourse about gentrification is full of stereotypes that the participants don’t recognize as such. For example, a widely-shared Buzzfeed article created an entire theory out of a single busybody who was responsible for half of the police complaints on their West Harlem block. The main check on stereotypes – “that’s racist” – only works when the stereotypes resemble the forms of racism society is most familiar with. The history of white racism against black people in the US is so different that it colors what Americans perceive as racial stereotypes and what they don’t. So as public service, I’d like to give some examples to draw commonalities between stereotypes in other cities I’ve lived in (Tel Aviv, Vancouver, Paris) and familiar anti-gentrification rhetoric.
Last decade, there was an influx of black refugees into working-class areas of South Tel Aviv, centered on Levinsky Park. The area is underpriced relative to its job access, courtesy of Central Bus Station, a failed urban renewal project that attracted crime; already in the 1990s it was nicknamed Central Stench (tsaḥana merkazit; Central Station is taḥana merkazit) and lampooned in a popular comic as a literal gateway to hell. The neighborhood’s response was violent, and the discourse within Israel is divided into people who wish the refugees imprisoned and deported from the country and people who wish them forcibly dispersed around the country.
Other parts of South Tel Aviv have been gentrifying since the 1990s, centered on Florentin. South Tel Aviv’s right-wing Jewish working class began connecting the two trends. A few years ago I saw a widely-shared Facebook post claiming that the influx of black refugees is deliberately engineered by developers as a ploy to gentrify the neighborhood. The theory, as I recall, is that black people are so odious that developers are using them to engineer white flight, after which they’ll evict the refugees, demolish the neighborhood’s mid-rise housing stock, and erect luxury towers.
In the last decade or so Vancouver has seen rising rents and even faster-rising housing prices, and the region’s white population is blaming Chinese people. In 2016, British Columbia passed a 15% tax on residential buyers who are not Canadian citizens or permanent residents; the tax was phrased neutrally, but the target was predominantly Chinese, and 21% of correspondence from citizens to the government on the issue was explicitly Sinophobic. In a city with rapid immigration, it should not be a surprise that new buyers tend to be immigrants, often on work or investor visas, but the region has a moral panic about Chinese people buying condos and houses as investments and leaving them empty.
The specific stereotypes of Chinese people in Vancouver vary. When I lived in Vancouver I encountered some light generic stereotyping (“people in Richmond are aggressive drivers”), but nothing connoting poverty, even though Richmond is poorer than Surrey, which some people I met compared with Camden, New Jersey. The language I see in the media concerning housing goes the other way: Chinese immigrants are stereotyped as oligarchs laundering ill-begotten wealth.
Like people in every other highly-toured region, Parisians hate the tourists. Seeing small declines in city population over the 2009-14 period, city electeds decided to blame Airbnb, and not, say, low housing construction rates (raising rents), a falling birth rate, or commercialization in city center. The mayor of the 1st arrondissement, Jean-Francois Legaret, called Airbnb “a true catastrophe for Central Paris.” The 1st arrondissement has high residential incomes; the lower-income parts of the city are the 10th, 11th, 13th, 18th, 19th, and 20th.
Rich and poor stereotypes
An ethnic or national group can stereotype another group as rich, poor, or both. White stereotypes of black people in the US and Europe are, within each ethnic group, associated with poverty: crime, aggressive physicality, laziness, indifference to education, proclivity for certain kinds of music and sport. Anti-Semitism today invokes stereotypes of the rich: greed, political subversion, disloyalty to the nation, corruption, success with money. Islamophobic stereotypes tend toward stereotypes of poverty, but are sometimes also bundled with stereotypes of Gulf money. In the last few decades Sinophobic stereotypes transitioned from ones of poverty (treating the Chinese as a faceless horde) to ones of wealth, similar to anti-Semitic stereotypes, to the point that people in Vancouver forget Richmond’s low incomes and people in New York forget the high poverty rates of Asian-New Yorkers and the overcrowding in Chinatown.
But as in the case of South Tel Aviv, the stereotypes can merge. The racists in South Tel Aviv blend two groups they hate – middle-class leftists and poor non-Jews – into one mass, blaming them for a trend that is usually blamed on the rich and the middle class. Historically, anti-Semitism was fully blended: the Jew was simultaneously poor and rich, wretched and exploitative, communist and capitalist, overly studious and overly physical. This blending of stereotypes was overt in Nazi propaganda, but also in the softer anti-Semitism directed against immigrants to the US.
The urban as a foreigner
Nationalists and populists stereotype cities like prewar anti-Semites stereotype Jews. The urban poor are lazy criminals, the rural poor are honest workers; the urban rich are exploitative capitalists sucking life out of the country, the rural rich are successful small business leaders; the urban middle class are bo-bo globalists, the rural middle class is the very definition of normality. This mentality is hard to miss in anti-urbanist writers like Joel Kotkin, and more recently in articles trying to portray an opposition between the Real Country (in the US but also in Israel and France) and the Urban Elites.
The definition of what is rural and what is urban is fractal. In the South, Long Island is part of New York; on Long Island, Long Island is Real America, distinct from the city that Long Island’s residents fled in the 1950s and 60s. Within cities the Real Country vs. Urban Elite opposition can involve the outer city vs. the inner city, as in Toronto, where Rob Ford won the mayoral election by appealing to outer-urban resentment of David Miller’s attempt to redistribute street space from cars to public transit. But it is in many cases demographic rather than geographic: the newcomer is the new rootless cosmopolitan.
In this mentality, the newcomer can be a rich gentrifier displacing honest salt-of-the-earth third-generation residents by paying higher rents or a refugee doing the same through living multiple people to a bedroom (or even both, in the case of some San Francisco programmers). In either case, the newcomer is a foreigner who doesn’t belong to the city’s culture and does not deserve the same access to city resources. People who build housing for this foreigner are inherently suspect, as are businesses that cater to the foreigner’s tastes. The demands – removal of access to housing – are the same regardless of whether the foreigners so stereotyped are poor or rich, and the stereotypes of wealth and poverty mix easily. That anti-gentrification activism looks so similar regardless of which social class it targets suggests that ultimately, any argument made is an excuse justifying not liking outsiders very much.
I wrote about infill stops on commuter rail two weeks ago, and said I cannot think of any example of anti-infill on that mode. But looking at Muni Metro reminded me that there is need for anti-infill on surface transit. This is called stop consolidation normally, and I only use the term anti-infill to contrast with the strategy of adding more stops on commuter trains.
The root of the problem is that in North America, transit agencies have standardized on 200-250 meters as the typical spacing between bus stops. In Europe, Australasia, and East Asia, the standard is instead 400-500 meters. Even without off-board fare collection, the difference in speed is noticeable. In Vancouver, the difference between the local 4 and the express 84 is substantial: on the shared segment between Burrard and Tolmie, a distance of 4.8 km, the 84 makes 5 stops and takes 10 minutes, the 4 makes 18 stops and takes 16 minutes. A bus with the normal first-world stop spacing would make 10-12 stops and take, linearly, 12-13 minutes. 23 km/h versus 18 km/h.
With off-board fare collection, the impact of stop spacing on speed grows. The reason is that a bus’s stop penalty consists of the time taken to stop and open its doors, plus the time it takes each passenger to board. The former time is independent of the fare collection method but depends on stop spacing. The latter time is the exact opposite: if the stop spacing widens, then there are more passengers per bus stop, and unless the change in stop spacing triggers changes in ridership, overall passenger boarding and alighting time remains the same. Another way to think about it is that judging by Vancouver data, there appears to be a 30-second stop penalty, independent of ridership. Off-board fare collection increases bus speed, so the 30-second stop penalty becomes more important relative to overall travel time; the same is true of other treatments that increase bus speed, such as dedicated lanes and signal priority.
In New York, there aren’t a lot of places with local and limited-stop buses side by side in which the limited-stop bus has on-board fare collection. One such example is the M4, meandering from Washington Heights down the 5th/Madison one-way-pair, over 15.3 km. At rush hour, the local takes 1:45, the limited-stop takes 1:30: 9 vs. 10 km/h. But the limited-stop bus runs local for 6 km, and over the other 9.3 km it skips 26 local stops if I’ve counted right. The B41 has a limited-stop version over 8.3 km (the rest is local), skipping about 17 stops; the time difference is 10 minutes.
One possible explanation for why the stop penalty in New York seems a little higher than in Vancouver is that the M4 and B41 routes are busier than the 4/84 in Vancouver, so every stop has at least one passenger, whereas the 4 in Vancouver often skips a few stops if there are no passengers waiting. Conversely, the higher passenger traffic on buses in New York comes from higher density and more traffic in general, which slows down the buses independently of stopping distance.
On subways, there’s reason to have more densely-spaced stops in denser areas, chief of which is the CBD. On surface transit, it’s less relevant. The reason is that absolute density doesn’t matter for stop spacing, except when expected ridership at once station is so high it would stress the egress points. What really matters is relative density. Putting more stops in an area means slowing down everyone riding through it in order to offer shorter station access times to people within it. On surface transit, relative density gradients aren’t likely to lead to variations in stop spacing, for the following reasons:
- Historically, surface transit stop spacing was always shorter than rapid transit stop spacing because of its lower top speed and the faster braking capabilities of horses vs. steam trains; often people could get off at any street corner they chose. So it induced linear development, of roughly constant density along the corridor, rather than clusters of high density near stations.
- If there is considerable variation in density along a surface transit line, then either density is medium with a few pockets of high density, which would probably make the line a good candidate for a subway, or density is low with a few pockets of higher density, and the bus would probably skip a lot of the low-density stops anyway.
Most importantly, the 400-meter standard is almost Pareto-faster than the 200-meter standard. In the worst case, it adds about 4 minutes of combined walking time at both the start and the end of the trip, for an able-bodied, healthy person not carrying obscene amounts of luggage. The breakeven time on 4 minutes is 8 skipped stops, so 3.2 km compared with the 200-meter standard. Bus trips tend to be longer than this, except in a few edge cases. In New York the average unlinked bus trip is 3.4 km (compare boardings and passenger-km on the NTD), but many trips involve a transfer to another bus or the subway, probably half judging by fare revenue, and transfer stations would never be deleted. If the destination is a subway station, guaranteed to have a stop, then the breakeven distance is 1.6 km.
This also suggests that different routes may have different stop spacing. Very short routes should have shorter stop spacing, for example the 5 and 6 buses in Vancouver. Those routes compete with walking anyway. This may create a spurious relationship with density: the 5 and 6 buses serve the very dense West End, but the real reason to keep stop spacing on them short is that they are short routes, about 2 km each. Of course, West End density over a longer stretch would justify a subway, so in a way there’s a reason short optimal stop spacing correlates with high bus stop density.
The situation on subways is murkier. The stop penalty is slightly higher, maybe 45 seconds away from CBD stations with long dwell times. But the range of stop distances is such that more people lose out from having fewer stops. Paris has a Metro stop every 600 meters, give or take. Some of the busiest systems in countries that were never communist, such as Tokyo, Mexico City, and London, average 1.2 km; in former communist bloc countries, including Russia and China, the average is higher, 1.7 km in Moscow. The difference between 600 meters and 1.2 km is, in the worst case, another 1.2 km of walking, about 12 minutes; breakeven is 16 deleted stops, or 20 km, on the long side for subway commutes.
One mitigating factor is that subway-oriented development clusters more, so the worst case is less likely to be realized, especially since stops are usually closer together in the CBD. But on the other hand, at 1.2 km between stations it’s easy for transfers to be awkward or for lines to cross without a transfer. London and Tokyo both have many locations where this happens, if not so many as New York; Mexico City doesn’t (it’s the biggest subway network in which every pair of intersecting lines has a transfer), but it has a less dense network in its center. Paris only has three such intersections, two of them involving the express Metro Line 14. Even when transfers do exist, they may be awkward in ways they wouldn’t have been if stop spacing had been closer (then again, Paris is notorious for long transfers at Chatelet and Montparnasse).
In all discussions of subway stop spacing, New York is sui generis since the lines have four tracks. On paper its subway lines stop every 600-700 meters when not crossing water, but many trains run express and stop every 2 km or even more. Average speed is almost the same as in Tokyo and London, which have very little express service, and it used to be on a par until recent subway slowdowns. This distinction, between longer stop spacing and shorter stop spacing with express runs, also ports to buses. Buses outside the US and Canada stop every 400-500 meters and have no need for limited-stop runs – they really split the difference between local and limited buses in North America.
On a subway, the main advantage of the international system over the New York system is obvious: only two tracks are required rather than four, reducing construction costs. On a bus line, the advantages are really the same, provided the city gives the buses enough space. A physically separated bus lane cannot easily accommodate buses of different speeds. In New York, this is the excuse I’ve heard in comments for why the bus lanes are only painted, not physically separated as in Paris. Mixing buses of different speeds also makes it hard to give buses signal priority: it is easy for buses to conflict, since the same intersection might see two buses spaced a minute apart.
Buses also benefit from having a single speed class because of the importance of frequency. In Vancouver, the off-peak weekday frequency on 4th Avenue is an 84 rapid bus every 12 minutes, a 44 rapid bus every 20 minutes, and a local 4 every 15 minutes. The 84 keeps going on 4th Avenue whereas the 4 and 44 divert to Downtown, but the 4 and 44 could still be consolidated into a bus coming every 10 minutes. If there were enough savings to boost the 84 to 10 minutes the three routes could vaguely be scheduled to come every 5 minutes on the common section, but without dedicated lanes it’s probably impossible to run a scheduled service at that frequency (pure headway management and branching don’t mix).
The example of 4th Avenue gets back to my original impetus for this post, Muni Metro. Only diesel buses can really run in regular surface mode mixing different speed classes. Trolleys can’t. Vancouver runs trolleys on the local routes and diesels on the limited routes. At UBC, it has different bus loops for diesels and trolleys, so people leaving campus have to choose which type of bus to take – they can’t stand at one stop and take whatever comes first.
On rail, this is of course completely impossible. As a result, American subway-surface trolleys – the Boston Green Line, SEPTA’s Subway-Surface Lines, and Muni Metro – all run at glacial speed on the surface, even when they have dedicated lanes as in Boston. In Boston there has been some effort toward stop consolidation on the Green Line’s busiest branch, the B, serving Boston University. This is bundled with accessibility – it costs money to make a trolley stop wheelchair-accessible and it’s cheaper to have fewer stops. Muni Metro instead makes one stop every 3-5 accessible (on paper), but keeps stopping at all the other stops. It would be better to just prune the surface stops down to one every 400-500 meters, which should be accessible.
If you view rail as inherently better than bus, which I do, then it fits into the general framework: anti-infill on surface transit has the highest impact on the routes with the best service quality. Higher speed makes the speed gain of stop consolidation more important relative to travel time; trolleywire makes it impossible to compensate for the low speed of routes with 200-meter interstations by running limited-stop service. Even on local buses, there is never a reason for such short stop spacing, and it’s important for North American cities to adopt best industry practice on this issue. But it’s the most important on the highest-end routes, where the gains are especially large.
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.
Note on definitions: for the purposes of this post, a tramway is a light rail line that runs predominantly on streets, interfacing with cross-traffic even if it has signal priority. It can be a legacy streetcar in mixed traffic, or a newer light rail line running on dedicated lanes. It is distinguished from lines that have substantial grade-separated segments, including subway-surface lines, where these segments are in city center while the suburban segments are in tramway mode, and tram-trains and most North American light rail lines, where these segments are in the suburbs while the city-center segments are in tramway mode.
Intermediate in capacity between the surface bus and the rapid transit train is the tram. Running on the street, perhaps with signal priority but without the absolute priority that mainline trains have at grade crossings, trams are still surface transit, but feature better ride quality, generally higher capacity in terms of vehicles per hour, and generally bigger vehicles. A number of cities have been building such transit in recent years, most notably Paris, which has been making the rounds on the Transit Center for having almost a million daily riders on its system. The Transit Center gives various recommendations based on Paris’s success, but those recommendations – frequency, fare integration, good transfers – say very little about where a city should be building tramway lines. In this post, I am going to sketch features of good corridors for tramways.
1. Tramways are surface transit
There are various features that make for good surface transit routes. Jarrett Walker, who has extensive experience in bus network redesigns, outlined some of them in a network design document he collaborated on for TransLink. These include high density along the route, relatively balanced demand in both directions, and the potential for a strong everywhere-to-everywhere grid. Additional important features of strong bus routes: a single street with few twists, since turns slow down surface vehicles a lot, and swerving to reach major destinations is often cumbersome; and a wide street, since in practice few cities will give transit dedicated lanes if there’s not enough room for cars as well. These rules do not apply to subways, which can zigzag between different streets or carve a new alignment. However, they do apply to tramways.
2. The strongest bus corridors are in most need of investment
In a city where the buses that can support high frequency already are frequent, the highest potential for extra ridership is on routes that are already strong. Imagine a bus that averages 15 km/h: replacing it with a 20 km/h tram that provides a smoother and more reliable ride has benefits in rough proportion to existing bus ridership. Since both buses and trams are surface transit and follow the same rules, it’s unlikely that there are routes that would make good trams but poor buses. This is in stark contrast with subways, where a potentially strong corridor may not have a continuous surface right-of-way for high bus ridership. On the surface, this corridor could not succeed as either a bus or a tram. This is a specification of the BMT’s all four concept (bus, trolleybus, tramway, subway), in which the four modes work in complement, and the busiest routes in each category are upgraded to the next based on a tradeoff between construction costs and operating costs.
3. In a city with subways, the tramways should be placed on routes that would make poor subway corridors
It goes without saying that tramways should not duplicate subways. But more than that, if a bus route is so strong that it’s a potential subway extension, it should not be turned into a tram. At first pass, this may look like the best bus routes to be turned into trams are not quite the busiest, but the next tier of busier buses. However, this has to do not just with ridership, but also layout relative to the subway system. The subway is almost invariably radial, so strong buses that make easy radials or branches of radials would be strong subway routes, while circumferential buses would not. A radial bus may also turn out to be a poor subway route, if it happens to point in a direction where a subway wouldn’t be a good fit, but this is less likely.
4. A connected network is beneficial, but not required
Ideally, all light rail routes – not just tramways, but also subway-surface routes and tram-trains if they exist – should form a connected graph, with track connections, to enable maximum flexibility in yard placement and reduce the required spare ratio. However, this is not a requirement. Large, busy systems in particular may economically have a yard serving just 1-2 lines, in which case the value of connectedness decreases. In conjunction with point #3, cities with large radial subway networks may have disconnected circumferential tramways, including Paris.
5. When there’s a choice between several tramways and a subway, tramways work better when there’s no dominant route
The construction cost of a subway, in developed countries that are not the US, is $100-300 million per km, with outliers outside the range in both directions. The construction cost of a tramway in the same countries is $15-50 million per km, again, with outliers. The choice of whether to build one subway or six tramways depends on how busy the strongest route is relative to the next five routes. If two strong bus routes are closely parallel, then both should be reckoned together for subway ridership estimates (and to some extent also for tram ridership), since people walk longer to better service, in this case a fast subway rather than a slow bus. Another consideration, more about construction costs than ridership, is whether there exists a good right-of-way for the subway, perhaps an abandoned or low-ridership commuter line that can be converted, that would make it possible to limit tunneling.
Boston has few long, wide roads; Massachusetts Avenue is one of very few exceptions. Downtown Boston and the surrounding neighborhoods have very narrow streets, which is why the Boston bus network is sparse downtown – the buses feed outlying subway stations, or stop at the edge of the central business district at Haymarket, and almost never enter the downtown core. Because of the Green Line, some strong radial routes, such as the Washington Street half of the Silver Line, and the 23 bus on Blue Hill Avenue, are naturally good extensions of the subway-surface network; they’d make good light rail, but not all-surface tramways.
In strongly gridded cities, including Chicago, Vancouver, Toronto, and Los Angeles, it doesn’t make too much sense to build individual tramways; instead, the entire frequent bus grid could be so upgraded, or possibly just the lines that are perpendicular to the rapid transit system in Chicago and Toronto. Unfortunately, this runs into high construction costs, which leads to questions of priorities: build an expansive light rail network, or extend a few subway lines.
I believe Los Angeles and Vancouver are doing right in choosing to prioritize subways on their strongest corridors. Vancouver in particular is an extreme example of point #5 pointing toward a subway, with 80,000 weekday riders on Broadway and another 40,000 on the routes interlining on 4th Avenue 500 meters away (not all on 4th, as two of the four 4th Avenue routes have substantial tails elsewhere), compared with 110,000 on the next five routes combined; Vancouver also seems to have an unusually low subway-to-tram cost ratio, only about 2.7 rather than 6. Los Angeles has a less extreme version of point #5, but Wilshire and very close-by routes dominate east-west traffic, and can also easily feed into the existing subway.
In Chicago, the circumferential nature of the top bus routes – north-south west of the Loop, east-west north and south of it – makes an L extension infeasible, so from point #3, any solution has to involve surface transit. The current plan is dedicated bus lanes. In Toronto this decision is more difficult, and acrid debates between a mostly-surface option and an all-underground option led to the latter choice, influenced by Rob Ford’s unwillingness to take road lanes from cars; right now Toronto is building one subway line (update: it’s mixed subway-surface), under Eglinton, and one tramway, on Finch West.
In New York, Bill de Blasio proposed a tram route near the Brooklyn and Queens waterfront earlier this year; see background articles here and here. This route is ill-suited for the technology proposed, or for any significant investment. The buses along the waterfront are all quite weak. In both Brooklyn and Queens, the busiest buses are in the interior, some going perpendicular to the subway, such as the Q44 on Main Street and B35 on Church, and some serving radial routes that have long been planned to be subway extensions, namely the B46 on Utica and B44 on Nostrand. Select Bus Service investments have targeted these routes, and now the Q44, B44, and most recently the B46 all have SBS features.
Another weakness of the proposed route is that it subtly combines circumferential and radial service; see here for why this is poor practice. While the line is for the most part straight, the north-south segment in Queens is essentially radial, going from Astoria to Long Island City, parallel to the N/Q subways, before switching to circumferential between Long Island City and Downtown Brooklyn. South of Downtown Brooklyn it becomes radial again, connecting to Red Hook and Sunset Park. Riders in Astoria going south are mostly interested in continuing toward Manhattan and not toward Brooklyn; riders in Sunset Park and Red Hook going north would first of all follow different routes (Sunset Park already has the N and R subways and has no use for a detour through Red Hook), and second of all be more interested in going to Manhattan than to Williamsburg and points north.
While de Blasio’s proposal is bad transit, there are routes in New York that could make strong tramways. None of them is on the city’s redevelopment agenda, based on the principle that US cities almost never invest in low- and lower-middle-income neighborhoods except when they are about to gentrify, but the bus ridership there is solid, even though the buses crawl.
The busiest routes in New York are the M15 on 1st and 2nd Avenues in Manhattan, the B46, and the Bx12 on Fordham Road; each has been the single busiest in one of the last few years, but usually the M15 is first. The first two are strong subway routes: the first phase of Second Avenue Subway will soon open, and the rest will be built when the city can find multiple billions per kilometer for them; Utica is also a strong route, and de Blasio proposed it last year before abandoning the idea. But Fordham satisfies point #4 perfectly: it is circumferential, and can only realistically extend the A train, already the system’s longest route, with a mismatch in potential ridership between the core radial segment and what a Fordham subway would get. The Bx12 was the first route to be turned into SBS, and is either the strongest potential tramway in the city, or one of the few strongest.
Going further down the list, we should eliminate the strong Brooklyn routes, except the B41 on Flatbush. The B44 is also a potential subway extension, and the three busiest circumferentials – the B6, B35, and B82 – all parallel the Triboro right-of-way, which by point #5 is a superior project to building multiple light rail lines. The busiest bus in Queens, the Q58, has a long segment between Queens and Brooklyn, about half its total length, that would be obviated by Triboro as well.
The B41 could be a tramway going between City Hall and Kings Plaza, using two dedicated lanes of the Brooklyn Bridge. In that case, the line would effectively act as subway-surface, or more accurately elevated-surface: a surface segment in Brooklyn, a grade-separated segment between Manhattan and Brooklyn. Subway-surface lines should branch, as all current examples do (e.g. Boston Green Line, Muni Metro, Frankfurt U-Bahn), because the subway component has much higher capacity than the surface components. This suggests one or two additional routes in Brooklyn, which do not have strong buses, but may turn into strong tramways because of the fast connection across the river to Manhattan. The first is toward Red Hook, which is not served by the subway and cut off from the rest of the city by the Gowanus Expressway. Unfortunately, there is no really strong corridor for it – the streets are not very wide, and the best for intermediate ridership in Cobble Hill and Carroll Gardens require additional twists to get into the core of Red Hook. Court Street might be the best compromise, but is annoyingly a block away from the F/G trains, almost but not quite meeting for a transfer. The second possible route is along Flushing Avenue toward the Navy Yard; it’s not a strong bus by itself, but the possibility of direct service to Manhattan, if a Flatbush tramway preexists, may justify it.
In the Bronx and Queens, a more conventional network is called for. The Bronx in particular has several strong bus lines forming a good grid, in addition to the Bx12. The east-west routes cannot possibly be made into subway extensions, while the north-south ones have nowhere to go to in Manhattan except possibly a Second Avenue Subway extension, and even that is doubtful (if there’s money to extend Second Avenue Subway north, it should instead go west under 125th Street). A light rail grid could consist of the Bx12 as outlined above, a Tremont line acting as a compromise between the Bx36 and Bx40/42 feeding into Manhattan on 181st Street, a 161st/163rd Street route going into Manhattan on 155th Street replacing the Bx6, a Southern/Manhattan 145th Street route along the Bx19, a Third Avenue route along the Bx15, and a Grand Concourse route along the Bx1/2. Grand Concourse has a subway, but the Bx1/2 nonetheless currently ranks 5th in the city in weekday ridership, and the street is so wide that it’s a good candidate for light rail. Update: a Webster Avenue route along the Bx41 is also feasible, I just forgot it when writing this post.
In Queens, there’s less room for a grid. Main Street is a strong route, connecting to Tremont in the Bronx via the Whitestone Bridge, as the Q44 SBS already does today. A second route between Flushing and Jamaica, on Kissena and Parsons, could also get a tramway. These two routes are uniquely bad subways, since they connect two busy subway lines, both of which could be extended past their termini outward. The main route on Kissena, the Q25, and another route slightly farther east, the Q65, rank 3rd and 2nd among the MTA buses, separate from the New York City Transit buses, with about 20,000 weekday riders each; they also continue north to College Point, which could get a tramway, or perhaps even a subway extension of the 7, depending on whether there are plans to redevelop the Flushing Airport site.
If there is not enough ridership on both Kissena and Main, then only Main should be turned into light rail. More potential corridors include the Q46 on Union Turnpike and the Q10 on Lefferts going to JFK (the busiest MTA bus). Unfortunately, Queens buses tend to be on the long side, e.g. the Q27, the borough’s number 3 bus after the Q58 and Q46, is 15 km long; in the Bronx the longest, Tremont, would be 13 km, cobbled out of busier buses, and most are about 10 km. The Q44 is even longer, at 20 km; light rail is only justified there because of extra local ridership coming from the Q20 local and from the fact that the Queens-Bronx segment over the bridge would be rapid transit. Even then, the tramway may only be justified from Flushing south.
I don’t want to make recommendations for priorities and an exact fantasy map in New York, as those depend on construction costs and the available budget. Fordham and Main Street are most likely the two strongest initial choices. Judging by the cost estimate for de Blasio’s waterfront proposal, tramways in New York are about $60-70 million per km, which in an inverse of the situation in Vancouver leads to an unusually high subway : tram cost ratio, 25 if we take the Manhattan subway extensions (Second Avenue and the 7 extension) as our examples, probably less but not much less if we look at a hypothetical Utica subway. This should bias New York rail extensions toward surface transit.
De Blasio proposed $1.5 billion for about 25 km of tramway on the waterfront. The waterfront idea is bad, and money can and should go elsewhere; 25 km is slightly longer than the combined length of the Bx12 and the Q44 from Flushing south. Those two together could be the start of a program to bring surface rail back to New York, using the same routing reasoning that made Paris’s program so successful. Using ridership on the existing buses and adjusting upward for rail bias, initial ridership on those two lines combined should be higher than 100,000 per day, and with more lines and a bigger network, fast multiplication of overall traffic can be expected.
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 about $2.1 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.
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:
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,
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.