New York’s Subway Frequency Guidelines are the Wrong Approach

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


  1. sajohnston

    The problem for the 1 is that it has segments where additional frequency would be quite welcome, and segments where the trains typically operate well under capacity. If there were capacity to short-turn trains and run a supplementary local service just between 34th St. and, say, 137th (since there’s a yard there), that might be highly useful in relieving consistent, all-hours crowding on the 1…but the trains always seemed to me to totally empty out south of 34th, so doubling frequency along the full line would be quite a waste.

    • Ed

      You are probably thinking about the stretch between 96th Street and Inwood. However, the 1 makes a lot of stops on that stretch, covering a lengthy piece of territory. Over-frequent trains will to some extent compensate for it being a slow line due to all the stops and the lack of any express or skip-stop line covering the route.

      • Alon Levy

        The 1 is actually pretty fast north of 116th, when stop spacing widens a bit. It’s not express or anything, but between the stop spacing and the not too high crowding levels, it averages 30 km/h. (Okay, to be fair, that’s the subway’s average speed, but that includes express trains.)

  2. Syd Chan

    Do you have any time-distance diagrams for each track segment and each line where it share track with other services? These diagrams show how each line interlace with the other lines that share its track, and where trains stop “due to train traffic ahead” while they wait for the slot to open up on the other line (for instance, where the northbound Q train always stops “for train traffic ahead” north of DeKalb St. while it waits for slots between successive N trains).

    Time-space diagrams are also fairly easy to reverse-engineer from the published timetables, given certain parameters such as standard dwell times at stations, and certain reasonable guesstimates like mileposts.

    • Alon Levy

      I don’t. I looked at the published timetables to find more accurate tph counts, but the timetables aren’t very clear on this, especially off-peak: they say things like “then every 7-8 minutes until:” for multi-hour blocks each day.

  3. Aubrey

    In Toyko, the subways have a schedule. The trains follow that schedule. There is no random pile up of trains waiting for their turn, even when tracks are shared. It’s the same every day.

    • michael.r.james

      And if there was one Metro system where one might expect some troubles with sticking to schedules it would be Tokyo (though I suppose Beijing must be the same these days)–ie with grotesquely overloaded peak hours where assistants have to squeeze pax onto trains so the doors can close.
      The Paris Metro & RER also has a formal timetable though no one really bothers looking at them.

      I note that London U suffers the same issues as NYC. Sydney too. Is it some weird Anglosphere thing? Or is it because they have been very slow at giving each line its own ROW? Massive and expensive work is finally getting done to disentangle this problem in Sydney but perhaps it is impossible for the busiest lines in London (where the Circle, Central and District lines share ROW at points and cross-over at others; don’t hold me to detail, this is by memory).

      • Alon Levy

        In London, the deep-level lines at least don’t share tracks. They all branch, but the only one that reverse-branches is the Northern line. The subsurface lines are a shitshow, though.

        In graph theory terms, we can draw a graph on the set of routes of each subway system, in which two routes are connected if they share tracks in normal daytime revenue service. In London, the four subsurface lines are connected, but each deep-level line is an isolated vertex, without connections to other vertices. So we get 8 connected components in the graph. In New York, we get 6 components: 1, 6, 7, L, 2/3/4/5, and all the rest. In Paris, each Metro line is isolated, while the RER has four components (A, B/D, C, E). While 6 is not much less than 8, New York has more track-length, the majority of which is in just one component, whereas in London the components are more balanced, and don’t have as much reverse-branching.

        • michael.r.james

          Right. My abiding memory of using the London U is getting on the train and ….waiting …. and waiting. Even with doors closed and I am pretty sure this will be those surface lines you mentioned (Circle, District, Central & maybe Metropolitan; I don’t have a map in front of me). There are some perfectly good lines in London (Jubillee, Victoria etc) but when moving around the centre you almost always have to use these old lines & connections.)
          Now, I acknowledge that they have the “excuse” of a legacy system formed by the public takeover and merger of pre-existing private systems. (CrossRail will be a revelation to most Londoners.) Paris had the benefit of being a single public system that could plan it correctly. I am sure none of that nonsense occurs in Beijing, Shanghai, Seoul etc. Right?

          Aside: last night watched a tv retrospective on journalist Stephen McDonell’s ten years in Beijing as (Australian) ABC’s China correspondent. When he arrived in Beijing in 2006 there were 2.5 Metro lines and today there are 18. This seems almost science fantasy to us westerners today but in fact most of the Paris Metro was also built in a frantic ten years.

          • Fbfree

            Central is a deep tube line. The subsurface lines are the Circle, Hammersmith&City, Metropolitan, and District.

          • Eric

            It’s reported that when London subsurface moves to CBTC the scheduling will become a lot more reliable.

            Even NYC’s system was nearly all opened between 1900 and 1940. Not as fast as Paris or Beijing, but super fast compared to what happened since 1940.

        • Nathanael

          Slight oversimplification of London service. The Piccadilly line is tied into both the District and Metropolitan lines, and both the District and Metropolitan lines are tied into the *mainline railways*. And of course the two trunks of the Northern Line are tied to two branches.

          Apparently one way London keeps things moving on schedule is that the District and Metropolitan lines are “primary”. If anything goes wrong, the Circle Line or Hammersmith & City Line trains get truncated or cancelled. This segregates the District Line operations from the Metropolitan Line operations to some extent. Likewise, if anything goes wrong in its area, the Uxbridge branch of the Piccadilly line is the first to go, which disentangles it from both the District and the Metropolitan lines.

      • Andrew in Ezo

        There are delays on the various Tokyo Metro lines, some more frequent than others. For example, the Hanzomon Line has delays of some duration or another *daily* during the AM rush, with a delay of greater than 10 minutes occuring on average 1.7 days out of a five day work week. These are mainly a result of run-through operations to private railways or JR East and the high frequency of knock-on delays which arise in such arrangements. On the other hand, “closed” lines (i.e. no interlining) such as the 1435mm gauge third rail Ginza Line have very few schedule disruptions, with few to no delays greater than 10 minutes in duration during the average work week.

        Click to access 001081639.pdf

        *It’s interesting to see that the private railway operator Keikyu, which has extensive interlining arrangements with both Toei (Tokyo Municipal Subway) and Keisei Rlwy, has a record of delays of greater than 10 minutes averaging only 0.2 days out of a 5 day workweek, which is tops in the Kanto Region. Speaks of their excellent traffic control management, which in fact won them a special award from the MLIT this October.

        • michael.r.james

          By Keikyu I assume you mean the Keihin set of 5 lines. It has 1.2m pax pa which is 3.2% of the total of Tokyo (all rail except Shinkansen). And a fraction of the government indirectly-owned (Tokyo Metro & Toei Subway) or formerly-owned (JR East) of 24m and 64.6% of the total. Keikyu may be good but not exactly a fair comparison?

          Yes, as you say, it is the interlining that inevitably causes delays in a system.

          • Andrew in Ezo

            I don’t understand what you mean by “fair”. Yes, Keikyu is only a small part of the total metropolitan transport network (the largest in the world), but what it does, it does well and it provides critical transport between the two major cities in the region as well as the biggest domestic/international airport. There is nothing to keep it from being used as a benchmark for other systems, if not for a whole network, then for certain lines/operating districts facing similar challenges. It was deemed worthy of study by SBB officials on a visit several years ago, apparently.

          • michael.r.james

            Andrew in Ezo (2015/12/16 – 00:51)

            I don’t understand what you mean by “fair”.

            I believe the likelihood of running a complex network without problems will scale to the inverse of the size. Even without interlining there are difficult to control interruptions: apparently suicides on the line is really the driving reason behind the bigger and busiest lines getting the aligned platform doors. I can’t remember stats but a doco I saw on the Tokyo Metro talked about a rather shocking level of suicide-by-train. It also causes driver shortages as many drivers involved (they get a front-row seat to these incidents) take sick-leave or never return.

            Also, I would think the most important factors in trains running on time and interlining smoothly is all down to signalling and computer control. The bigger the system the more expensive and complicated it is to upgrade these things.

            Keikyu may well be very good but is there any confidence it could scale to something ten times the size (and more in complexity)?

      • Max Wyss

        In Paris, the Métro frequency is sufficiently high that it is not necessary to look at schedules. But for the RER (unless you are just transferring within the city core), you better do, because of the excessive branching (just have a look at the RER C, for example).

        • michael.r.james

          Of course you are correct. Mine was the blinkered view of a Parisian who rarely ventured into the banlieu! Beyond the point I couldn’t use my Zone 1-2 Carte Orange and actually have to pay, horreur! The northern section of the RER-B is also simplicity, direct to CDG airport without branching and no real need to look at the timetables. Though I had to use RER-D4 a bit to reach Evry where new labs were built to house an overflow part of the Human Genome Project in the early 90s that couldn’t squeeze into our central Paris building; eventually the local RER station took its name from this (onetime famous) lab/concept: La Bras de Fer-Evry Genopole. Possibly the only train station in the world named after a genetics lab complex? And it was tricky because you had to remember to take the train that took the southern anabranch. (A part of the giant SNECMA aero-engine factory was converted to ultramodern genome lab and played a role in nurturing a completely different new industry.)

          • michael.r.james

            Alon Levy (2015/12/20 – 08:11)

            The RER B has two northern branches, no?

            Yes. Typically the moment I read the freshly posted words I thought, hmm no maybe not? I have tried to remember if the branch (B5, which is being extended further into the suburbs) happened during/after my Paris sojourn but my memory is not up to it. It was possibly always there. (I do remember that the extension of line B under the Seine–to connect the northern and southern sections–happened in my second year in Paris, 1985 I think.) Of course soon-ish there will be a dedicated airport RER with its exclusive unshared track, CDG-Express (not clear if it is due to open next year or 2023?). But it terminates at Gare de l’Est so in some ways not as convenient as the old service; it will solve the slowness and overloading of the current service but it won’t really be any faster since you’ll have to factor in a transfer (B has 7 stations within Paris so a lot of people would have been within walking distance as indeed I was in all three main places I lived).

          • michael.r.james

            Yikes, here’s the kicker (kick in the head):

            A one-way ticket on the CDG Express is projected to cost €24, compared with under €10 for the suburban train.

            That is quite expensive and hardly worth a marginally shorter trip that dumps you at Gare de l’Est. They are also putting a €1 levy on all pax flying into the airport. I guess all this is designed to cope with the €1.7 bn cost of the project.
            I reckon they could have solved the various problems by discontinuing the B3 line going all the way into Paris and simply terminating at Aulnay-sous-Bois and make everyone transfer (which could/should be same-platform). This would have been essentially cost-free but would have removed their problems with the main suburban line B (B5). This may not look or sound as good as “Express to Paris” but when that express terminates at Gare de l’Est forcing you to transfer anyway (in one of the less salubrious and crowded interchange stations—as I recall, one problem of “correspondance” at Nord/l’Est is that steps are almost always involved) …
            And I just realized, between Aulnay-sous-Bois and the airport are three suburban stations, so presumably they are still running regular B3 trains to service these and this means they have retained this problem (hard to believe and maybe the “express” is not quite correct?)

          • Eric

            It strikes me they could have solved the problem much more nicely by building a spur of the RER D to CDG.

          • michael.r.james

            Eric (2015/12/21 – 04:47)

            It strikes me they could have solved the problem much more nicely by building a spur of the RER D to CDG.

            The basic problem is similar to the big city airports everywhere. JFK’s A-line, Heathrow’s Piccadilly line, and Paris CDG. City Metro systems being stretched to do double service to what is another mini-city, the airport with ten million rail pax p.a. When HK built the links to HKI it did it the right way: four tracks so that the “domestic” traffic line (to Tung Chung) is totally separate to the Airport Express even though they terminate within half a km of each other. The HKI Airport line now carries 10m pax pa. and gets them from go to wo in about 20 mins.
            The Paris RER-B (B3) carries about 8m pax to the airport but obviously continues to grow and it carries suburban commuters and is interlined (and serves Gare du Nord which makes sense but that is the busiest train station in Europe with >100m mainline + Eurostar pax so I guess this takes some pressure off the station (though you’ll still be able to correspond thru that rabbit’s warren of pedestrian tunnels). RER-D is already carrying 145m pax and there would be more stations en route to CDG than line B3; it is also a huge line, 190km actually reaching beyond Ile de France both to the north and the south. So I guess one understands why they are biting the bullet and separating airport traffic out from commuter lines like NYC, London and HK have done.
            This logic, which is impeccable really, is why my whinge about the new CDG-Express terminating at Gare de l’Est is, I suppose, wrong. (I still like my idea of changing at Aulnay-sous-Bois because I would rather do it there than at Gare de l’Est but I suppose most pax would prefer “express”.) Obviously running it on to Chatelet would be hyper-expensive (new tunnels) as it is already busier than one wants to think about.

          • Alon Levy

            Why would any city bother to separate a line that gets just 10 million passengers per year? That’s 33,000 per weekday, usually without much of a rush hour peak. The RER A has a million passengers per weekday, with a pronounced westbound morning peak.

  4. Eric

    “The peak crowding on all lines in New York, with the exception of the non-branched 7 and 1, occurs in the Manhattan core”

    Do you mean 7 and L?

    • Alon Levy

      No, I mean 7 and 1. Peak crowding on the westbound 7 is in Queens, just before the transfer points to the E/F and to the N/Q; peak crowding on the southbound 1 is in Uptown Manhattan, just before the transfer point to the 2/3.

      • EJ

        So by “non-branched” you mean the portion of the 1 where it’s not interlined? I was confused by that too.

        • Alon Levy

          No, I mean the 1 does not share tracks with any other service except late at night and during service changes. It shares route, but it has dedicated local tracks.

          • EJ

            Ah, got it. It’s been so long since I’ve been on that line I forgot it doesn’t actually share track with the 2 & 3.

  5. Adirondacker12800

    maintain the current scheduling system just because it’s how things have always worked.

    They went and built the IRT south of what is now Times Square and north of Grand Central. I’m sure there were some service changes when they did that. Afterwards the Broadway/7th Ave local ran to Harlem and the express ran to Van Cortlandt Park. Some trains would terminate at 137th. South Ferry was built for what are now the Lexington Ave trains.
    The BRT and later the BMT used numbers as train designators. They ran all sorts of local and express service. To places that got abandoned and torn down. Then the city went and built the Chrystie Street connection. All sorts of experiments have ensued. Lets not forget the rehab of the WIlliamsburg Bridge.
    …. the QT ran via the tunnel, hence T. The QB ran via the bridge hence the B… It wasn’t very long ago that the started using 9 as a train designator on the West Side….
    Eventually locals on the IND and BMT were “double” something or other. The expresses were single letters. And the rush hour services had things like QB.

    …. an example.

    • Nathanael

      Back in the old days, they were much more willing to change things than they are now. The IRT *de-interlined* their system when they built south of Times Square and north of Grand Central, *eliminating one-seat rides* and forcing people to make *three seat rides* (using the Shuttle) instead of their previous one-seat rides.

      Today’s management seems incapable of conceiving of such things.

      • Adirondacker12800

        …Like sending the M to midtown instead of downtown? Canceling the V?

        • Nathanael

          Pretty small changes compared to the “H plan”.

          Frankly I blame mayor Hylan and the IND. Both the IRT and the BMT were pretty coherently designed systems with sound operating plans. The IND wasn’t; it was designed to run the IRT and BMT out of business. And it’s the IND with the most problematic branching patterns.

          • Jet Dawg

            Well there’s also the fact that the IND was never really completed, as the infamous Second System plan was never completed. In my experience the IRT lines are much more popular than the IND in Manhattan as they run more frequently and predictably while passing through more sensible locations. Only the IRT serves Grand Central and the Broadway and Lexington Avenue are located roughly in the center of the upper east and west sides, while the 8th Avenue Line is fairly useless north of 59th Street. It boggles me that the West Side gets 8 tracks while the doubly sized East Side gets 4 (soon 6) tracks.

  6. Fbfree

    It is possible, with some compromises, to obtain a nearly complete removal of reverse branching and poor interlining for the NYC subway. I spent a weekend working it out about a year ago, checking that existing frequencies could be approximately maintained while ensuring that enough existing rolling stock existed. I made the plan into a spreadsheet now available here. This is a very major change to existing routes and felt a bit to crayonista for me to make a post about. I’ve only included the B division lines, and I’m mostly ignoring the BMT Eastern Division (L/J/Z).

    On the plus side, the only reverse branching remaining is with the F and the G, with interlining on both the Culver and QB local tracks. Both services would run with multiples of 7tph. The Queens cross-town runs about 6 minutes faster than the 6th Ave local, so a G should be able to slip into the slot ahead of the F in front of it on each run with about 90 seconds to spare. All other reverse branching is eliminated, and schedules are set to keep line branching at multiples of each other’s frequencies.

    There are some well and not so well discussed sacrifices to be made and difficulties with such an overhaul:
    Well discussed problems:
    1) The 59th/Lex transfer would need to be cutoff from Queens Blvd. This is partly compensated for by the opening of SAS. The QB lines would also be cutoff from Astoria and capacity would be slightly reduced between the QB locals and Manhattan.
    2) Many more cross-platform transfers would be required.
    3) No significant yard would serve the Astoria/4th Ave local service.
    Not so well discussed problems:
    a) The new H (combination of A in Brooklyn/Queens, F in Queens) would be an extremely long route, at a 105 minutes run time.
    b) Running all CPW expresses down 6th Ave. leaves an excess number of trains on the express tracks towards Brooklyn. While the 2nd Ave turnback tracks and the Crystie St. connection can take some load, they connect to the local tracks. Crossing the F on the level would be required.
    c) Currently unused turnback capacity on the 8th Ave express might not be suitable for regular use.
    d) Canal St (Bway) customers going to the Brighton line would have to take the Q local, or walk to a 6th Ave express station.

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  8. Henry

    The issue with unfurling the reverse branch situation on the B-Division in Queens is that it doesn’t actually provide more capacity on QBL. It might provide more capacity utilization by replacing the R with a 8th Av local, but there is no net increase in capacity, which is bad considering the line is probably the second most congested trunk in the system during the peak hour. On top of that, the unfurling completely gets rid of one of the few remaining possible capacity outlets available to the QBL; the provisioning still exists to build the Queens Blvd Bypass and link 63 St to Forest Hills and provide additional capacity in the east, or relieve Flushing by linking the PW line to 63 St and taking it over for subway operations, or what have you.

    Really, long-term the set of tracks under 60th St should be quadrupled, with an “express” tunnel making a single stop at Lexington/59 before linking to both Astoria and QBL local, the way the 63 tunnel links to both QBL local and QBL express.

    • Alon Levy

      There are three lettered track pairs in Queens: Astoria, QB local, QB express. There are three tunnels to Manhattan: 53rd, 60th, 63rd. The reverse branching problem is that only 2.5 of the tunnels are used – 63rd is underutilized because of issues like “the transfers to other lines in Midtown suck” and “the QB lines go to all three tunnels.” Adding a fourth tunnel isn’t going to change this; a new trunk line in Queens would be needed.

      • al

        More like 2.1. The max combined AM E and M frequency through 53rd St tunnel is 22 tph. The 60th st tunnel runs 26 tph. There is 14 or 15 tph through the 63rd St tunnel

      • Henry

        A new trunk line is needed, either in the shape of a Queens Blvd Bypass, or something else. However, the most recent plans for it circa the ’80s would’ve used the half-capacity 63 St tunnel to provide additional service. If you use up that remaining capacity, then a new tunnel under the East River has to be built to provide this extra service.

        (There are actually four track pairs if you include the Crosstown, but the Crosstown will always be the red-headed stepchild of the IND and MTA.)

        • Alon Levy

          Yes. It’s just, the QB bypass is kind of a terrible idea – it takes LIRR slots and makes the excessive interlining problem even worse than it already is, while putting trains on a line that’s exactly parallel to QB. Not terribly useful. If the point is to use the LIRR as a QB relief line, just use the LIRR, with fare integration and reasonable off-peak frequency at Forest Hills and Kew Gardens. If the point is to add more service in Queens, put it in an area without existing subway service, and then, Northern is the best corridor, taking pressure off both QB and the 7.

          Another possibility, in parallel with Northern: if the 11th Street Connection is severed, then it’s useful to extend the Astoria Line east, either along Astoria or to LGA, just to let more people take it rather than the 7.

          • Adirondacker12800

            The LIRR doesn’t go to Rockefeller Center, Times Square, 14th Street or Wall Street.

          • Eric

            Those who want to go to those places can continue to take the Queens Blvd line. Those who want to go elsewhere, which is a lot of people, can take the LIRR.

          • Joey

            The LIRR doesn’t go to Rockefeller Center, Times Square, 14th Street or Wall Street.

            It might be time to look at long-term plans to remedy that.

          • Adirondacker12800

            One of the 137 alternative examined for ARC was to go to Grand Central and continue to Rockefeller Center. it didn’t make sense because people use the fastest method. Which is to get off the train in Penn Station and take the subway.

            It gets rather pricey


            I suspect that Wall Street is a bigger destination than Rockefeller Center or Union Square etc. It’d probably make the most sense to consider that first. Especially since there is existing underutilized ROW relatively close.

          • Eric

            “they can today and they don’t.”

            Because LIRR costs much more than the subway. That should change.

          • Adirondacker12800

            the people in Forest Hills can afford it. They don’t use it.

          • Henry

            @Joey: Even if we were to have regional rail tomorrow, the fact is that regional rail can’t really have more than one or two stops going crosstown due to how narrow the island is; a 34 St East Side station was considered as an East Side Access alternative, but dismissed because it was impractical. Unless regional rail goes north-south from Midtown to Downtown, the subway will always be needed to distribute people. In cases where people must take the subway to the LIRR to the subway, or bus to the LIRR to the subway, the additional transferring may make the LIRR more unappealing than the subway.

            @Alon: The best corridor for another subway line to Flushing is actually the PW corridor. The PW corridor west of Flushing is well suited for two or three stops serving Elmhurst and Corona, the area is underserved because trains don’t actually stop between Citi Field and Woodside, the trains are already crowded coming from the east and could benefit from subway levels of pricing and frequency, and in any case the bus ridership on the parallel Q58 is significantly better than on the Q66. If you can link the PW pair of tracks to the upper level of 63 St, you’ve just provided a brand new, up to 15TPH service to Great Neck and beyond while also relieving the 7 without using Main Line capacity.

          • Alon Levy

            There are three problems with using the PW Branch as a subway branch:

            1. Unless you’re completely severing the branch from the LIRR, you’re introducing even more schedule dependency into the system, this time between the subway and mainline rail. The PW Branch is already fragile because of single-tracking east of Great Neck.

            2. There’s considerable demand north of the 7, not just south of it. East Elmhurst is a dense neighborhood, with about 25,000 people per km^2.

            3. The PW Branch is needed to feed the East River Tunnels. After ESA opens, there are going to be eight mainline tracks (NEC, PW, Main Line*2) feeding Manhattan from points east, and six tunnel tracks into Manhattan (ESA, East River Tunnels*2). But the NEC tracks can’t be used at high capacity, because they host mainline trains at what is supposed to be high speed, and trying to run more than about 6 regional tph on them leads to timetable nightmares. This means that if PW doesn’t feed the mainline tunnels into Manhattan, there is going to be less capacity in Queens and the Bronx than in the tunnels to Manhattan, which is the ur-problem of reverse branching.

          • Henry

            1. Completely severing it sounds like a great idea, especially because it solves the issue of mixing compliant and non-compliant FRA stock. To be fairly honest, the single track east of Great Neck isn’t particularly useful anyways.

            2. Okay, but that doesn’t change the fact that the PW corridor is easier to serve. With a Northern Blvd line, you presumably need to dig up all of Northern Blvd at least to Flushing, and if the 63 St upper level is being used to de-interline the Queens Blvd Line, a new pair of East River Tunnels connecting to something in Manhattan. The PW corridor is in good shape, already has platforms long enough (with the exception of Murray Hill), and can use a rail connection being built as part of ESA between 63 St Upper Level and Sunnyside Yard, so in 2077 or whenever Phase III of SAS actually opens, you could have direct service from Great Neck to the LES.

            3. If you need more than 6TPH on the NEC, most, if not all of the NEC corridor from the Hell Gate and points north looks like it can accommodate four tracks; you can see the pair of tracks currently in service and a cleared right of way with some old rails in it next to it. There are also 8 tunnels now, but at some point a pair of East River Tunnels is going to have to be shut down for post-Sandy work that never happened, and it’ll be fine. Besides, the LIRR has had these mismatches in the past; there were six tracks going into Jamaica and eight tracks going out of it when the Lower Montauk still saw passenger service.

          • Alon Levy

            2. East of the point of realignment (around where I think Sunnyside Junction should go), it’s a few km of tunnel to Willets Point. In Willets Point itself, tracks could go above ground – Willets Point is much lower than both Flushing and East Elmhurst, and there are no residents (read: NIMBYs) who’d complain. The main view is toward the Mets’ home pitch and not toward anything that the train could block. The ultimate destination is the LIRR Broadway station, but that can come later.

            Yes, this involves spending money on tunnels. Realigning 63rd Street to the LIRR tracks involves spending money, too. Hell, getting NEC traffic to fill a tunnel involves spending way more money than would be spent on Northern.

            3. It’s not about two vs. four tracks – or, rather, not about two vs. four tracks south of New Rochelle. Even with four tracks, there is too much schedule dependency between intercity and commuter trains, because of the need for express commuter trains. The New Haven Line could go all-local, but there’s enough demand from far out that it’s not a good approach. The idea is as follows: with so much schedule dependency, trains of all three classes (local, express, intercity) have to have the same frequency, or multiples of the same frequency, for example multiples of 6 tph; then, the track sharing on Hell Gate and the southern approach to it makes it difficult to run 12 local commuter tph, and even 8 tph is hard. It’s easy enough to have 6 tph local and 6 tph express, or 12 tph intercity, because nonstop trains don’t have to be sequenced regularly; but then, if the trains aren’t serving the Bronx stations, what’s the point of running them through Sunnyside rather than through the Harlem Line and Grand Central?

            Grand Central is currently fed by six tracks merging into four: two Hudson, and four Harlem + New Haven. But the Hudson Line is needed for its own Penn Station access project, which means it can’t realistically feed much traffic into the tunnel. The Harlem Line can easily fill two tracks, but then the New Haven Line has to feed a very large amount of traffic into Grand Central to make use of the infrastructure, on the order of 16+ tph. This means that if the Hell Gate tracks could accommodate 20-24 tph, by sending express commuter trains on them, either the Park Avenue Tunnel would have too little service, or there would be too much service on the New Haven Line. (16 + 20 = 36, which you can do on four tracks if there is no variation in stopping patterns at all, i.e. only local and intercity trains.) Anything below 20 leaves room that only PW trains can fill.

          • Henry

            If you look at page 2-20 of the ESA EIS, East Side Access included a tunnel from 63 St upper.

            As far as I know, the Hudson Line has been quietly dropped from Penn Station Access plans, since it’s been a while since anything regarding the fate of that part of the project has come out. Even then, wouldn’t capacity be limited by the fact that there’s a significant single-track stretch on the approach to Penn Station?

          • Alon Levy

            There’s room for two tracks without extra civil infrastructure, except on Spuyten Duyvil Bridge, and my understanding is that it, too, was designed for future double-tracking.

          • Adirondacker12800

            The point of Penn Station Access for Metro North is to divert as many people as they can out of the Park Avenue Tunnels. Side benefit is that it gets people out of the Grand Central subway station too.

          • Joey

            Henry may be right about the Penn station approach: all the diagrams I’ve seen show it as only one track wide. The rest is definitely wide enough for two tracks, including the Spuyten Duyvil Bridge.

        • johndmuller

          As far as I know, the Hudson Line has been quietly dropped from Penn Station Access plans,

          I hope that this isn’t true, but when Cuomo hyped the Bronx stations without even mentioning the Manhattan counterparts, it made me wonder.

          Right now, it is sometimes possible to go between MN stations on the Hudson line and Penn, transferring at Yonkers or Croton, but the Amtrak fare is much higher than the MN fare would be and you pay the MN fare in addition to the Amtrak fare. Furthermore, somewhere around a third to a half of the Amtrak trains bypass Yonkers, the obvious transfer point, particularly during rush hours (probably to thwart commuters wanting to do just that).

          It’s true that there is no great difficulty getting from GCT to Penn or taking the subway to Penn from Marble Hill, but one of the main reasons for wanting to go to Penn in the first place would be to take an Amtrak train from Penn, in which case you might want to have a more dependable trip and/or a more luggage friendly one. Besides, going to Penn is not the only point of PSA, one might also imagine other possibilities including one seat rides to Jamaica or Citi Field, or even Montauk and the Hamptons.

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  10. metaphorical

    “The people in Forest Hills can afford it. They don’t use it.”

    I’m one of those people in Forest Hills, and I guess I can afford it, but (a) There’s no integrated pass for the LIRR and my regular MetroCard (compare the Express Bus weekly pass, which includes regular MetroCard usage). So it really does get pricy. (b) The transfer between the subway and the LIRR at Penn Sta is far more inconvenient than transferring between two subway lines. (It’s also surprisingly hard to know which train is going to FH next, a problem that could easily be solved but hasn’t been for, well, forever.) (c) Penn Sta isn’t always convenient to people going to FH.

    To use the 63 St tunnel more, Q trains could stay on 6th Ave instead of Broadway, as it used to, and the R could go to Astoria instead of Forest Hills, as it used to. It would have to skip the local stops between QP and Roosevelt, so M service would need to increase to accommodate the local stops between QP and Roosevelt.

    Another Queens issue: If the 7 express could stop at Roosevelt Ave, ridership patterns throughout Queens would change significantly (e.g., getting from east side locations like Union Sq to Jackson Heights and Forest Hills).

  11. Eliyahu Neiman

    Is it not practical to run shorter trains more frequently for less crowded routes and/or times? Another way to look at this is that cars/train * trains/minute = cars/minute. You can increase TPM and decrease CPT while keeping capacity (CPM) constant.

    • Adirondacker12800

      It cost money to break trains apart and put them back together again. And it introduces reliability problems. Not that individual cars can easily be taken off or added these days.

  12. former New Yorker

    former New York City resident. over age 51+- 5 quasi. Learned to ride bicycle at city and mostly survived.

    1.) Engineering , unlike pure math is about practical and iterations, heuristics, so one semi-conlusion with no
    3.)my solutions are NOT advice, other legal disclaimers and what works for me a long time ago may laikely not work for you.
    4.) Get to work in the morning on time or get fired. so worst case analysis is required. not median ONE sigma.
    5.) ride bicycle through HARLEM, keep alert for gunshots. Always take the A train. the 1,2,3 (yes Columbia U alumni
    know this secret!) the tunnels tend to flood.
    6.) I skip the three horrow stories for cocktail parties.
    7.)the bicycle system may naot work presently, amazingly despite riding throught the parks (DANGER!) and
    on the sidewalks, never got a big ticket.
    8.)Take the METRO NORTH LINE at 125th street. This strategy is superior sincea since it avoid the cross town
    midtown congestion vortex.
    9.)the key advantage is that you have a private seat. You eat breakfast. You sleep and snore. Activities that are not
    possible on NYC subways.
    10.)no politics expertise claimed. YMMV. In the USSR, higher variation of ‘dominant politicians’ than NYC coulld be
    a cause of dysfunction.a
    11.)the NJ Governor Chris Christie Bridgegate scandal could be a pattern found in the NYC, World Leading City
    Transport Situation.
    12.)similar meta-patterns include the MIT – NEW APPROACH to avoiding parking the airplane on
    the tarmac. Simple case of no hire Mathematican. No hire Operations Research. No hire engineers with
    ‘common sense’??

    14.) simple solutions like. a:) cell phone reservations. Sure, maybe 20% are liars, however the system works for
    the ‘airline transports’?
    15.) ahhhh. alas I must say. WARNING DANGER. the most dangerous time and station is Rockefeller Center D line.
    16.)Answer. it’s 14:55 or 5 minutes to 3pm. SUDDENLY the station is full of young kids. One victem (which I saw)
    had ahis glasses shattered and bleeding from a ‘bbrick’. Obvioiusly, it wold be dificult to pick out 2 bad criminals
    (who were not deterred by juvenile detention) out of the HUNDREDS.
    17.)My strategy is simple. Big crowd of “slighty angry people’? AVOID. Avoid the 3pm school going home crowds.
    Avoid the uptown lines going to the South Bronx or ‘the known ‘bad areas’ in Brooklyn, etc.
    Alas, I must add, I am a minaority…. born in USA, so
    18.)this is the difference of New York City versus other great cities of the world.

    22.) the Airline inudstry has statistics. There is airline tracking on the ianterest. Hacker News shows a NY Times
    reporter who uses i airplane SDR – software defined radio..

    23.)Like the PLANES PARKED ON THE TARMAC (4 hours of heat exhaustion?) there shlould NEVER be any
    trained backup in the tunnels!

    24.) One of the hundredd possible simple solutionss. I am not a mathematician, I just read a bit about Polya…
    Some Cars are STANDING ROOM ONLY. Tjese cars are closest to the exits.

    25.)the DATA should be available so UNCERTAINTY is reduced and a reasonable calculation of odds,
    after all most people are optimistic; craetures of habit, doing the similar ‘dumb’ things over and overiii

    26>) summary. multi-modal transpoort via bicycle, even electric vehiclie shuttle BETWEEN hub stations.
    or better East West or crosstown integration to the GRAPH NETWORK can be considered.

    11b.) the laternative to the 125th st station of Metro North is the black car or radio dispatch.
    I called the mostly Hispanic services, other ethnics at random and simply held up CASH in HAND
    while ona the street. Fortunately no yellow cab, ina the days of pre-Uber complained.

    PS. Humor. It is fun to imagine Superman as I change into a business suit in the washroom of the
    Metro North to Grand Central.

    Thanks for a fine article. Mathematical ‘fairness’ and probable median worst case calcs have not been done.

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