New York is unique among the major subways of the world in the extent of interlining its network has. All routes share tracks with other routes for part of the way, except the 1, 6, 7, and L. The advantage of this system is that it permits more one-seat rides. But the disadvantages are numerous, starting with the fact that delays on one line can propagate to nearly the entire system, and the fragile timetables lead to slower trains and lower capacity. New NYCT chief Andy Byford just released a plan calling for investment in capacity, called Fast Forward, focusing on accessibility and improved signaling, but also mentioning reducing interlining as a possibility to increase throughput.

I covered the interlining issue more generally in my article about reverse branching, but now I want to explain exactly what it means, having learned more about this issue in London as well as about the specifics of how it applies to New York. In short, New York needs to reduce the extent of reverse branching as much as possible to increase train speed and capacity, and can expect serious gains in maximum throughput if it does so. It should ultimately have a subway map looking something like this:

Lessons from London

In London, there is extensive interlining on the Underground, but less so than in New York. The subsurface lines form a complex interconnected system, which also shares tracks with one branch of the Piccadilly line, but the Northern, Central, Victoria, Jubilee, and Waterloo and City lines form closed systems (and the Bakerloo line shares tracks with one Overground line). The Northern line reverse-branches: it has two central trunks, one through Bank and one through Charing Cross; one southern segment, with through-trains to both trunks; and two northern branches, each sending half its trains to each trunk. The other closed systems have just one trunk each, and as a result are easier to schedule and have higher capacity.

As the Underground moves to install the same high-capacity signaling on more and more lines, we can see what the outer limit of throughput is on each system. The Northern line’s new moving-block signaling permits 26 trains per hour on the Bank trunk and 22 on the Charing Cross trunk. When the Battersea extension opens, reverse branching on the south will end, pairing the older line to Morden with Bank and the new extension with Charing Cross, and capacity will rise to 32 tph per trunk. Planned improvements to transfer capacity at Camden Town, the northern branch point, will enable TfL to permanently pair each northern branch with one central trunk, raising capacity to 36 tph per trunk. Moreover, TfL expects moving block signaling to raise District line capacity from 24 tph to 32, keeping the current reverse branching. The Victoria line already runs 36 tph and the Jubilee line soon will too, while the Central line runs 35 tph. So 36 vs. 32 seems like the difference coming from the final elimination of reverse branching, while more extensive reverse branching reduces capacity further.

The reason complex branching reduces capacity is that, as delays propagate, the schedule needs to incorporate a greater margin of error to recover from unexpected incidents. It also slows down the trains, since the trains are frequently held at merge points. The general rule is that anything that increases precision increases capacity (such as automation and moving block signaling) and anything that reduces precision reduces capacity; reverse branching reduces timetable precision, because each train can be delayed by incidents on more than one line, making delays more common.

What deinterlining in New York entails

NYCT has its work cut out for it when it comes to deinterlining. There are eight different points in the system where reverse-branching occurs – that is, where lines that do not share track in Manhattan (or on the G trunk outside Manhattan) share tracks elsewhere.

1. The 2 and 5 trains share tracks on the Nostrand Avenue Line.
2. The 2 and 5 also share tracks in the Bronx.
3. The A and C trains share tracks on the two-track narrows through Lower Manhattan and Downtown Brooklyn.
4. The A and D share the express tracks on Central Park West while the B and C share the local tracks.
5. The E and F share the express tracks on Queens Boulevard, while the M and R share the local tracks, the E and M share the tunnel from Queens to Manhattan, and the N, R, and W share a different tunnel from Queens to Manhattan.
6. The B and Q share tracks in Brooklyn, as do the D and N.
7. The F and G share tracks in South Brooklyn.
8. The M shares the Williamsburg Bridge tracks with the J/Z but runs in Manhattan on the same tracks as the F.

NYCT should work to eliminate all of the above reverse branches. The easiest to start with is #6: the junction at DeKalb Avenue should be set to keep the B and D trains together and to keep the N and Q together rather than to mix them so that the B shifts to the Q tracks and the D to the N tracks. This requires no changes in physical infrastructure, and has especially high benefits as the junction delays trains by several minutes in each direction. Moreover, the loss of one-seat rides is minimal: the BDFM and NQRW run closely parallel in Manhattan and intersect with a transfer at Herald Square in addition to the inconveniently long BQ/DNR transfer at Atlantic Avenue.

Another relatively easy reverse branch to eliminate is #8, a recent introduction from the 2010 service cuts. Previously, today’s M route in Queens and Manhattan was covered by the V train, which turned on the Lower East Side, while the M ran the same route as the J/Z, merging onto the R and thence the N in Brooklyn at rush hour. Today’s route is thus an M-V merger, which railfans including myself hoped would help decongest the L by creating an alternative route from Williamsburg to Midtown. Unfortunately, such decongestion has not happened, perhaps because gentrification in Williamsburg clusters near the L and not near the J or M.

Harsh decisions

Fixing the reverse-branching at DeKalb Avenue and on the Williamsburg Bridge is painless. The other reverse branches require a combination of hard decisions and new infrastructure.

Fixing reverse branches #3 and #4 requires no capital investment, just political will. Reverse branch #4 is there because there’s demand for two routes’ worth of capacity in the tunnel from Brooklyn but there’s only one express line on Eighth Avenue, and that in turn is the result of reverse branch #3; thus these two issues should be tackled together.

NYCT should decide between having the A and C trains run express between 145th and 59th Streets and the B and D trains run local, or the other way around. This is not an easy decision: either Washington Heights or Grand Concourse would get consigned to local trains. North of 145th the total number of boardings is 102,000 at B/D stations compared with 79,000 on the A/C, but conversely Concourse riders can change to the express 4 trains whereas Washington Heights’ only alternative is the local 1. However the A and C run, express or local, the E should run the opposite in Manhattan – it can merge to either the local or express tracks – and the express trains should continue to Brooklyn. The map I made doesn’t distinguish local from express service, but my suspicion is that Washington Heights should get express trains, on account of its long commutes and lack of fast alternatives.

The same problem of harshness occurs in reverse-branch #5. In theory, it’s an easy fix: there are three track pairs in Queens (Astoria, Queens Boulevard local, Queens Boulevard express) feeding three tunnels to Manhattan (63rd, 60th, and 53rd Streets). In practice, the three Manhattan trunks have astonishingly poor transfers between them in Midtown. Nonetheless, if it does nothing else, NYCT should remove the R from Queens Boulevard and route all 60th Street Tunnel trains to Astoria; together with fixing DeKalb Avenue, this would separate the lettered lines into two closed systems, inherited from the BMT and IND.

However, undoing the connection between the BMT and the IND probably requires constructing a transfer station in Long Island City between Queensboro Plaza and Queens Plaza, which involves a few hundred meters of underground walkway. Even then, the connection cannot possibly be convenient. The saving grace is that Eighth Avenue, Sixth Avenue, and Broadway are close enough to one another that passengers can walk to most destinations from any line.

Subsequently, NYCT should make a decision about whether to send express Queens Boulevard trains to 63rd Street and Sixth Avenue and local trains to 53rd and Eighth, as depicted in the above map, or the other way around. The problem is that the merge point between 53rd and 63rd Street Tunnels is one station east of Queens Plaza, at a local station, and thus the true transfer point is Roosevelt Avenue, far to the east. Riders on the local stations west of Roosevelt would get no choice where to go (though they get little choice today – both the E and M serve 53rd Street, not 63rd). The argument to do things as I depict them is to give the local stations access to 53rd Street; the argument to switch the lines is that there is more demand on 53rd than 63rd and also more demand on the express tracks than the local tracks, so the busiest lines should be paired. However, this in turn runs into turnback capacity limitations on the E in Manhattan, at the World Trade Center bumper tracks.

Potentially, NYCT could try to convert 36th Street into an express station, so that passengers could connect cross-platform. But such a dig would be costly and disruptive to operations. There were plans to do this at 59th Street on the 1/2/3 a few decades ago, for the transfer to the A/B/C/D, but nothing came of them.

Where new infrastructure is needed

The remaining reverse branches get increasingly more difficult. Already #7 requires new turnouts. The South Brooklyn trunk line has four tracks, but there’s not enough demand (or space in Manhattan) to fill them, so only the local tracks are used. There are occasional railfan calls for express service using the F, but it’s better to instead use the express tracks to segregate the G from the F. The G could be turned at Bergen Street on the local tracks, while the F could use the express tracks and then transition to the locals on new turnouts to be constructed at Carroll Street.

Also in the category of requiring new turnouts is #1: Rogers Avenue Junction is set up in a way that briefly forces the 2, 3, and 5 trains to share a short segment of track, limiting capacity. This can be resolved with new turnouts just east of the junction, pairing Nostrand Avenue Line with the local tracks and the West Side and the portion of the Eastern Parkway Line east of Nostrand with the express tracks and the Lexington Avenue Line. Trains on Eastern Parkway could either all go local, or keep the current mixture of local trains to New Lots (currently the 3) and express trains to Utica (currently the 4), skipping a total of two stations. This fix also reduces passengers’ access to one-seat rides, but at least there is a reasonable cross-platform transfer at Franklin Avenue, unlike on Queens Boulevard or at 145th Street and St. Nicholas.

And then there is #2, by far the most difficult fix. Demand on the White Plains Road branch in the Bronx is too strong to be a mere branch: the combined number of boardings at all stations is 166,000 per weekday, and besides, the line branches to Dyre Avenue near its outer end and thus needs the frequency of either a trunk or two branches to ensure adequate service to each other branch. This is why it gets both the 2 and 5 trains. There is unfortunately no infrastructure supporting a switch eliminating this track sharing: the 4 and 5 trains could both use this line, but then the 2 has no way of connecting to Jerome Avenue Line without new tunnels.

On the map, I propose the most obtrusive method of fixing this problem: cutting the 3 trains to a shuttle, with a new pocket track at 135th Street, letting passengers transfer to the 2, ideally cross-platform. With all through-trains running on the 2, there is no need (or space) for the 5 on White Plains Road, and instead the 5 should help boost the frequency on Jerome Avenue. In addition, some work is required at Woodlawn, which currently has bumper tracks, fine for a single branch but not for a non-branching trunk line (the bumper tracks on the L limit throughput to 26 tph no matter how good the electronics are).

Additional infrastructure suggested by deinterlining

Deinterlining is a service increase. Lines that today only get half or two-thirds service would get full trunk frequency: Second Avenue Subway would get the equivalent of the Q and N trains, the Astoria Line would get the entirety of 60th Street Tunnel’s capacity, Eighth Avenue would get more express trains, and 63rd Street Line and the South Brooklyn Line would get more than just the half-service of the F. With six track pairs on the lettered lines through Midtown and six north and east (Central Park West*2, Second Avenue, Astoria, Queens Boulevard*2), there is no room for natural branching to give more service to busy areas than to less busy ones.

One solution to this situation is targeted development on weak lines. Even with half service, South Brooklyn has underfull F trains, and Southern Brooklyn’s B, D, N, and Q trains aren’t much busier, making this entire area an attractive target for upzoning.

However, it’s more interesting to look at lines with extensions that suggest themselves. Second Avenue Subway has the obvious extension north to Harlem in phase 2, and a potential subsequent extension under 125th Street to Broadway, which is less obvious but popular among most area railfans (including one of my inside sources at NYCT). The Astoria Line has a natural extension to LaGuardia, ideally elevated over Ditmars to capture local ridership on Astoria as well as airport traffic; while the steel el structures in New York are soundboxes, it is possible to build quieter els using concrete (as on the 7 el over Queens Boulevard in Sunnyside) or a mixture of concrete columns and a steel structure (as on the Metro 2 and 6 els here in Paris).

The Nostrand Avenue Line provides an especially interesting example of a subway extension suggested by deinterlining. The terminal, Flatbush Avenue, was intended to be temporary, and as a result has limited turnback capacity. To prevent it from constraining the entire 2 route, which became the city’s most crowded even before Second Avenue Subway began decongesting the 4 and 5, it would be prudent to extend the line to Sheepshead Bay as the city intended when it planned the line in the 1910s.

In contrast, a subway extension under Utica, a stronger bus corridor than Nostrand with a strong outer anchor at Kings Plaza, loses value under deinterlining. It could only get a branch and thus have lower capacity than Nostrand. It would also definitely force branching on the express trains, whereas without such an extension they could run as a single unbranched line between Woodlawn and New Lots Avenue via Jerome Avenue, Lexington Avenue, and Eastern Parkway. A Utica subway should wait until there is political will to fund an entirely new crossing into Manhattan, presumably via Williamsburg to help decongest the L.

A second extension I have occasionally mooted, a subway under Northern, loses value even more. Such a subway would be a fourth trunk line in Queens and have to come at the expense of capacity on Queens Boulevard. It is only supportable if there is an entirely new tunnel to Midtown, passing under the mess that is the tracks in Long Island City.

A deinterlined New York City Subway

Fast Forward proposes moving block signaling on the most crowded subway segments, but typically only on trunks, not branches, and in some cases not even entire trunks. But in the long term, New York should transition to moving blocks and automation on all lines – at the very least the highly automated system used on the L, but ideally fully driverless operation, in recognition that wages are going up with economic growth but driver productivity isn’t. Simultaneously, deinterlined operations should allow tph counts in the mid 30s or even more (Metro 13 here runs 38 tph and Metro 14 runs 42).

Instead of the potpourri of lines offered today, there would be fewer, more intense lines. Nomenclature would presumably change to deal with the elimination of some services, clarifying the nature of the subway as a nine-line system in which five lines have four tracks and four lines have two. Each of these fourteen track pairs should be able to support a train every 90-105 seconds at the peak; not all lines have the demand for such frequency, and some have capacity-limiting bumper tracks that aren’t worth fixing (e.g. the 1 at Van Cortlandt Park), but many lines have the infrastructure and the demand for such capacity, including the express lines entering Midtown from Uptown or Queens.

Off-peak, too, service would improve. There is ample capacity outside rush hour, but turning the system into one of lines arriving every 4-5 minutes with strategic transfers rather than every 8-10 minutes would encourage people to take the trains more often. The trains would simultaneously be faster and more reliable, since incidents on one line would wreck service on other trains on the same line but leave the rest of the network unaffected.

With service improvements both during and outside rush hour, New York could expect to see substantial increases in ridership. Raising peak frequency from the current 24 tph to 36 tph on the busiest lines (today’s 2/3, 4/5, A/D, and E/F) is equivalent to building an entirely new four-track subway trunk line, and can be expected to produce similar benefits for passengers. The passups that have become all too familiar for riders on the 4, L, and other busy trains would become a thing of the past unless ridership rose 50% to match the increase in capacity.

Last week, I wrote about which regional rail lines should run local and express trains and which should only run locals. I gave various guidelines, specific to that mode of transportation. The same question makes a lot of sense for subways (or elevated lines), and is especially important for large cities building new metro networks, typically in developing countries. The key difference is that subway trains almost always run so frequently that the only way to have local and express services is to build four-track mainlines, like in New York. So really, this is a question about when it’s useful to build four-track subways instead of two-track subways.

Costs

The cost of a four-track subway is higher than that of a two-track subway. However, the difference depends on the method of construction. Cut-and-cover four-track subways do not appear to be much more expensive than two-track subways; in the 1900s, New York had little to no cost premium over London or Paris. The First Subway’s underground segments, slightly less than half of which are four-track, cost $39 million per km in today’s money, compared with about $29 million per km in Paris in the same era (see sources in this post). The Metropolitan line in London cost about the same: £1.3 million for 6 km in the early 1860s, or about $30 million per km.

In contrast, boring four tracks appears to cost twice as much as boring two. It’s hard to find examples, since four-track bores are extremely rare; the examples I do know, such as the East River Tunnels and the tunnel carrying the Lexington Avenue Line under the Harlem River, are short. There are bound to be efficiencies in engineering and sitework reducing the cost of boring, just as there are with cut-and-cover, but the majority of the cost of tunneling is the boring and the systems. The majority of the rest is stations, and the local stations can be built for not much of a premium over stations on a two-track line, but the express stations require considerably more excavation.

What this means is that cities that build cut-and-cover should probably aim to build four tracks rather than two. In retrospect, Paris should have built Metro Line 1 with four tracks: the narrowest street segment, Rue de Rivoli, runs for 3 km and is about 20-23 meters wide, which can take four tracks if there are only local platforms, and everything else is at least 30 meters and could take four tracks and express platforms. The only express station under Rivoli would probably be Chatelet, where there is a wide square where the station footprint could expand.

The question of whether to use cut-and-cover today is a separate issue. It’s easier for the first few lines than for subsequent lines, which have to cross under the old lines. Nonetheless, it’s still in use, for example in China; the lack of express tracks on Chinese subways has led to criticism on some railfan forums, particularly by Japanese railfans, who are used to the fast express trains of the JRs through urban areas. But in India, the longest underground segment in Delhi, on the Yellow Line, appears to be bored, running deep under Old Delhi. The one potential pitfall is that bored tunnels, while generally more expensive to construct than cut-and-cover tunnels if wide streets are available, are nimbler, making it easier to build lines to high standards, with wide curves.

Benefits

The two obvious benefits of express subways are speed and capacity. New York averages a decent speed, just under 30 km/h, buoyed by express trains that average about 36 km/h. When frequency on both the local and express tracks is adequate, which it regrettably isn’t most of the time in New York, it’s possible to use cross-platform local/express transfers to improve trip times even for people on the local stations.

The capacity benefits are sometimes compromised by transfers. In New York, the express tracks are consistently more crowded than the local tracks on the main lines, and the Upper West Side in particular sees the city’s most overcrowded trains on the express tracks run alongside the second least crowded on the local tracks. However, on the East Side, the local and express trains under Lexington are both quite full. The number of passengers they carry would overwhelm any two-track line: to carry the same number of passengers on just two tracks at the current peak frequency, each train would need about 2,100 passengers, more per unit of train floor area than the most crowded Tokyo Metro lines.

There are also indirect effect of four-tracking. The most distant stations are presumably express-only, or, if not, passengers will transfer to an express train at the first opportunity. This means that adding local stops does not increase trip times for passengers far out, which in turn argues in favor of tighter stop spacing on local trains, to provide more coverage. Evidently, New York has one of the smallest interstations (on local trains) of any major metro network in the world, surpassed only by Paris, which built the Metro without regard for the suburbs. Second Avenue Subway, built with just two tracks, has wider stop spacing than other Manhattan north-south mainlines, missing 79th Street, with the planned phase 2 stopping at 106th instead of 103rd and 110th.

Network effects

I have hammered repeatedly that metro systems need to avoid three pitfalls of network planning:

1. Tangential lines, starting as radial farther out but becoming circumferential closer in rather than staying radial and serving city center.
2. Reverse-branching: a common trunk in an outlying area splitting into branches in city center, the opposite of the more normal branching arrangement.
3. Missed connections, in which two lines intersect without a transfer.

It is easier to miss connections when the stop spacing is wider, because city centers are so small that line 1 can easily miss the road that line 6 will later run under. The Paris Metro has just one missed connection (M5/M14), and the city made a failed effort in the 1900s to bring Line 5 to what would be the transfer station, Gare de Lyon. New York has only two missed connections among the lines built from 1900 to the 1920s (Junius/Livonia on the 3/L, Bowling Green/Whitehall on the 4-5/RW), both of which are easy to fix; the city’s tens of misses come from a deliberate decision to avoid transfers in the lines built in the 1930s. Systems with wider stop spacing have more opportunities for missed connections, such as Tokyo, Shanghai, and Moscow.

Four-track mainlines short-circuit this problem doubly. First, fewer lines are required to provide the same coverage and capacity. On the eve of the Great Depression, New York had six subway mainlines, three with four tracks and three with two, and 2 billion annual riders. Even if a city insists that all transfer stations be express (which is the case in New York among lines built before the 1930s, though at one station express platforms were only retrofitted decades later), there are fewer potential intersections; at city center, even the express lines are unlikely to have very wide stop spacing.

Moreover, it’s fine to miss transfers on express lines. The reason missed connections are so bad is that the alternative option typically requires a three-seat ride. For example, the 1 passes between Columbus Circle-59th Street and 50th Street without a connection to the E train, leaving connecting passengers with one of two options: ride to Times Square and transfer there, which is both a detour and a very long walk between the platforms, or change to the B or D at 59th and then again to the E at 53rd; the latter option is the faster one, saving about 5 minutes of in-vehicle time and 3 minutes of transfer time.

But if one of the transfers is cross-platform, then a three-seat ride is less onerous. This is especially true if this transfer is local/express on a long shared trunk line, where the transfer stations usually don’t get as crowded as between two separate trunks. This means that it’s possible, if there is no better option, to have local-only transfers. Two of the top stations in New York, 53rd/Lex and Columbus Circle, are local-only transfers.

Scale

Small cities don’t need to think about express trains very much. Transit cities with about 2 million people in their metro areas, such as Vienna, Stockholm, Prague, Budapest, and Hamburg, make do with a handful of metro lines, sometimes supplemented by regional rail. But as they grow, the number of urban rail lines they need grows to the point that a coherent two-track network is too difficult, not to mention too slow. Paris manages to make do with the RER acting as the express layer, but outside India and Pakistan, cities that are just beginning to build their metro networks don’t have large legacy commuter rail networks to leverage for express service. In Africa between the Sahara and South Africa, nearly everything has to be built from scratch, and the same is true of Bangladesh and much of Southeast Asia and Latin America.

Moreover, in developing countries, a large number of cities either are megacities or can expect to grow to that size class soon. This is less true in Latin America, nearly all of which has at- or below-replacement birth rates, already high urbanization rates, and negative net migration (thus, the main case for four-track subways in Bogota hinges on the fact that the city has absurdly wide roads for cut-and-cover, not on future scale). However, in poor countries with high birth rates and low urbanization rates, cities can expect to increase their population many times over in the next few decades. Lagos and Dhaka are already huge, and midsize cities such as Nairobi, Kampala, Dar es Salaam, Addis Ababa, Khartoum, Accra, Abidjan, Douala, and Sanaa can expect to grow to that size class within a generation, as can midsize cities in countries with lower birth rates, such as Chittagong, Hanoi, and Ho Chi Minh City. In such cities, transportation planning should presume much greater scale than may seem warranted today.

A smaller-scale version of this principle can be found in cities that are growing rapidly due to immigration, especially Singapore but also Sydney, Melbourne, Toronto, Vancouver, and Stockholm. Such cities might want to consider infrastructure investments based not on their present-day population levels, but on those that they can expect after 30 more years of high migration rates. Vancouver and Stockholm are too small for express subways no matter what, and Toronto has already built its central spines with two tracks (and is upgrading its regional rail network to act as an express layer), but Singapore, Sydney, and Melbourne should all think about how to plan for the possibility that they will have 10 million people within 50 years.