Infrastructure for Mature Cities

A post by Aaron Renn just made me remember something I said in the Straphangers Campaign forum ten years ago. I complained that New York was building too little subway infrastructure – where were Second Avenue Subway, Utica, Nostrand, various outer extensions in Queens and the Bronx that we crayonistas liked? Shanghai, I told people in the forum, was building a lot of subway lines at once, so why couldn’t New York? The answer is not about construction costs. Ten years ago, China’s construction costs relative to local incomes were about the same as those of New York; even today, the difference is small. Rather, it is that China is a fast-growing economy that’s spending a lot of its resources on managing this growth, whereas the US is a mature economy without infrastructure problems as urgent as those of developing countries.

Aaron posits that American cities are too conservative, in the sense of being timid rather than in the sense of being on the political right. He gives examples of forward-looking infrastructure projects that New York engaged in from the early 19th century to the middle of the 20th century: the Manhattan grid, the Erie Canal, the Croton Aqueduct, the subway, the Robert Moses-era highways and parks. Today, nothing of the sort happens. Aaron of course recognizes that “New, rapidly growing cities need lots of new infrastructure and plans. Mature cities need less new infrastructure.” The difference is that for me, this is where this line of questioning ends. New York is a mature city, and doesn’t need grand plans; it needs to invest in infrastructure based on the assumption that it will never again grow quickly.

If not grand plans like building the Manhattan grid far beyond the city’s then-built up area, then what should a mature city do? Aaron talks about dreaming big, and there is something to that, but it would take a profoundly different approach from what New York did when its population grew by 50% every decade. I stress that, as with my last post critiquing another blog post, I agree with a substantial part of what Aaron says and imagine that Aaron will treat many of the solutions I posit here as positive examples of thinking big.

Rationalization of Government

Mature societies have accumulated a great deal of kludge at all levels, coming from social structures and government programs that served the needs of previous generations, often with political compromises that are hard to understand today. Welfare programs are usually a kludge of different social security programs (for the disabled, for retirees, for various classes of unemployed people, sometimes even for students), housing benefits, reduced tax rates for staple goods like food, child credit, and in the US food stamps. A good deal of the impetus for basic income is specifically about consolidating the kludge into a single cash benefit with a consistent effective marginal tax rate.

In transportation, bus networks have often evolved incrementally, with each change making sense in local context. When a new housing development opened, the nearest bus would be extended to serve it. In Israel, which grew late enough to grow around buses and not rail, this was also true of dedicated industrial zones. In cities that used to have streetcar networks, some buses just follow the old streetcar routes; the Washington bus system even today distinguishes between former streetcars (which have numbers) and routes that were never streetcars (which use letters). Jarrett Walker‘s bus network redesigns are partly about reorganizing such systems around modern needs, based on modern understanding of the principles behind transit ridership.

Governance often needs to be rationalized as well. In the early 20th century, it was important to connect outlying neighborhoods to city center, and connections between lines were less important. This led to excessively radial surface transit (rapid transit is always radial), but also to rail lines that don’t always connect to one another well. Sometimes due to historical contingency the lines are run by separate agencies and have uncoordinated schedules and different fare systems charging extra for transfers. Occasionally even the same agency charges for bus-rail transfers, often because of a history of separate private operators before the public takeover. In the US and Canada, the special status of commuter rail, with different unions, fares, schedules, and management is of particular concern, because several cities could use commuter rail to supplement the rest of the transit network.

In New York, this points toward the following agenda:

  • Modernization of commuter rail, with full fare integration with the subway and buses, proof-of-payment fare collection to reduce operating costs, high off-peak frequency on the local lines, and through-running where there is infrastructure for it (i.e. Penn Station).
  • Some bus service reorganization. New York already has extensive frequent buses, but some of its network is still questionable, for example some branches of the Third/Lexington and Madison/Fifth one-way pairs in Harlem.
  • Subway reorganization. The subway branches too much, and at several places it could have higher capacity if it reduced the extent of reverse-branching; see discussion here and in comments here. Some elevated lines could also see their stops change to support better transfers, including the J/M/Z at Broadway and Manhattan to transfer to the G, and maybe even the 7 at 108th Street to enable a transfer to a straightened Q23 bus.
  • Fare integration with PATH, and demolition of the false walls between the PATH and the F/M trains on Sixth Avenue, to enable cross-platform transfers.

Serve, Don’t Shape

There are two models for building new infrastructure: serve, and shape. Serve means focusing on present-day economic and demographic patterns. Shape means expecting the project to change these patterns, the “build it and they will come” approach. When New York built the 7 train to Flushing, Flushing already existed as a town center but much of the area between Long Island City and Flushing was open farmland. I’ve argued before that third-world cities should use the shape model. In contrast, mature cities, including the entire developed world except a few American Sunbelt cities and analogs in Canada and Australia, should use the serve model.

The serve model flies in the face of the belief that public transit can induce profound changes in urban layout. In reality, some local transit-oriented development is possible, but the main center of New York will remain Midtown; so far Hudson Yards seems like a flop. In the suburbs, more extensive redevelopment is possible, with apartment buildings and mixed uses near train stations. But these suburbs, built after WW2, are less mature than the city proper. In fast-growing cities in North America outside the traditional manufacturing belt the shape model still has validity – Vancouver, still a relatively new city region in the 1980s, got to shape itself using SkyTrain. But in New York, there is no chance.

This also has some ethnic implications. Jarrett likes to plan routes without much regard for social circumstances, except perhaps to give more bus service to a lower-income area with lower car ownership. But in reality, it is possible to see ethnic ties in origin-and-destination transit trips. This is why there are internal Chinatown buses connecting Chinatown, Flushing, and Sunset Park, and a bus connecting two different ultra-Orthodox neighborhoods in Brooklyn. In Washington, there is origin and destination data, and there are noticeable ties between black neighborhoods, such as Anacostia and Columbia Heights.

In a mature city with stable ethnic boundaries (Harlem has been black for ninety years), it is possible to plan infrastructure around ethnic travel patterns. This means that as New York disentangles subway lines to reduce branching, it should try choosing one-seat rides that facilitate known social ties, such as between Harlem and Bedford-Stuyvesant. While New York’s ethnic groups are generally integrated, this has special significance in areas with a mixture of linguistic or religious groups with very little intermarriage, such as Israel, which has two large unassimilated minorities (Arabs, and ultra-Orthodox Jews); Israeli transportation planning should whenever possible take into account special ultra-Orthodox travel needs (e.g. large families) and intra-ethnic connections such as between Bnei Brak and Jerusalem or between Jaffa and Nazareth.

Integrated Planning

A few years ago, I wrote a post I can no longer find talking about building the minimum rail infrastructure required for a given service plan. In comments, Keep Houston Houston replied that no, this makes it really difficult to add future capacity if demand grows. For example, a single-track line with meets optimized for half-hourly service requires total redesign if demand grows to justify 20-minute frequency. In a growing city, this means infrastructure should be planned for future-proofing, with double track everywhere, no reliance on timed overtakes, and so on. In a mature city, this isn’t a problem – growth is usually predictable.

It is relatively easy to integrate infrastructure planning and scheduling based on today’s travel patterns, and impossible to integrate them based on the future travel patterns of a fast-growing city such as Lagos or Nairobi. But in a slow-growing city like New York, future integration isn’t much harder than present-day integration. Alone among North American cities, New York has high transit mode share, making such integration even easier – transit usage could double with Herculean effort, but there is no chance that a real transit revival would quadruple it or more, unlike in cities that are relatively clean slates like Los Angeles.

Since the mature city does not need too much new infrastructure, it is useful to build infrastructure to primarily use existing infrastructure more efficiently. One example of this is S-Bahn tunnels connecting two stub-end lines; these are also useful in growing cities (Berlin built the Stadtbahn in the 1880s), but in mature cities their relative usefulness is higher, because they use preexisting infrastructure. This is not restricted to commuter rail: there is a perennial plan in New York to build a short tunnel between PATH at World Trade Center and the 6 train at City Hall and run through-service, using the fact that PATH’s loading gauge is similar to that of the numbered subway lines.

In New York, this suggests the following transit priorities:

  • Open commuter rail lines and stations based on the quality of transfers to the subway and the key bus routes. For example, Penn Station Access for Metro-North should include a stop at Pelham Parkway for easy transfer to the Bx12 bus, and a stop at Astoria for easy transfer to the subway.
  • Investigate whether a PATH-6 connection is feasible; it would require no new stations, but there would be construction difficulties since the existing World Trade Center PATH station platforms are in a loop.
  • Change subway construction priorities to emphasize lines that reduce rather than add branching. In particular, Nostrand may be a higher priority than Utica, and both may be higher priorities than phases 3 and 4 of Second Avenue Subway. A subway line under Northern Boulevard in Queens may not be feasible without an entirely new Manhattan trunk line.
  • Build commuter rail tunnels for through-running. The Gateway project should include a connection to Grand Central rather than Penn Station South, and should already bake in a choice of which commuter lines on each side match to which commuter lines on the other side. Plan for commuter rail lines through Lower Manhattan, connecting the LIRR in Brooklyn with New Jersey Transit’s Erie Lines, and, accordingly, do not connect any of the lines planned for this system to Penn Station (such as with the circuitous Secaucus Loop in the Gateway project).

Conclusion

New York still needs infrastructure investment, like every other city. Such investment requires thinking outside the box, and may look radical if it forces different agencies to cooperate or even amalgamate. But in reality the amount of construction required is not extensive. More deeply, New York will not look radically different in the future from how it looks today. Technological fantasies of driverless flying cars aside, New York’s future growth is necessarily slow and predictable, and cities in that situation need to invest in infrastructure accordingly.

In my post about third-world transit, I posited an epistemological principle that if the presence of a certain trait makes a certain solution more useful, then the absence of the trait should make the solution less useful. The shape vs. serve argument comes from this principle. The same is true of the emphasis on consolidating the kludge into a coherent whole and then building strategically to support this consolidation. A fast-growing city has no time to consolidate, and who’s to say that today’s consolidation won’t be a kludge in thirty years? A mature city has time, and has little to worry about rapid change obsoleting present-day methods.

But at the same time, the same epistemology means that these changes are less critical in a mature city. In the third world, everything is terrible; in the first world, most things are fine. New York’s transportation problems are painful for commuters, but ultimately, they will not paralyze the city. It will do well even if it doesn’t build a single kilometer of subway in the future. Nothing is indispensable; this means that, in the face of high costs, often the correct alternative may be No Build. This illustrates the importance of improving cost-effectiveness (equally important in the third world, but there the problem is the opposite – too many things are indispensable and there isn’t enough money for all of them).

I emphasize that this does not mean transportation is unimportant. That New York will not be destroyed if it stops building new infrastructure does not mean that new infrastructure is of no use for the city. The city needs to be able to facilitate future economic and demographic growth and solve lingering social problems, and better infrastructure, done right, can play a role in that. New York will most likely look similar in 2067 to how it looks in 2017, but it can still use better infrastructure to be a better and more developed city by then.

More Things that are not Why New York’s Construction Costs are High

The most annoying person I regularly deal with on social media is Walkable Princeton/YIMBY Princeton, a biology professor at Rutgers who constantly criticizes my writings on comparative construction costs, and usually raises good points. Dealing with zombie arguments (China, anything Elon Musk says, etc.) is so much easier. A few days ago, he put up a post summarizing 20 potential reasons why subway construction costs in New York (and in the US in general) are high. He’s also repeatedly made a separate argument on social media, not mentioned in the post, expressing skepticism that the construction cost differences are real, rather than just statistical artifacts.

In this post, I am going to purposely not talk about the two biggest criticisms – the claim about the statistical differences, and the argument from local expertise (points #7 and #8 in his post). Those require dedicated posts, and the argument from local expertise should really be tackled in two separate posts, one about project size (comparing cities that build long subway lines with ones that build many short subway extensions) and one about the undisputed negative correlation between construction costs and the extent of construction across cities. I will deal with this in the next few weeks or months, depending on publishing schedules elsewhere. In this post I’m instead going to deal with the weaker criticisms.

The first five points made in the post come from arguments I discussed here, saying that they are not real reasons why US construction costs are high. The sixth point concerns project size. Since the seventh and eighth point will be a dedicated post, I will start with the ninth point.

Of note, many of the explanations offered are serious and relevant, just not to the specific problem of high construction costs of urban rail. They are relevant to some construction costs problems for high-speed rail, and operating costs, and rolling stock procurement costs. But the explanation for expensive urban tunneling is most likely elsewhere. Only one point below, #13, begins to address that specific issue, and even it seems to me to be at most a partial explanation.

9. ‘Buy America’ provisions – Regulations requiring transit agencies to purchase equipment built in the US may drive up costs, as overseas manufacturers have to build a factory in the US to produce the needed kit. Other nations buy transit equipment more regularly, so have ready access to an efficient supply chain.

Buy America provisions indeed raise American costs for small orders – but only for rolling stock. Dedicated factories, often built in-state for added protectionism, make trains for $3-5 million per car (for example, compare Muni Metro’s $4 million/car order for 23-meter cars with Strasbourg’s $4 million/car order for 45-meter cars). Only the biggest orders, such as those for the New York City Subway, the LIRR, and Metro-North, have enough scale to control costs.

However, this is not an issue for infrastructure construction. The bulk of the cost of civil infrastructure is not specialized machinery, which American cities import anyway (the tunnel-boring machine for the 7 extension was made in Germany). It’s local labor and materials, and less specialized machinery for digging earthworks for stations.

10. Bad attitude – Call it a ‘New York state of mind’ – MTA old dogs may prefer to see a project fail than to be proven wrong or see praise go to an agency rival. Not clear that New Yorkers have a worse attitude than people from other big cities, but certainly worth considering.

11. Chaotic political environment – Transit projects must be agreed by too many agencies and personalities, some of whom may have conflicting priorities. For example, NY Governor Andrew Cuomo doesn’t seem to get on with Mayor Bill DiBlasio, and the less said about Governor Christie the better. Personality clashes and inter-state squabbling at the Port Authority board have frustrated long-term planning. Donald Trump controls federal funds that may be needed to fund new transit projects.

These are really the same criticism: agency turf battles. Those can make cities build the wrong project, or overbuild a tunnel in order to avoid sharing facilities with another agency. The bulk of the construction costs of high-speed rail on the Northeast Corridor, and a large fraction of those of California HSR, come from this. Readers who are familiar with debates about California HSR will know about the Altamont vs. Pacheco Pass controversy and about avoidable tunnels like Millbrae.

However, this isn’t really what’s happening in urban subways. The Gateway project has unnecessary scope like Penn Station South, but even the bare tunnel is estimated at $11 billion.

12. Lack of stable long-term funding – Long-term funding for transit projects is uncertain, and even part-built projects can be canceled at any moment (see Governor Christie, ARC tunnels). New York has a long track record of abandoning transit projects, and the Second Avenue Subway project took nearly 100 years to do.

Midway cancellations are really a symptom of high costs rather than a cause. At cancellation, ARC was projected to cost $10-13 billion, up from $3 billion in the major investment study from 2003. This is not unique to the United States: high costs and construction impact for Stuttgart 21 led to widespread opposition to the project from within Stuttgart, leading to the election of Germany’s first Green-led state government; the Green Party opposed Stuttgart 21 and proposed a cheaper, lower-impact project without tunneling. It did not cancel the project, but put it up to referendum, which failed – the majority of state voters, and even of Stuttgart voters, wanted the project to keep going. Going to a second referendum on canceling a project, rather than canceling it by executive fiat as in New Jersey, is not unique to Germany: in Florida, Governor Jeb Bush put a second referendum on the ballot in 2004, successfully killing high-speed rail.

13. Project bloat – Planners may over-do transit infrastructure, for example by hiring a superstar architect like Santiago Calatrava to design the Port Authority PATH station instead of ‘Joe Goodenough’. Cavernous two-level stations in the new Second Avenue Subway stations may not contribute substantially to function, and drive costs up a lot.

This is indeed a serious problem! New York has been overbuilding stations since the 1930s, when the IND subways had full-length mezzanines. I encourage the New York-based readers to compare the size of the stations on the IND, such as West 4th Street or 145th Street on the A/B/C/D, and that of the stations on the IRT and BMT, such as Union Square. The Calatrava-designed PATH terminal was massively expensive more recently, and Second Avenue Subway is expensive in part because of the large stations.

And yet. Even relatively utilitarian American projects aren’t always cheap – again, the bare Gateway tunnel. Moreover, some of the project bloat is not really about overdesign, but about wrong political choices. Second Avenue Subway had no cut-and-cover construction except at 96th Street to stage the tunnel boring. Second Avenue is wide and the entire line could be built cut-and-cover. Cut-and-cover is highly disruptive to street merchants, but a hybrid solution, with cut-and-cover stations and bored tunnels between them, is possible and widespread in several low- and medium-cost cities, such as Madrid and Copenhagen. But even the stations were bored, which limited surface disruption at each station to a few cross streets, but made construction take much longer; the corner of 72nd and 2nd was unpleasant to walk around for most of the duration of the ten-year project.

14. Fire safety regulations – Modern standards for smoke clearance and emergency evacuation may require larger two-level stations that appear bloated.

15. Environmental regulations – Disruption to fragile ecosystems may not be as tolerated in the New York area as in some other countries, driving up costs.

16. ADA standards – Transit stations in New York must comply with federal accessibility requirements, meaning many elevators that drive up costs.

These issues exist throughout the developed world. New subways are step-free even in cities that make no effort to retrofit the rest of the system for wheelchair accessibility, such as Paris. We also know how much it costs to add elevators to stations, and it is a rounding error: during construction, making five more Crossrail stations accessible costs £19 million. Even retrofitting an old subway station for accessibility after construction is $25-40 million in the US (source: article about New York, interview with an accessibility planner in Boston). And as for environmental regulations, I doubt there are endangered species on the Upper East Side under Second Avenue.

17. Americans don’t care about transit – Other nations may take pride in their fancy rail systems, but we’ve got aircraft carriers and don’t care if the subway looks pretty worn.

18. High levels of sprawl – Whereas NYC is dense at the core, the surrounding metro area is not very dense. The Los Angeles metro area is in fact denser than the New York metro area. Low housing density, especially in the areas where rich folks live, makes transit less efficient and undermines public support for expensive transit investments.

Suburban drivers may not want to spend money on subways, but that should not make subways more expensive to build. It should reduce cost per rider, in the sense of lowering the maximum cost per rider that the political system is willing to build; but the effect on cost per km should be neutral.

19. Corruption – Is the Mob siphoning off loads of the money that is supposed to go to build transit??

It probably is. And yet, corruption levels in Italy are far higher than in the United States, and yet costs are pretty low. Corruption levels in Spain and South Korea aren’t especially low. And Singapore, renowned for its clean government (below the level of the prime minister, at least, but he doesn’t decide on subway alignments), is a serious contender for most expensive subway outside the United States.

20. Terrible leadership – Ronnie Hakim, the current MTA Director, is supposedly seen as incompetent by many of her staff. Joe Lhota, the MTA Chair, doesn’t even work full-time at the job. The Port Authority Board is stuffed with Chris Christie stooges, some of whom may know nothing about transit.

Hakim is incompetent and I have sources within the MTA who are exasperated with her indifference to one of the most fundamental goals of rapid transit (namely, being rapid). Much like explanation #9, there is a serious problem here, but it doesn’t affect tunneling costs. It affects operating costs, which appear to be higher in New York than in any other city participating in CoMET (see PDF-p. 7 here: the highest-cost system on the right is in fact New York). But it is not about tunneling. Unlike Hakim, long-time MTA Capital Construction chief Michael Horodinceanu is not hated by the junior and mid-level planners who leak to the press, and unlike Lhota, he works the job full-time worked the job full-time until retiring earlier this year.

Commuter Rail Infill Stops

This is a close second option in a poll I conducted among my Patreon backers. Thanks to everyone who participated. The winning option, about branching and transfers, I covered last week.

Modernizing commuter rail to run it like rapid transit means a lot of things. It means high all-day frequency, fare integration, good transfers to local transit (which requires fare integration), and ideally through-running in order to hit multiple business districts. In North America, these are absent, resulting in low ridership. So let’s posit that these problems are already being solved: commuter rail is being run frequently, the lines are electrified, the fares are the same as on local transit with free transfers. What should the stop pattern look like? This is not a purely hypothetical discussion, because in Toronto the under-construction RER system includes high off-peak frequency, electrification, and through-running, with fare integration under consideration.

So let’s imagine a city with modernized regional rail, maybe in the early 2020s. Trains run every 15 minutes off-peak, charge the same fare as local transit, and run fast EMUs, on track that’s good for 130 km/h outside station throats. The stop pattern, expressed in kilometers out of city center, is any of the following:

Line Stop #1 Stop #2 Stop #3 Stop #4 Stop #5 Stop #6
Chicago Metra Electric 1.3 2.3 3.6 4.3 5.2 9.5
Chicago UP-North 4.5 10.5 15.1 17.7 19.3 21.4
GO Transit Lakeshore West 3.2 10.8 15.4 20.6 26.9 34.4
GO Transit Lakeshore East 8.4 13.8 17.1 20.3 26.6 33.6
SEPTA Paoli/Thorndale Line (PRR Main Line) 8.7 9.7 10.9 11.9 13.7 13.7
Metrolink Antelope Valley Line 9.3 17.5 24.9 35.4 48.3 55.1
Metrolink Orange County Line 14.4 27.1 35.2 41.3 50.2 53.5

(Metrolink data comes from measuring on Google Earth, the rest comes from Wikipedia.)

Two patterns emerge:

  1. Metrolink and GO Transit have very wide stop spacing. GO has straight track it owns outright on the Lakeshore lines, and Metrolink is straight with few curves on the Orange County Line (but freight owns much of the route) and straight until stop #4 on the Antelope Valley Line, Sylmar. EMUs could average 90 km/h on these lines, counting schedule padding.
  2. SEPTA and Metra have wide stop spacing in the core but very narrow spacing in the suburbs; I discussed this issue for Metra in an old post comparing its stop distribution through stop #12 with that of the RER. Metra Electric has a few inner stops, e.g. for the convention center (stop #4), but then there’s a 4-km gap from stop #5 to stop #6 (Kenwood).

Both patterns are compatible with modernized rail operations. But both have problems with dealing with passenger demand. Consider what happens to a transit user in Burbank (stop #2 on Antelope Valley), or Ravenswood on the North Side of Chicago (stop #2 on UP-North), or Danforth and Main (stop #1 on Lakeshore East). Such a passenger would get an incredibly fast train to the CBD, running either nonstop or with one stop. Demand would boom. But is this really the most efficient way of running transit? Not really. This is for the following reasons:

  • The downstream locations would still be very attractive infill train stations, with potential for high ridership. After all, they’d get fast service, too.
  • If you get a 1-stop, 10-minute train ride to work, then adding four more stops to turn it into a 15-minute ride sounds like an imposition (it raises trip times by 50%), but it really isn’t, because most likely your actual commute is 30 minutes, with 10 minutes of walking at each end.
  • With fare integration, buses should really be feeding the major train stations. Making every bus feed a small number of stations with fast commuter rail service compromises the rest of the network, whereas siting train stations at the intersections with the major grid buses in cities like Toronto, Chicago, and Los Angeles facilitates transfers better.

As a result of these principles, my proposal for Electrolink in Los Angeles, built out of the Antelope Valley and Orange County Line, involves extensive infill stops. See map below:

I drew even more extensive (and somewhat fanciful) maps for Los Angeles and Chicago, with more infill, but I want to focus on my Electrolink map, because it showcases some caveats.

Of note, there is much more infill on the Antelope Valley and Ventura County Lines than on the Orange County Line. This is because there is less residential density near the Orange County Line, and much more industrial land use. Los Angeles has a strong manufacturing sector, using the railroad for freight access, so residential upzoning near potential infill station locations is speculative. In the San Fernando Valley the land use near the railroads is not great, but there is a decent amount of residential density beyond the near-railroad industrial uses, there are strong bus corridors intersecting the railroads (and potential for light rail); the corridors also have less freight, so it’s easier to kick out industrial uses from station sites and do residential and commercial upzoning.

In New York and Boston, there are other caveats, explaining why my various regional rail proposals for these cities call only for mild infill. The biggest caveat is that there exist parallel subway lines. Boston’s Old Colony trunk passes through relatively dense areas in Dorchester and Quincy, with just three stops: JFK/UMass at km-point 3.7, Quincy at km-point 12.7, Braintree at km-point 17.6. But the Red Line runs parallel to the trunk making more stops, enabling commuter rail to work as an express overlay. Thus, only the busiest locations deserve a commuter rail stop, and those are precisely the three existing stops. In Somerville, the Green Line Extension plays a similar role, providing local service that commuter rail would otherwise have to provide under any modernization scheme. As a result, my proposal for how to run the Old Colony Lines and the Lowell Line through Somerville is more intercity rail than local commuter rail.

In contrast, the Worcester Line has no parallel subway except on the innermost few km, so it’s already getting two infill stops (Boston Landing and West Station) and I’ve called for several more. The same is true of the Fairmount Line, which is expanding from five stops including the endpoints to nine.

There is an analog for this in Paris, on the RER. Within the city and La Defense, the RER A mostly runs as an express overlay for Metro Line 1, stopping at the major stations, omitting just Bastille, which is too close to Gare de Lyon. But the RER B really has two separate stop regimes. North of Chatelet, parallel to Line 4, it expresses to Gare du Nord, and then doesn’t stop again until reaching the suburbs. But south of Chatelet, all trains make 5 stops in 5 km to Cite-Universitaire, even ones that run express in the suburbs; this is the older part of the line, much of which predates the Metro, so Line 4 was built along a different alignment via Gare Montparnasse.

In New York, the commuter trunks going north and east are closely parallel to the subway, which is often four-tracked. Since the subway already provides relatively fast service, with stops every 2-3 km, commuter rail should be even faster, with sparser stops. The principles here are,

  • Infill stops are more justified at intersections with major orthogonal bus or rail corridors or in dense, transit-deprived areas. Areas with little residential development are to be categorized based on redevelopment potential.
  • Infill stops are less justified parallel to a subway line. The faster the subway is, the faster commuter rail should be.
  • Infill stops are more justified on a shorter line than on a longer line. Here, “shorter” and “longer” do not mean the length of the line to the endpoint, but the length to the endpoint of local service, if the infill stops would not be served by express trains.

Metro-North is parallel to the four-track Lexington Avenue Line, which has four tracks. Between 125th Street and Grand Central, the 4 and 5 trains make just two intermediate stops, at 86th and 59th Streets. Metro-North runs nonstop between 125th and Grand Central, and because the 4 and 5 exist, it has no reason to make more stops, even at 59th for additional service to Midtown

In the Bronx the trunk line isn’t so close to the subway, but already makes multiple stops. There may be plausible infill in Morrisania between Melrose and Tremont. But even that is marginal – for one, Melrose, Tremont, and Fordham are all located at the intersections with high-ridership east-west bus routes, whereas nothing in between is. This distinction between an inner and outer part of the same line also holds for the Atlantic Branch: west of Broadway Junction it parallels the four-track A/C, so no infill is needed, but farther east it parallels the slower J/Z and isn’t even that close to the subway, so infill is useful.

Going east, the LIRR Main Line is parallel to the Queens Boulevard Line, like the Lex a four-track line. There is no real point in infill, except at Sunnyside Junction, where the line meets the Northeast Corridor. The Port Washington Branch is a shorter line than anything on the Main Line, even the Hempstead Branch (but not by much), and isn’t as close to the 7 as the Main Line is to the Queens Boulevard Line; the 7 is also slower. This means an infill stop or two may be justified – my map has three (at Queens Boulevard, Broadway, and Junction), but that may be too much.

It’s the west direction that is the most speculative, toward New Jersey. I have called for new Hudson tunnels to feature a station at Bergenline (building a station in the existing tunnels would disrupt current service and slow down express trains) based on the above principles. Additional infill is possible, but only subject to transit-oriented development plans alongside the line. The land use from just west of Bergen Hill, including Bergenline, to just east of Newark, is a combination of industrial warehouses and wetland preserves. The warehouses should be redeveloped, but until there is rezoning, it is pointless to add more stops. Moreover, Secaucus Junction is already in the middle of the warehouse area, so rezoning should start from there, and if the newly-built residential neighborhood grows big enough so as to justify a second station, a second station can be added later.

The upshot is that even though New York has very wide stop spacing on commuter rail near the core, it does not need as much infill as Los Angeles or Chicago. What about Toronto, the original impetus for the post? There, Metrolinx is already considering minor infill. But if the principles emerging from how I think about infill in the US and on the RER are correct, Toronto needs far more infill. The Lakeshore lines are not really close to the subway: they run east-west, as does the Bloor-Danforth Line, but Lakeshore West is about 2 km from Bloor, and Lakeshore East is mostly 1 km from Danforth, with just a short segment within walking distance. The inner areas of Lakeshore West are very dense, with some blocks at 30,000 people per km^2, and only served by buses and slow mixed-traffic streetcars; even some areas along Lakeshore East are fairly dense, more than 10,000/km^2. Toronto’s bus and streetcar grid hits or can be extended to hit several potential station locations, offering better connections than riding to the Bloor-Danforth Line and then changing to Yonge to reach the CBD.

The one drawback in Toronto: the commuter lines are very long. Not all trains have to make all stops, but if there’s one stopping pattern making 3 stops in 15 km and another making 12, then it isn’t really possible to mix them on the same tracks at high frequency. The core lines have four tracks, but Lakeshore needs to eventually mix four classes of trains: local commuter rail, longer-range commuter rail, intercity rail, freight. There are ways around four-way mixture (for example, there is little freight on Lakeshore in Toronto proper, where the local trains would run), and intercity trains can probably share tracks with long-range commuter trains. It’s solvable, just like the three-way track-sharing between local, express, and eventual high-speed trains around New York, but it isn’t trivial.

In general, North American commuter trains make too few stops in the urban core. Tellingly, while I can come up with many examples of lines that require infill, I can’t name five good examples of anti-infill, where a station served by commuter trains full-time should be closed. But not all commuter lines are equally good candidates for infill stops, and there are large networks, such as Metro-North, where the current stop spacing is fine, just as there are ones, such as GO Transit and some Metra lines, where some inner segments could plausible see the number of stops quadruple.

Branching and Transfer Breaking

This is the winning option in a poll I conducted among my Patreon backers. Thanks to everyone who participated. Another option, about commuter rail infill stops, came a close second, and I will likely tackle it later this month.

The New York City Subway is unusually branched. I’ve written about the general concept here, and specifically criticized reverse-branching on the subway here. In this post, I want to talk about a more specific feature of complex branching arrangements: they have station locations that make it hard to disentangle the branches without breaking transfers.

 

The left image is a common way junctions are set up. In this image, it’s possible to travel from any leg to any leg; an example of this is BART, with its three-way junction in Oakland between the East Oakland Line carrying trains to Fremont and Pleasanton, the line to the north carrying trains to Berkeley, and the line to the west carrying trains to San Francisco. In many other cases, the branching is simpler, with a clear trunk and two branches, and it’s often not possible for trains to travel between the two branches without backing up; this is like the depicted image with one of the connections missing.

New York has one current example like the left image: the A/C/F/G junction in Downtown Brooklyn has a northern leg (A/C/F), an eastern leg (A/C/G), and a southern leg (F/G). All legs have four tracks and not every track pair connects to every other track pair, but each leg connects to both other legs. It has one former example: the junction between Sixth Avenue Line and 53rd Street Line, with the B/D going south-to-west (then north), the E going east-to-west (then south), and the F going south-to-east. The E/F shared tracks to the east, but neither service shared tracks with the B/D to the south or west.

The problem with this arrangement is that it makes the schedules more fragile. A delay on one branch can cascade. Toronto at one point ran its subway line this, with an eastern and western leg under Bloor Street (continuing to Danforth to the east), and a southern leg under University (looping back north under Yonge); it subsequently ended branching by extending the University leg to the north along the Spadina Expressway right-of-way and operating two independent lines.

The rub is that such an extension usually breaks transfers. Look at the right image: running the lines without branching means no transfers, since there is no station located at the crossing. Toronto dodged this problem because of how the original branching was laid out – in fact, there are two adjacent transfer stations. But usually, it is not hard to convert a branching like the left image into two lines with a simple transfer in the middle.

The 53rd/Sixth situation in New York is a good example of the problem. New York realized it needed more capacity going east, toward Queens, since there were only three track pairs – 53rd Street, plus two more disconnected from the system depicted. For this, it built a tunnel under 63rd Street, and connected it to Sixth Avenue, routing the F through it and creating a new service for Sixth-East 53rd trains, then called the V and now called the M. The junction now looks like an incomplete version of the right image, missing the two upper arcs. The F continues north under Sixth, and only diverts east under 63rd, and has no transfer with the E, which runs east-west under 53rd. The next transfer between the two services to the south is at West 4th Street; the next transfer to the east is at Roosevelt Avenue/74th Street, well into Queens, since the alignment of 63rd Street Tunnel into Queens prevents it from intersecting the E closer in, at Queens Plaza in Long Island City.

The highly-branched nature of the subway in New York makes sure that it is possible to travel between legs even when there’s no transfer, provided one is okay transferring between lines with not-great frequency. The first station south of the junction on Sixth, 47th-50th Streets-Rockefeller Center, lets passengers transfer wrong-way, between southbound and northbound trains. I have used this before to transfer from the B/D to the F on my way between Columbia and Queens, which are not well-connected to each other. Going from east to south is already easy on the M; going from east to north is possible via the M and F, but is unusual, since ultimately both legs lead into the same line in Queens.

However, it is hard to disentangle this to reduce branching. If one believes that reducing branching is useful for reliability and capacity, then one must believe it is necessary for New York to figure out how to split branching in the least painful ways. Partial data from the London Underground is suggestive (see international benchmarking, PDF-p. 15) – the non-branching Victoria and Piccadilly lines are more reliable than the complexly-branching Northern line. Moreover, the intensive service in Moscow, topping at 39 trains per hour without any automation, only works since none of the lines branches. This compels New York and other cities with highly branched systems to disentangle lines.

In the Bay Area, the situation is relatively easy, in the sense of requiring relatively little capital construction. There is no real need for a one-seat ride between East Oakland and Berkeley. The reason there are any trains running on that leg is that Downtown Oakland is on the leg to Berkeley and not on the leg to San Francisco. This was bad planning, and was noted as bad planning even in the 1960s.

What is required is a short bypass tunnel. There are two options. First, a tunnel from the east, replacing the Lake Merritt station with a station a few blocks to the north, effectively moving the junction one station north, so that 12th Street-Oakland City Center can be on the western leg toward San Francisco. Second, a tunnel from the west, between West Oakland and Downtown Oakland. This would not move any station, and put 12th Street on the eastern leg toward East Oakland; Downtown Oakland has a second station, at 19th Street, which would stay on the northern leg, for Berkeley-Downtown Oakland service. Either option would break East Oakland-Berkeley transfers, but make the remaining system more robust.

In New York, disentangling reverse-branches is considerably more difficult. On the numbered lines, it isn’t too difficult to shuffle the 2, 3, 4, and 5 so that the only track sharing is between the 2 and 3, and between the 4 and 5. On the lettered lines, first of all one key connection has to be severed: 11th Street Connection, letting the R go between 60th Street Tunnel toward Manhattan and the Queens Boulevard Line. All trains via 60th Street would go to Astoria; in comments, Alexander Rapp suggests flipping the connection at Queensboro Plaza, letting trains from 60th Street (such as the R) go to Flushing and the 7 go to Astoria, matching the busier line in Queens (Flushing) with the more popular route into Manhattan (60th Street). Queensboro Plaza and Queens Plaza have no transfer, and one would need to be constructed, but even with moving walkways, transferring would involve several minutes of walking between platforms.

Then, the Queens Boulevard Line would be left with local and express services, feeding 53rd and 63rd Street Tunnels. Trains on 63rd have to go to Sixth Avenue. This requires all 53rd Street trains to serve 8th Avenue – the east-west line shown in the images. No more M, just a more frequent E train, with implications for how the A/C run (probably both express between 145th Street and Chambers, where the E terminates). This breaks the transfer, and there is no possible way to create a new one. Transfers between the E and trains on 63rd would only be at Roosevelt and West 4th, and trips from East 53rd to Sixth would require a wrong-way transfer on the western leg using the B/D.

It’s possible to keep the limited reverse-branching and have Queens Boulevard trains of either type, local and express feed either 53rd or 63rd Street Tunnel. Local-local transfers would then be available immediately east of Queens Plaza. The problem is that this still introduces schedule dependence, on what is most likely the most crowded line in the city now that Second Avenue Subway has taken pressure off of 4/5/6 on Lexington. Conversely, without reverse-branching, both choices of how to match lines have drawbacks: sending locals to 63rd and expresses to 53rd means there is no connection between local stops in Queens and Long Island City, whereas doing the opposite makes the connections better but matches the busier Queens trunk (the express tracks) with the less desirable Manhattan connection (63rd).

That said, despite the drawbacks, something like this disentanglement is requires. New York needs more capacity, and shuffling trains like this effectively creates another half a tunnel’s worth of capacity between Queens and Manhattan and allows higher frequency on Second Avenue Subway, useful given the high population density in the part of the Upper East Side that it serves.

For other cities, let this be your lesson: do not build infrastructure that looks like the left image, unless you know how you can convert it to two intersecting lines with a transfer, the way Toronto did. Branching may look like a nifty way to provide one-seat rides between more pairs of origins and destinations, but it will reduce your capacity, and in the distant future force you into difficult choices in which anything you do, including the no action alternative, will screw someone over. What looked like good planning when the IND built subways under Sixth and 53rd in the 1930s turns out to be bad planning today with what we know of how subways operate around the world.

Faster-than-Conventional Rail: Where Could It Work?

Note: this post is secretly about Hyperloop and Elon Musk’s most likely fraudulent claim about the Northeast Corridor. But it’s an interesting discussion more in general. Not all such technology is vaporware the way Musk’s efforts are. See more on The Boring Company’s false claims in a piece I published at Urbanize.LA a few days ago.

The upper limit of conventional high-speed rail seems to be 360 km/h. In Japan, experiments at that speed have succeeded, but there already are problems with noise, stopping distance, and catenary wear, and currently trains top at 320; plans to go at 360 depend on a future Shinkansen extension to Sapporo. In China, the maximum speed is 350, with trains capable of reaching 380 but not doing so in practice. In Continental Europe the maximum speed for new lines is 320-330 km/h, whereas in Britain HS2 is designed for about 350 km/h (220 mph).

Faster technologies exist, in service, today. Shanghai’s Transrapid tops at 431 km/h in service, and JR Central’s under-construction maglev line is targeted at 500 km/h, with tests at 600. Vactrains can go even faster, but are still untested technology (and this includes Hyperloop variants). The question is, where is there room for such technology? So far, Siemens’ attempts to sell Transrapid failed beyond the Shanghai airport connector, an orphan 30 km line going from the airport to the edge of the built-up area of the city. JR Central is building the Chuo Shinkansen maglev between Tokyo and Osaka, but so far there are no plans to extend this technology elsewhere – even within Japan, the state is continuing with building Tokyo-Sapporo as conventional Shinkansen rather than maglev.

The Tokyo-Osaka line is somewhat sui generis. JR Central is currently running about 14 trains per hour at the peak on the Tokaido Shinkansen between Tokyo and Shin-Osaka, each with 1,323 seats, and they’re generally full. It is also old – as the first HSR line in the world, it has a curve radius of 2.5 km (newer lines start at 4 km and go up), and a top speed of 270 km/h. This is exactly the sort of situation that favors new technology. The Tokaido Main Line was a popular intercity line in the late 1950s, but Japan National Railways couldn’t add more express trains without bumping against the capacity limit imposed by slower trains using the line; this tilted it in favor of building the Shinkansen. The Paris-Lyon main line was similarly busy in the 1970s, encouraging the construction of the LGV Sud-Est as a bypass. Nowhere in the world except Tokyo-Osaka is there a full conventional HSR line, except Paris-Lyon – but see later why it is a poor candidate for faster technology.

Track sharing

The main tradeoff with maglev, or even faster technology, is cost. This comes from two places. First, higher top speed requires much more advanced civil engineering, with wider curves, which means more tunnels and viaducts. Conventional HSR can limit costs by climbing steeper grades than legacy trains (the LGV Sud-Est has no tunnels, the legacy Paris-Lyon line does). Maglev can climb even faster grades, but once the speed crosses into the vactrain range, the vertical curve radius required to achieve a steep grade is so wide that it is no longer possible to vertically hug terrain the way European HSR lines do.

The second place is the urban approaches. In theory, this should be a strength of faster-than-conventional rail technology, which has a lower minimum curve radius than HSR at equal speed. But in practice, conventional HSR can leverage existing railroad lines on the urban approaches. At lower speed the stopping distances are shorter, so capacity is higher; the upper limit at speed maybe 12-15 trains per hour, but on a low-speed approach it’s closer to 24-30, so it’s possible to share tracks with legacy commuter and intercity trains.

In Japan, Spain, and Taiwan the HSR track gauge is different from the legacy gauge, so track-sharing is not possible in the major cities, driving up the cost of urban approaches. In smaller cities, Japan and Spain have gauge-change technology, which takes too much time to be of use in capacity-constrained big cities but can allow track sharing on branches. But unconventional technology cannot share tracks anywhere, requiring tunnels on urban approaches. The cost of 20 km of urban tunnel can easily match that of 200 km of at-grade greenfield HSR outside urban areas. The Chuo Shinkansen’s cost, around $200 million per km, comes from the fact that 70-80% of the line is underground, in urban areas and under mountains.

This implies that unconventional technology is most useful when there is limited benefit to be gained from track sharing. This includes the following situations:

  1. The cities served do not have usable legacy rail approaches, or else have a surplus of space within which to build a new approach.
  2. There is no need to branch and use legacy track at lower speed.
  3. There is no preexisting high-quality track that HSR can use, either at high speed outside cities or at medium speed on approaches.

In North America, FRA regulations traditionally led to situation #1. But FRA regulations seem to be changing, which makes track-sharing on approaches more feasible; practically every city has approaches with a surplus of passenger rail capacity (yes, even New York – Amtrak runs 4 trains per hour into Penn Station from the west at the peak, it just uses these slots poorly). In Europe, cities with poor approaches are more likely to be served on a branch, since the rest of the network is so strong. Situation #2 never applies here – branching is always useful, letting the LGV Sud-Est carry not just Paris-Lyon trains but also Paris-Marseille, Lille-Lyon, London-Lyon, Paris-Geneva, etc.

Some of the stronger intercity travel markets are in situation #3, but most aren’t. In North America, the Northeast Corridor has long stretches of high-quality track, either already capable of high speed or capable with a small number of curve modifications. That characteristic alone makes it exceptionally bad for unconventional rail technology: such technology would need a new alignment through hundreds of kilometers of suburbia in Massachusetts, Rhode Island, New Jersey, Pennsylvania, and Maryland. Toronto is also a poor candidate for unconventional technology, since it has a long stretch of suburbia in both directions with high-quality four-track commuter rail, straight enough for 200 km/h or even more. Significant suburban tracks are also useful in California (Caltrain, parts of Metrolink) and Chicago. Only the Pacific Northwest, Portland-Seattle-Vancouver, has a real shortage of usable legacy track even on the approaches. So is it a good candidate for unconventional technology? No, for reasons of distance.

The optimal distance

Faster-than-conventional rail is silly at short distance. The difference in travel time is smaller and does not justify the expense. Access and egress times are fixed, and may even go up if the station locations are less central (the Chuo Shinkansen won’t serve Tokyo Station but rather Shinagawa, a few km south of the CBD). So focusing on in-vehicle time is less useful. The Chuo Shinkansen is really at the lowest end of what is acceptable. It works because, again, the Tokaido Shinkansen is at capacity. Tokaido is also relatively circuitous in order to avoid mountains – the distance from Tokyo to Shin-Osaka is 515 km on the Tokaido Shinkansen, 438 on the Chuo Shinkansen, and 405 on a straight line. On the Northeast Corridor, the New York-Washington distance is 362 km on the railroad and 330 on a straight line, a much smaller difference.

Conversely, faster-than-conventional rail is questionable at very long distance. At maglev speed, a New York-Los Angeles train would take perhaps 12 hours, not really competitive with planes for people who don’t mind flying. At vactrain speed, the train would be competitive. However, in either case, trains require linear infrastructure, and repackaging them as a new Hyperloop doesn’t change this basic fact. Ignoring the effects of terrain, a 4,000 km vactrain or maglev line costs ten times as much as a 400 km line. This is not the case for air travel, which requires no fixed infrastructure between the airports.

There should be a good zone in the middle, say the 1,000-1,500 km range. This includes city pairs like Beijing-Shanghai, New York-Chicago, Tokyo-Sapporo, Tokyo-Fukuoka, Delhi-Mumbai, Delhi-Kolkata, and some international European pairs like Paris-Madrid. Going up to 2,000 there are also New York-Miami, Chicago-Dallas-Houston, Beijing-Guangzhou, and Los Angeles-San Francisco-Seattle; in China, where conventional HSR is faster, even 1,000-1,300 km is well within conventional HSR capabilities (Beijing-Shanghai is 1,300).

However, the fact that there is this sweet spot for unconventional rail does not mean that the construction costs are affordable. This remains a question mark. Maglev costs are either in line with HSR costs at equal tunnel proportion, or somewhat higher. The Shanghai maglev cost 10 billion RMB in 2003, which in PPP terms is maybe $100 million per km for an elevated suburban/exurban line (bad, but not terrible), and in exchange rate terms (imported technology) is somewhat more than half that. The Chuo Shinkansen seems to be $200 million per km, 70-80% underground, which is in line with urban tunneling costs in Japan but high by the standards of exurban tunneling (the 60% tunneled extension of the Tohoku Shinkansen to Shin-Aomori was $55 million per km).

The upshot is that a New York-Chicago maglev is likely to cost like 1,200 km of HSR. The western half of this line is easy – maybe a short tunnel in suburban Chicago is required, but there’s so much right-of-way space that an above-ground urban approach should be fine. The eastern half of this line consists of 600 km of pain in the Appalachians, suburban New Jersey, and a new tunnel under the Hudson. Costs approaching $100 billion are likely, and I don’t know that the benefits are commensurate.

Can you start big?

A short maglev or vactrain is of little use. Given the expense of approaches, the best use of expensive infrastructure may well be to build multiple lines using the same approach. For example, not just New York-Chicago or New York-Atlanta-Miami, but both at once, to take advantage of the same maglev tunnel under the Hudson. By itself New York-Chicago might be good enough, but it’s unclear – it’s nowhere the huge benefit/cost ratio coming from a program for conventional HSR on the Northeast Corridor at normal first-world rates.

I think this is the biggest risk with unconventional rail technology. Its basic characteristics suggest that there should be a distance range at which it works well – not too short so as to offer too little benefit versus conventional HSR, not too long so as for construction costs to grind it down. But it’s equally possible that the two bad zones, too short and too long, really overlap, so that 1,200-km lines are still too expensive to compete with planes while not offering enough speed benefit over conventional HSR to justify all this new construction.

The problem, then, is that it’s difficult to start big with a risky technology. The shortest useful maglev segment, Tokyo-Nagoya, is still well over $50 billion, and Tokyo-Osaka approaches $100 billion. This is on a route with proven demand; what about routes that don’t parallel overcrowded conventional HSR? Some government will need to take a $100 billion gamble on a long route hoping that the 1,200-km niche really exists.

The Lagos Metro

Lagos is the second-largest city in the world without rail rapid transit (the largest is Karachi). Sources disagree on its population, but it looks like 21 million in the built-up area, consisting of most of Lagos State plus a few suburbs just outside it, such as Ota and Ijoko – in total, 1,000 km^2, someone more including the suburbs. All of the problems that rapid transit intends to fix – traffic jams, pollution, long commutes, overcrowding, unpopular jitneys – are present. I don’t want to repeat the case I made in this post in favor of aggressive investment in subway systems in Lagos and other big third-world cities. Instead, I want to talk about concrete features.

Here is the map – it’s slightly different from the version I circulated in previous posts. Note the following features:

1. Four of the lines – East-West (blue), Main Line (red), Ikorodu (brown), North-South (purple) – are four-track. This is because Lagos is so big that its outer margins require very wide stop spacing, which requires four tracks. The first three also run in wide enough rights-of-way for significant stretches, making four-track elevated structures easier to construct. Express stops are denoted with squares, local ones with circles. If two four-track lines intersect, the stop is denoted with a square, and is express for both lines. All four-track lines have two-track tails – the farthest-out square is the last station with four tracks, where locals turn, while expresses keep going to the end. Only one four-track line has an end without a tail: the Main Line terminates all trains at Leventis.

2. On the four-track stretches, the average interstation is a little less than 4 km. Average speed can approach 60 km/h, given that the rights-of-way are often quite straight. On the local tails of these lines the average looks like 2 km, or around 50 km/h. On the two-track radial lines, the average interstation is a little less than 1.5 km, or around 40 km/h; the difference with the local tails of the four-track lines is that the local tails are in suburban areas.

3. Every pair of radials intersects, usually in Lagos Island but sometimes elsewhere. Four circumferentials – Apapa (dark red), University (ochre), Ishaga (dark green), Idimu (magenta) – intersect all the radials. Whenever two lines intersect, there’s a station. Doing this requires a lot of lines to run in the same alignment in the center. This is not track sharing, but multi-track tunnels. The only eight-track tunnel, where the Main and Ikorodu Lines run together between Eko Bridge and Leventis, has a wide road to go under; the only ten-track el, where the East-West, Ota, and Ikorodu Lines parallel around the National Theatre, has an entire expressway to go over.

4. The southern ends of the Ota (yellow) and Ikeja (silver) Lines are in open water today. This is because the area is slated for land reclamation and intense development, called Eko Atlantic. The western margin of that area, around the station I call Eko Atlantic, is already reclaimed, but still undeveloped. That entire area (Victoria Island) is the favored quarter of Lagos, and is commercializing; farther east, in Lekki, there are grand plans for suburban redevelopment, and an immense amount of casual marketing in the media (“buy now and the land will triple its price in five years”).

The system I’m proposing differs from the current proposal. The current proposal only has five radials (with apparently just one crossing from the Mainland to Lagos Island), corresponding to my East-West Line, Main Line, Ota Line, and a hybrid of the Ikorodu Line and the two branches of the North-South Line; there is one circumferential, vaguely corresponding to my Idimu Line.

Some of the features of the current proposal are a good start. It’s not possible to build eighteen lines at once, and some prioritization is required. It’s even fine to start with shared tracks into Lagos Island and subsequently give lines their own way into Lagos Island. (On my map, everything paralleling the three existing road bridges is a bridge, the rest are tunnels).

However, the existing proposal suffers from several shortcomings, which will need to be fixed later:

  • The stop spacing is too wide even in the center, intermediate between my local and express tracks.
  • There is far too much branching. In any reasonable sequencing of the lines, the East-West Line will fill before the later ones (i.e. the ones going north-northeast) open, requiring new routes into Lagos Island.
  • There isn’t enough service in Victoria Island, which is developing as a CBD, as is common for rich neighborhoods.

But the worst problem is that the under-construction route goes elevated along the Ring Road, skirting Lagos Island, with just two stops, Ebute Ero and Marina. This segment has little value and should be demolished once direct underground routes with more stops open. According to a paper that’s no longer online, one of the reasons third-world subway lines tend to underperform ridership expectations is that many of them use available rights-of-way and skirt the CBD, instead of building short tunnels to get to the center. This paper in turns is one of the references used by Bent Flyvbjerg in his paper arguing that in general urban rail has cost overruns and ridership shortfalls.

The big obstacle for constructing any subway system is cost. This is especially true in Lagos, where the construction cost of the current project (the Blue Line, corresponding to the inner part of the western half of my East-West Line) looks like $180 million per km, entirely elevated. I say “looks like” because while the cost is consistently $2-2.4 billion in exchange rate terms (around $5 billion in PPP terms), it’s not completely clear whether this is the Blue Line or also the Red Line.

My proposal is largely elevated, but the Lagos Island segments have to be tunneled. So do some other segments, for examples the inner parts of the North-South and Ikeja Lines, and most circumferentials. The system, totaling about 900 km, of which 200 is four-tracked, looks like it could be built only about one-quarter underground, or slightly more. Moreover, much of the underground construction could be cut-and-cover, including several segments in Lagos Island, and most of the circumferentials; only the underwater crossings and a few off-grid Lagos Island connections have to be bored.

The main analytic point here, carrying over to other cities, is the importance of prior planning. My map has 18 lines. This is useful because figuring out where stations should go, which stations on four-track lines get to be express stops, and how to sequence the lines should be based on long-term considerations. As I hinted in a post written right after I finished the first version of this map, about subway lines that intersect without a transfer, building the best lines 1-3 requires having a good idea where lines 4-12 will go. So even if Nigeria runs out of money after the first two lines are built, figuring out the built-out network is not useless – it informs the current network, and makes adding future lines less painful.

This is true for reducing construction costs, and not just for a good network. One of the positive features of the Paris Metro is that nearly all of it was planned as a whole, and as a result, difficult stations like Chatelet, Etoile, and Nation were built with the intention to have multiple Metro lines serve them. This meant that the stations could be built once, rather than multiple times, once for each line. Two lines, Metro 8 and 9, even run alongside each other for 1.7 km under the Grands Boulevards, which are wide enough for a four-track subway.

The planners of every system, regardless of whether it’s a metro for a city that doesn’t have any urban rail or an extension in a city with fifteen lines, should always think ahead. What are the future plans? What are the future needs? What is the expected future growth? In Lagos, the answer to the last question is “fast demographic and economic growth,” and this means the city should plan on a large system – hence my almost gridlike system of radials going north and northwest and circumferentials crossing the Mainland going southwest to northeast. But really, every city needs to ask itself how it wants its rail network to look, and plan the highest-priority segments accordingly.

A Marshall Plan for Third-World Infrastructure?

At the G-20 meeting, an Ivorian journalist asked President Macron about the Marshall Plan and if Europe would do the same for Africa. Macron gave a long-winded response, including some deservedly-mocked zingers about Africa’s “civilizational” problems and how women have 7-8 children (see my own response here). But buried in that there was an interesting point I’d like to expound on, about the difference between the Marshall Plan and current aid:

I don’t believe in this reasoning, forgive me for my directness. We among the West have been discussing such Marshall plans for Africa for many years and have in fact given many such plans already. So if it was so simple it would be fixed already. The Marshall plan was a reconstruction plan, a material plan in a region that already had its equilibriums, its borders and its stability.

Jane Jacobs said something similar, in either The Economy of Cities or Cities and the Wealth of Nations, I forget which. Her argument was as follows: postwar Europe lay in ruin, but the business culture, social networks, and so on were still there, so rebuilding infrastructure could restore prewar prosperity and seed future growth. Even with the disruption caused by the mass carnage, there were enough skilled workers who knew the local business culture for the economy to recover. Thus, per Jacobs, and per Macron, Marshall Plan-type programs for developing countries, which are poor rather than in ruins, have no chance of succeeding.

And yet. There are some complexities in the above description. The first is that postwar reconstruction in South Korea, which had never been a developed or even middle-income country at that point, was useful. Literacy rates rose rapidly, after WW2 and again after the Korean War, going from 22% in 1945 to about 71% in 1960. The schools were often built not by the Korean government but by the US or by Christian missionaries (Korea was the cause celebre at the time, and the origin of the trend of Americans adopting children from poor countries).

The second complication is that in post-conflict situations, there is a role for reconstruction aid. Libya was never a developed country, but it was richer before the civil war than it is today, and could have used reconstruction before the war resumed in 2014. Niger and Mali (two of the few countries that are so poor Macron’s epithet about 7-8 children per woman might apply) in particular have had recent conflicts, dragging down growth, especially in Niger.

The third is the subject of this post: infrastructure. In theory, this is a one-time investment, which can be done with an outside infusion of cash plus some tech transfer. This means, first-world consultants helping design rail networks, water infrastructure, roads, subways, and power plants, and on the way training local workers in how to do maintenance and how to design and engineer future expansion. Europe and the US practically never do that anymore, but Japan still does and China has started doing so as well; Kenya is building intercity rail with Chinese money, buying Chinese equipment. In theory, this is worthwhile investment, since the recipient countries have very weak currencies and high expected growth rates, which depresses current-dollar construction costs while maintaining decent future current-dollar profits.

And yet. There’s a number of subway projects in developing countries built with foreign financing and technical expertise, chiefly Japanese. I singled out two for their high construction costs, in Dhaka and to a lesser extent Jakarta. Dhaka is setting world records for elevated construction costs – higher in absolute terms than in the US, and unimaginably higher relative to local incomes. Jakarta’s costs have risen further since I last wrote the post, and currently stand at $1.7 billion, or $5.4 billion after PPP adjustment, a total of $350 million per km for a line that’s only 60% underground.

There is a dearth of indigenous expertise in how to build rail infrastructure in developing countries. Unfortunately, the first world cannot supply this expertise, because the first world’s expertise is in how to build rail infrastructure in rich countries. As I noted a month ago, rapid transit construction in the third world needs to take into account the difference in relative costs of labor and capital between rich and poor countries; in comments, Ian Mitchell suggested resuscitating the methods of the 1910s, when American incomes were about the same as in the more functional third-world countries today, like India and Nigeria. There is no real expertise in how to do that, and it is unlikely that international consultants, who expect to do most of their work in rich countries, will bother to learn.

After the initial construction phase of the Delhi Metro, the system worked on indigenizing itself – that is, on using more local capital rather than relying on foreign consultants. The cost reduction, as far as I can tell from links that are now dead, was 15% – substantial, but not a game changer. India remains one of the highest-cost countries in the world. It’s possible that it learned all the wrong lessons – as it developed local expertise, it figured out how to build rapid transit using the construction methods of the first world.

This is unlikely to have been an accident. Poor countries, and even middle-income ones, are full of cultural cringe, in which acting like the rich world is a positive status marker; ex-colonies frequently act this way toward their former colonizers. The political system within the countries in question encourages elites to show that they can be just like the Europeans or Americans or high-income Asians. Those elites are fervently nationalistic, but this often means showing the world that India can have what Britain and the US have. Thus there is an internal political bias toward solutions that do not work. Ironically, first-world consultants are the best-placed people to recommend using different construction techniques, suitable for low labor costs, but they are unlikely to suggest them, again since their expertise is in high-labor cost environments.

So having a Marshall Plan-style program in which rich countries build infrastructure in poor countries is a recipe for high construction costs. Can it at least result in good projects? The answer is, again, mixed, for two reasons.

The first reason is that it isn’t easy to realize profits from infrastructure investment in foreign countries. The poorest ones have a high risk of relapse into civil war. The next tier of countries – the Kenyas, the Bangladeshes, the Vietnams – are more stable, and in theory offer a good investment, with reduced risk of economic collapse. The problem is that as they get richer, they will necessarily be more nationalistic and more capable of asserting themselves. The same xenophobia that leads people in expensive British, American, and Canadian cities to scapegoat foreign investors, often Chinese, for high housing costs, applies just as well to poor countries. A richer Kenya is a Kenya that is more likely to find it offensive that it depends on China for its railroad network. If there is significant profit extraction from Kenya to China, then it’s because Kenya’s economy has grown, allowing it to threaten to impose capital controls or nationalize the railroad. This means that a strategy of spending money in a poor country now to make profits later as it gets richer has too much political risk, regardless of how much the country signals commitment to letting foreigners make a profit in it today.

The second reason is that the projects themselves may not be optimal. This is the same problem as the construction cost problem. International consultants are used to principles that are true in the cases they have the most experience in, which are usually in rich countries and occasionally in middle-income ones. I’ve had trouble drawing good fantasy maps in Israel, a borderline rich country, purely because its ethnic divisions are so different from those of any other rich country: in comments here and at Sandy Johnston’s place, Shlomo reminds us that the ultra-Orthodox use transit profoundly differently from everyone else. With my knowledge of European mores, I can confidently say that even in European countries I don’t know well, like Spain, this is at most an edge case. Can I say this of Nigeria? Maybe not. Can I say this of Niger? Lol.

This lack of local knowledge is compounded by the fact that, as with the construction cost problem, local elites want the appearance of a Western- or high-income-Asian-looking system. This does not mean they want to build subways, rail networks, modern sewage systems, household electrification, etc. just for show. On the contrary, in the better-functioning third-world countries even very corrupt leaders genuinely want their respective countries to be more successful. The problem is that they are unlikely to be experts on what a good subway, sewage, etc. system should look like, and base their ideas of what works on what they have seen work in the first world. Third-world adaptations are often creatively different, for example an NGO is installing elevated water pipes in Kibera, to avoid expensive underground engineering required to eliminate seepage, and to deter metal and water theft (Kibera is notorious for both).

There is no way around painstakingly developing local expertise in infrastructure construction and operations. It’s something that engineers in poor countries can learn from rich countries, but they would need a good understanding of first principles in order to adapt to local situations. It’s not something that a consultancy could trivially do.

So, is there room for a Marshall Plan? The poor countries in question could certainly use the money. The problem is that the sum total of what they need to invest in – physical infrastructure, schools, public health, legal institutions – stretches not just their tax capacity but also the generosity (some would say guilt) of any first-world country. What I think Lagos needs to spend on building a metro system is on the order of $200 billion in PPP terms; in exchange rate terms that’s $60 billion, compared with $90 billion in annual aid given by EU members, in total. Lagos needs more investment than just the subway, Nigeria is more than just Lagos, and the total population of countries poorer than Nigeria is more than a billion. Even counting foreign investments that the donor country intends to recoup but probably will not, this is not nearly enough. So what we’re discussing is not really a Marshall Plan equivalent in which the donors help rebuild infrastructure in the recipient countries, but usual foreign aid politics, in which (from the perspective of the recipients) foreign aid is one additional revenue stream with its own strings attached.

Line Spacing, and Intersections Without Transfers (Hoisted from Comments)

This post is inspired by two separate things. The first is my work on a fantasy subway map for Lagos; here is the current live version. There are twelve radial lines, all serving the western half of Lagos Island, converging on nine transfer stations. Under the principle that whenever two lines intersect there should be a transfer station, this greatly constrains the paths the lines can take. Result: the path between two CBD stations, Eko Bridge and Leventis, carries ten tracks underneath it. This is under a wide street, and it might be possible with a double-deck four-track-wide tunnel and two more tracks deep-boring around it, but it’s not easy to construct.

The second inspiration is a post by Brian Stokle about subway line spacing. Brian looks not at spacing between successive stops on one line, but at spacing between parallel lines, averaging a few North American examples. The average is a little higher than half a kilometer, narrower than the typical stop spacing. On Twitter, Joshua Mello notes Boston’s spacing was narrower; in comments, I add examples from New York and Paris, which are a bit narrower than Brian’s examples but wider than Boston (New York is one block in Midtown, so 280 meters, and Paris is 300 between Metro 3 and Metro 8 and 9).

These two examples together illustrate the tradeoff in subway construction. Most subways have a stop every 1-1.5 km; newer systems are at the high end of this range, mostly because of the demographic weight of China. It’s normal for stop spacing to tighten in the core, but not to a large extent. In Tokyo, the average stop spacing is 1.2 km, and in Central Tokyo it’s perhaps 800 meters. In London, the Tube lines seem to tighten from an average of 1.2-1.5 km to 600-800 meters in Central London.

At the same time, subway line spacing is necessarily short. The reason is that modern CBDs are geographically small. Midtown is maybe 4 km^2, from 30th to 60th Streets and from between 2nd and 3rd Avenues to between 8th and 9th. The Paris CBD, from just west of Les Halles to just east of Etoile, is also about 4 km^2 (see job density on PDF-p. 6 here). The Tokyo CBD, defined around Otemachi, Nihonbashi, Hibiya, Shimbashi, and increasingly Roppongi, is maybe 5-6 km^2, in a metro area of 38 million people.

Subway networks in such CBDs are necessarily crowded. The CBD is where people want to go. A subway line can get away with skirting it – Paris M4 does, and is in a near-tie with M1 for highest ridership per km. But avoiding it entirely is a ridership killer, except specifically for circumferential lines concentrating off-CBD travel: in Paris this suppresses M10 ridership, and in New York, it suppresses ridership on the J/Z (even though they serve Lower Manhattan) and the L (even though it serves Union Square). This means that the CBD of a large city will have many subway lines converging on a relatively small area. New York has its five north-south lines through Midtown.

Ensuring that every pair of intersecting subway lines has a transfer in this environment is difficult. Line spacing is usually narrower than station spacing, requiring kludges like the block-long walkways in New York, such as between Times Square at 42nd/7th and Port Authority at 42nd/8th. Paris managed to have an almost perfect network – before M14 was built, it only had one missed connection, between M9 and M12 (built by a competing private company) – but only by having very short station spacing, unusual even by the standards of the early 1900s, ruling out significant suburban extensions of the kind that are routine in London and Tokyo.

The situation in smaller cities is actually easier. The CBD is very small, often smaller than a square kilometer, but there are fewer lines, so it’s easier to make sure lines intersect properly. It’s also much easier to get line spacing right outside the CBD, where there’s less intense demand, allowing line spacing compatible with stop spacing on any intersecting or circumferential line.

The fundamental issue here is really about planning for the future. It’s not hard to gets lines 1, 2, and 3 to intersect nicely, or even lines 1-6. But beyond that, a city will often find itself in a situation where the best street alignment for line 7 happens to be right between two stations on line 1, spaced too far apart for a transfer. This is what happened to Tokyo. In New York, the three constituent systems (IRT, BMT, and IND) were each internally planned cohesively, so when two lines within the same system intersect, there’s a transfer, and, with difficulty, the IRT/BMT intersections have transfers as well. But the IND connects poorly to the other two systems, sometimes deliberately, and the IND’s layout made future extensions and service changes break transfers. My proposal to reduce reverse-branching in New York runs into the problem of breaking the transfers designed by the IND around a specific service plan.

When lines are designed together, it’s easier to avoid this problem. Paris M8 and M9 share a route through the center, as they were built simultaneously as the street is wide enough for four tracks. In contrast, building a line under or next to an existing line is much more difficult; New York did it anyway, under Sixth Avenue, but this led to cost overruns that doomed the IND’s early plans for further expansion. It is also difficult to build a new station under an existing transfer station, as it usually requires underpinning; in Paris, this problem means that transfer stations tend not to have closely-aligned platforms, requiring long walks between lines. When I’m proposing running multiple lines in the same tunnel in Lagos, this is from the point of view of assuming coordinated planning, with sequencing that allows entire streets to be dug up at once.

However, in reality, even coordinated design has its limitations. Subway networks take multiple decades to build, and in the interim, the city changes. Planners can attempt to use zoning to shape city development in a way that facilitates further expansion, but some tendencies are too uncontrollable. For instance, high-income neighborhoods tend to commercialize; I mentioned Roppongi as a growing part of the Tokyo CBD earlier, which is an example of this trend. The hottest new part of New York commercial development, the Meatpacking District, is really not a subway hub. This means that even if a city plans out lines 1-12 to share tunnels appropriately, it may not be able to control where there will arise the most demand for line 13. Coordinated long-term planning makes things easier, but it will not solve the basic problem of optimal subway spacing and CBD size.

My Patreon is Live

Here is my Patreon page. Donations get processed on the 1st of every month; if you contribute today, my understanding is that it will still only get processed in August. I’m still working on the Lagos post solicited via Twitter, but should be done in a week, depending on how much time I have. (The subway meltdown in New York and Cuomo’s laconic response thereto mean that I’m on deadlines at a bunch of outlets that want my opinions.) When I’m done I’ll start doing internal Patreon polls about the next post’s topic.

My posts are going to remain public. Instead, the rewards are as follows:

$2/month (“diesel bus”): you get to vote in the polls about my topics. Not all posts will be polled, but at least one per month, ideally 2-3, will be.

$5/month (“trolleybus”): you get dedicated content, in the form of various examples or caveats that are cut from my published pieces due to length. Things that I cut because I couldn’t find good enough evidence for them don’t count; only things that I’d be comfortable saying in public, but didn’t because of length or flow, do.

$10/month (“tramway”): you get listed as a supporter on a sidebar of this blog.

$25/month (“rapid transit”): you get to tell me what to write about, bypassing the polls, a couple times a year – at least twice, possibly more depending on schedule and on how many people ask for the same thing. (If two people keep asking for the same thing, they really get a minimum of two posts each, so four total.)

My current target is a total of $200/month, based on what people said on Twitter. If I get a lot more than that, I can start committing to more than one post a week.

Modeling Jitney-Bus Competition

I just published a piece at the Bay City Beacon about Lyft Shuttle, the company’s foray into fixed-route buses. In the piece, I mentioned briefly that adding a competing operator can reduce the average quality of service. The piece, nominally 500 words, really 700, was far too short for me to expound on the model, even though people on social media had asked me about it before. So here it is.

The first assumption is that the routes are identical. This is largely true for some of the more northern Lyft Shuttle routes, duplicating Muni’s 2 and 41 buses (the 41 duplicator skips some inner stops, though).

The second assumption is that the bus has a fixed schedule, but the jitney can schedule itself in response to the bus. This is true of the case studies I know of (and, to make it very clear, “case study” means “I’ve read an article” or “I’ve heard it discussed on social media”): Israel’s Sherut vans, and Hudson County’s private jitneys. Both use dynamic schedules, which in plain English means drivers radioing each other (in Israel) or employing lookouts (in New Jersey); the bus companies have fixed schedules that are slower to change.

The third assumption is that marginal riders take whichever route they see first. This is the case with regular jitneys. Not all riders are marginal: there might be an explicit ethnic dimension, e.g. dollar vans in New York are more popular with unassimilated immigrants, because they provide amenities like use of their own language rather than English. Lyft Shuttle is booked via app, so the situation there is murkier; however, most likely the use case will involve passengers buying a ticket a few minutes in advance, possibly checking against a bus app to see which will come first. Some people will stick with one system over the other (tech boosters seem to hate public services, people without other reasons to download the Lyft app will probably stick to the bus), but some will be flexible.

Let us work this out first assuming perfect scheduling and then introducing schedule irregularities due to bunching.

Now, let’s assume the public bus arrives every 6 minutes. If the transit agency wishes to double service, it will schedule additional service at the midpoint between each pair of successive trips, providing 3-minute frequency. But if additional service comes from a private operator, the incentive is to schedule to compete and not to cooperate. Say the public bus arrives at my station at :00 on a 6-minute takt. The private operator can schedule itself to arrive at :03 on a 6-minute takt and get half of my station’s traffic, or it can schedule itself at :05 and get 5/6 of its traffic. Let’s set the fudge factor at 1 minute for now: if the separation is smaller, for example if the jitney comes at :05:30 and the public bus at :06, then I see both at the same time and am indifferent as to which to ride.

By itself, this still means adding service. However, it’s likely that there is going to be some service diversion – that some public bus riders will switch to the private service (e.g. because it usually comes first). If one quarter of the bus riders switch, then the schedule is cut to a bus every 8 minutes. The jitney still aims to arrive 1 minute before the bus for maximum revenue, perhaps getting bigger vehicles if it needs the capacity, as the New Jersey jitneys did. So now my bus comes at :00, :08, etc., and the jitney comes at :07, :15, etc. Average wait time is 3.125 minutes, whereas before it was 3 minutes.

The formula in general if both vehicles come every x minutes and are separated by 1 minute is \frac{(x-1)^2 + 1}{2x} and this equals 3 at x = 4 \pm \sqrt{14} \approx 7.74, corresponding to about 23.5% reduction in transit use; any higher reduction makes average wait times worse. If the original headway was y, then we have x = 1 + y/2 \pm \sqrt{(1 + y/2)^2 - 2}, or just under 2 extra minutes; the fixed separation, 1 minute, means this calculation is not scale-invariant.

Now, let’s introduce schedule irregularity into this system. As a toy model, let’s look at what happens if the bus can be up to 1 minute behind or ahead. If the route only has public buses, and one bus is off by 1 minute, then instead of two 6-minute gaps there’s a 5-minute gap and a 7-minute gap, for an average wait of 3:05. If the route has public buses and jitneys, scheduled 1 minute apart as above, then a 1-minute error is good for passengers if it evens out the schedules (it converts a 3.125-minute wait to a 2.5-minute wait), but bad for passengers if it makes the bus and the jitney arrive at exactly the same time (the wait rises to 4 minutes).

But really, bus schedules are an unstable equilibrium. (So are train schedules, but the instability is too slow to cause bunching). If a bus is a minute behind, then at the next bus stop it will have an above-average crowd size, since people had more time to show up and wait. Boarding time is a significant fraction of bus travel time, so the bus will go behind even further, until the bus behind it will catch up, at which point the two buses will leapfrog each other. It’s possible to reduce this effect by cutting boarding time, via low-floor buses and off-board fare collection with all-door boarding; Muni has implemented both, but this is still not enough to remove the instability. In practice, this imposes a minimum headway of about 3 minutes – below it, buses bunch so much that adding service doesn’t add any capacity. In theory it’s possible to go lower, but when ridership is high enough to justify 3-minute headways, it’s high enough for dwell times to make lower headways infeasible.

Jitneys do not have a 3-minute minimum headway; they’re more flexible about running express if they’re already full. This, in turn, means that schedules on jitney routes are more irregular than on buses, making wait times less predictable, and ultimately longer (since, at equal service, less even intervals translate to longer average waits). But more to the point, jitneys still aim to schedule themselves to come just before the bus does. This means that jitney arrival irregularity largely tracks bus arrival irregularity. So with this in mind, if the city bus gets delayed by a minute again, and the jitney adjusts, then we have the following service gaps, in minutes: 8, 1, 6, 1. Average wait time is now 3.1875 minutes.

So the question is, what effect does demand diversion from buses to jitneys have on bus irregularity? The answer is, not much. This depends on additional assumptions on dwell times and the initial delay. Delays compound exponentially, but the exponent (“Lyapunov exponent” in dynamics) is low; on a 6-minute bus route, a 1-minute delay means that future dwell times go up by 1/6, and at 2.5 seconds of variable dwell time per boarding or alighting (Muni average with all-door boarding, see PDF-p. 16 here) it takes 60*6/2.5 = 144 boardings and alightings to delay the schedule by another minute. Muni averages 127 boardings and alightings per hour, so it takes more than an hour for the 1 minute of delay to compound by another minute (strictly speaking, by \sqrt[6]{e} \approx 1.18 minutes). The busiest bus in North America, Vancouver’s 99, averages 320, so the compounding takes just 27 minutes (almost a full one-way trip); Vancouver buses with comparable ridership to the routes Lyft is duplicating average maybe half that.

The point of this exercise is that on the timescales relevant to a bus route, schedule irregularity is approximately linear. So demand diversion from buses to jitneys has a linear effect on schedule irregularity: 25% diversion means that instead of a 1-minute delay there’s only a 45-second delay. A 1-minute delay with 6-minute buses is still better than no delay with 8-minute buses an jitney spaced a minute apart, so the jitneys still remove value. At higher delays, this is no longer true (average wait time is quadratic in the delay); the point of equality is about 1.61 minutes of bus delay due to schedule instability (other delays, like traffic, affect all routes equally regardless of frequency). So jitneys can add value on long, busy routes (don’t forget – the lower the headway, the more significant the assumed 1-minute separation is). But the routes the Lyft Shuttle jitney runs are less busy, and more importantly are short, with less opportunity for delay compounding; delays do not compound past the terminus with decent dispatching.

The upshot is that jitneys do not universally remove value from transportation networks. But on short 6-minute routes, they do even under mild assumptions on ridership diversion. There’s more service in operation, but from the riders’ perspective, wait times have increased and regularity has degraded. The logic of competing private companies is not always the logic of better service for passengers. Sometimes, having a government monopoly inherently improves efficiency.