Density and Subway Stop Spacing

Normally, the best interstation distance between subway or bus stops does not depend on population density. To resurrect past models, higher overall density means that there are more people near a potential transit stop, but also that there are more people on the train going through it, so overall it doesn’t influence the decision of whether the stop should be included or deleted. Relative density matters, i.e. there should be more stops in areas that along a line have higher density, for example city centers with high commercial density, but absolute density does not. However, there is one exception to the rule that absolute density does not matter, coming from line spacing and transfer placement. This can potentially help explain why Paris has such tight stop spacing on the Métro and why New York has such tight stop spacing on the local subway lines.

Stop spacing and line spacing

The spacing between transit stops interacts with that between transit lines. The reason is that public transportation works as a combined network, which requires every intersection between two lines to have a transfer. This isn’t always achieved in practice, though Paris has just one missed connection on the Métro (not the RER), M5/M14 near Bastille; New York has dozens, possibly as many as all other cities combined, but the lines built before 1930 only have one or two, the 3/L in East New York and maybe the 1/4-5 around South Ferry.

The upshot is that the optimal stop spacing depends on the line spacing. If the line spacing is tight – say this is Midtown Manhattan and there is a subway line underneath Lex/Park, Broadway, 6th, 7th, and 8th – then crossing lines have to have tight stop spacing in order to connect to all of these parallel lines. In the other direction, there were important streetcars on so many important cross-streets that it was desirable to intersect most or ideally all of them with transfers. With so many streetcar lines extending well past Midtown, it is not too surprising that there had to be frequent subway stops.

So why would denser cities have tighter line spacing?

Line spacing and density

The intuitive relationship between line spacing and density is that denser cities need more capacity, which requires them to build more rail lines.

To see this a bit more formally, think of an idealized city on a grid. Let’s say blocks are 100*100 meters, and the planners can figure out the target density in advance when designing the subway network. If the city is very compact, then the subway could even be a grid, at least locally. But now if we expect a low-density city, say 16 houses per block, then the subway grid spacing should be wide, since there isn’t going to be much traffic justifying many lines. As the city densifies, more subway is justifiable: go up to missing middle, which is around 30-40 apartments per block; then to the Old North of Tel Aviv, which would be around 80; then to a mid-rise euroblock, which is maybe 30-40 per floor and 150-200 per block; then finally a high-rise with maybe 500-1,000 apartments.

Each time we go up the density scale, we justify more subway. This isn’t linear – an area that fills 500 apartments per block, which is maybe 100,000 people per km^2, does not get 20 times the investment of an area on the dense side of single-family with 16 houses per block and 5,000 people per km^2. Higher density justifies intensification of service, with bigger and more frequent trains, as well as more crowding. With more subway lines, there are more opportunities for lines to intersect, leading to more frequent stop spacing.

Even if the first subway lines are not planned with big systems in mind, which New York’s wasn’t, the idea of connections to streetcar lines was historically important. A stop every 10 blocks, or 800 meters, was not considered on the local lines in New York early on; however, stops could be every 5 blocks or every 7, depending on the spacing of the major crosstown streets.

Dense blobs and linear density

Line spacing is important to stop spacing not on parallel lines, but crossing lines. If a bunch of lines go north-south close to one another, this by itself says little about the optimal spacing on north-south lines, but enforces tight spacing on east-west lines.

This means that high density encourages tight stop spacing when it is continuous in a two-dimensional area and not just a line. If large tracts of the city are very dense, then this provides justification for building a grid of subway, since the crosstown direction is likely to fill as well; in New York, 125th Street is a good candidate for continuing Second Avenue Subway Phase 2 as a crosstown line for this reason.

In contrast, if dense development follows a linear corridor, then there isn’t much justification for intense crosstown service. If there’s just one radial line, then the issue of line spacing is moot. Even if there are two closely parallel radial lines in the same area, a relatively linear development pattern means there’s no need for crosstown subways, since the two lines are within walking distance of each other. The radial urban and suburban rail networks of Tokyo and Seoul do not have narrow interstations, nor do they have much crosstown suburb-to-suburb service: density is high but follows linear corridors along rapid transit. Dense development in a finger plan does not justify much crosstown service, because there are big low-density gaps, and suburb-to-suburb traffic is usually served efficiently by trips on radial lines with a transfer in city center.

29 comments

  1. Martin

    What do you think of mitigation of long stop spacing via longer trains. For example, 400 meters worth of city blocks are within 100 meters of train with a 200 meter long platform.

    It definitely feels like there’s a also a phycological closeness to the train once you step underground from the street. Even if you still walking a bit to the platform it feels closer and safer from crime and elements when you have long mezzanines or tunnels to the actual fare gates and platforms.

    • Alon Levy

      Having more entrances to each station helps – Berlin generally has two entrances per statio, one at each end of the platform – but train length only matters if passengers walk along the platform while waiting for the train or inside the train while it is in motion.

      • Richard Mlynarik

        Both long trains and multiple access points, especially extending from the ends of the platform, do help!

        The geographical “reach” of the station out into the neighbourhood increases. And in addition once one moves into the periphery of the station (escalator of stairs up or down) pedestrian movement is often freer than on surface streets and sidewalks, impeded by car traffic, human congestion, traffic signals, urban clutter. (Not saying urban clutter is a bad thing, but sometimes one just wants to get to the train.)

        In stations with good access from their extremes I do find myself walking the length of the platform (or mezzanine, if that’s present and superior) in order to pop up to (or descend down to) to street level with a head start on my journey by foot.

        It’s frustrating — ok in my case it’s actively infuriating — when know-nothing architects and the transit-industrial complex work against this, as they do with so many gated fotress stations. Access points are controlled and hardened and expensive and few and centralized, rather than free-flowing and wide-ranging. For example I just loathe approaching an elevated BART station, being right under the end of a platform when I can see a train arriving, but miss the train because I am obliged to walk 100m parallel to the platform to reach the central congested fare-gate security control, and then and only then take stairs up to the platform, and wait for a later train. Oh yes, this also inhibits even passenger loads along trains as too many stations in the system provide only a central access point to platforms and so trains end up lightly loaded at the comparatively inaccessible ends and overcrowded in the middle. Likewise getting off a train and trying to go somewhere — I can see where I want to be, but I have to walk along the platform to the constrained vertical access point and then walk back at a different elevation, among cars and other stuff, to where I started off.

        So anyway, yes, a 200m platform with stairs fanning away say 30m away from the plaform ends means that there is 260m of linear space where I’m at most 30m of unimpeded walking from being able to hustle to catch a train. With shorter trains/platforms or fewer access points and with fare gate delays I’m further away from the goal of getting somewhere.

        • John Muller

          There are several elements in play w/r the number and location(s) of street entrances/exits: user convenience; security; and economics.

          Obviously, the more entrances the more convenient, but OTOH, also the more expensive to build and (probably) to staff and maintain. A station with a long mezzanine outside of fare control could mitigate the staffing issue if there was only one staffed location, but if that meant that meant that all pax needed to enter or exit at that location the walking back and forth outside the platform problem would be back, just moved inside the station instead of outside.

          Martin seems to feel secure once he gets off the street, but long confined passages can be pretty dangerous too; quite a few NYC subway entrances and/or passageways were closed at least in part for safety issues.

          In NYC, some of these access points remain closed because opening them could trigger requirements that the station be retrofitted for handicapped access.

        • Tonami Playman

          I always dread those BART single entrance stations. The 3 downtown SF stations and 2 downtown Oakland stations do have multiple entrances along the station length but they all feed into a smaller mezzanine area above the platforms. You still can’t access the mezzanine from one end and go directly to the platform. You have to walk a bit towards the center, but not as much as you would with the elevated stations.

          Even if BART is averse to the idea of Proof of Payment system, just placing unstaffed fare gates at multiple ends would be way for convenient for riders. If concentrating passenger flow on one entrance is to enforce anti-fare evasion measures, then they are woefully unsuccessful because people frequently jump the barriers or use the emergency exits right in front of the station agent. And the agents don’t seem to care.

  2. Tonami Playman

    The parallel lines with no crosstown lines is very prominent in Kobe. Where the Hankyu Kobe, JR Kobe, and Hanshin lines run parallel to each other for over 20km with line spacing varying from 200m to 500m and no cross connection except for the Rokko Island line connecting the JR Kobe and Hanshin lines to Rokko Island.

    • Vishek

      Those three lines are suburban commuter lines (RER) whereas an underground metro system exists for crosstown services.

  3. Rover030

    Do you think there is a point where high absolute density leads to crowding problems on local transit if subway stop spacing is too wide? I could imagine this happening with 1,5km subway stop spacing (busses running parallel with 3 or 4 stops per subway stop) if the subway misses some key destinations on the corridor. Or do you think still enough people walk/transfer to the subway because of its higher speed?

    Most of your work on bus stop and route spacing seems based on grid-like cities. I’d be interested in your thoughts on radial cities as well, where the route spacing keeps increasing if you follow the main roads out of the city, but may be too tight in central areas. I imagine there is some balance between branching, frequency and walking distance you could model.

    • Paul

      Yes. In your example, if a lot of rail passengers use the parallel bus for access/egress along the corridor then you’d expect the highest passenger loads on the bus to be as it’s approaching/leaving the subway stations. It’s not as much of a problem with access because the people furthest away from the subway station get on the bus first. If you’re one bus stop away from the subway station and the bus is usually full before it gets to your stop, you might just decide to walk instead. For egress, the capacity of a subway train is obviously a lot more than a bus so if you have a big group of passengers exiting the subway station that all want to board the same local bus, it could easily overwhelm the bus. People may self-select here, too, but it’s easier to be selfish and ride the bus for one stop in the egress direction. Ways to deal with the problem might be lining up several buses to meet each train (hard with high-frequency subways, easier with commuter rail), shorter subway spacing, or local/express subway service (then local/express capacity is more similar).

      Also related is the question of whether local service parallel to the rail line is even needed. If the rail stop spacing is pretty short, then you can probably do without parallel buses. It will be faster for most people to walk to the nearest rail station than to wait for a bus and transfer to rail. Paris intramuros is like this. There is a bus system, but it’s quite possible to get around using only Metro/RER and many people do.

    • Alon Levy

      For what it’s worth, Tokyo has a very weak bus network because people just take the subway or JR East. Key destinations usually just get a station – stop spacing notably narrows in city center, with stops maybe 700 meters apart in the CBD and more like 1.5 km apart in outer neighborhoods. This comes straight out of 1-dimensional optimization – stop spacing should be tighter in areas with higher relative demand, because people are disproportionately likely to travel to and from these areas rather than through them.

      • Andrew in Ezo

        Alon, could you clarify what you mean by “very weak”? Because the bus network in Tokyo and its suburbs is quite dense, at least to my eyes. However, as you say, most people rely on the subway, private railways, and JR East for the majority of their journey. Buses primarily serve to funnel passengers from residential areas to the nearest biggish railway station. This is especially prevalent in the suburban areas which are served by the private railway companies, which often also run the bus services (Odakyu, Tokyu, Keisei, Keikyu, et al). Though there are likely some bus routes that serve as “cross-country” services perpendicular to the radial lines or corridors.
        Route map of Toei Bus (Tokyo Municipal)- gaps or lack of services in some wards/neighborhoods will likely be due to other bus companies providing the service:

        Click to access 2020allmap_high.pdf


        Private railway companies often are the main providers of bus services in the outer (i.e. outside the Yamanote loop) wards of Tokyo . For example, Tokyu is dominant in Setagaya Ward (right center area of the map):

        Click to access 00_all.pdf


        Keisei Bus all system map. A presence in the eastern wards of Tokyo (“shitamachi”), of course in Chiba Prefecture as well where the “feeder to stations” pattern is quite apparent:

        Click to access all_routemap.pdf

        • michaelrjames

          Isn’t the key word in Alon’s statement of the bus network being weak is “network”. Buses are mostly feeders to the train which forms the network, not the buses, at least not a bus network.

          • Vishek

            The density and the willingness of Tokyoites to walk to a metro station simply makes the buses less popular. I’ve never once taken an urban bus in Tokyo, in fact the last time I took a bus in Tokyo was when I first landed there many years ago and was following online transit directions. Generally the bus network is weak throughout Japan for various reasons. People either walk or cycle or drive rather than wait for a bus. Tokyo is one of those places were the rail density is so high that walking is easier – it’s similar in places like Paris and London where walking was/is the norm, but in Europe it’s common to take buses across town for what would be a train journey in Japan.

  4. Alex Francis Burchard

    Great write-up! I’d like to just point out that save for a number of cities that can be counted on one hand, on this planet, mid-rise blocks are denser than high-rises practically almost everywhere. In places like where I live, it’s an extreme difference, where high-rise districts often plummet to 10-40.000/sqmi, while mid-rise districts soar to well over 200.000/sqmi densities.

    Theoretically, yes, high rises should be denser, but practically, that is almost never true. Just wanted to point that out 🙂

    In İstanbul, we seem to have started off with the finger plan, but we’re moving to a more gridded plan, because while largely our city follows the main roads that are radial from central İstanbul more or less, the density doesn’t fall much between the corridors, and it’s just too far to ride 40 minutes to the center, and transfer then go back out another 40mins if you want to go from edge-to-edge neighborhoods. Megacity problems… Hopefully things go as planned and by the end of 2021 we will have a grid network. Today we have a strong finger and parallel route network.

    • SB

      Can transit in İstanbul considered gridded if there is only one transit line across the Bosporus?
      Or you treating European and Asian sides as separate?

      • Alex Francis Burchard

        You are ignoring Metrobüs. Metrobüs is the highest quality transit line in the city by a long shot, busses every 9 seconds. It takes longer to cross the street to get to the station than it does to wait for a bus to take you along the line. So, there’s two lines across the Bosphorus presently (Metrobüs, Marmaray) (well, and I don’t know if it’s worth counting the ferries, but they go all over the place). But even with two major crossings, I’m more or less considering each side separately. The completion of T5, M3, M7, M9, and M11 will grid the European side, and Bostanci-Dudullu, and Goztepe Umraniye lines will grid up the Asian side – and to be honest, that’s just us getting started (those are all under active construction – map of construction here – http://www.metro.istanbul/Content/assets/uploaded/İstanbul%20İnşaat%20Halindeki%20Raylı%20Sistemler%20Haritası.pdf ) 🙂 The long term plan, if we ever get our finances fixed is for an insane grid of metros, including 2 or 3 more Bosphorus crossings. Some day.

          • Alex Francis Burchard

            Every 9 seconds. our holiday schedule is every like 20 or 25 during the day, 8 minutes at night, regular schedule is 9 ish seconds in the day, 2-5minutes overnight. (It’s 24 hours) 🙂 It’s a wonderful transit line. Has its own lanes for all but about 2 of the 50km of its length. (It mixes with traffic on the Bosphorus bridge, but it’s the last merge on, and first merge off, so it rarely seems to get delayed significantly by the bridge).

            The frequency varies by what part of the line you’re on though – There are 7 services (endpoint pairs) For example at my stop, I can catch 4 different services (34AS, 34BZ, 34, 34G) There’s also 34Ç, 34U, 34Z – though I’m not sure about 34U, I don’t ever recall seeing it. I think at my station (center of downtown) the peak frequency is like every 15 seconds, out between Çevizlibağ and Avcılar is where you get the 9 second frequency.

          • df1982

            That surely sounds like a candidate for conversion to higher-capacity vehicles (i.e. metro rail). The savings in labour costs would be enormous (even with the low-ish labour costs of Turkey). Also you have a huge peak-base ratio (15-30:1 it seems), which adds to the inefficiencies. And even with segregated lanes it’s impossible to maintain even headways with that kind of frequency, so you have bus bunching and significantly longer waits.

            Better to have a metro train with a large capacity (up to 2000 is possible) running reliably every couple of minutes. The trunk can be rail and the service variations can be transformed to feeder bus routes.

          • Alex Francis Burchard

            Ahh, but what I didn’t mention, it’s built to bunch. Platforms are 4-5 bendy busses long, so you reliably get a squadron of busses every minute ish. the busses operate almost train like when at peak. And the reason it’s not metro is because of the Bosphorus crossing, that’s such an expensive and long-term endeavor. We plan to build a few more metro crossings some day, but when that will happen is not clear, right now we can barely afford to continue the construction started 5 years ago due to the state of our economy and government.

            Also I’ve never heard the term Peak-Base ratio – can you explain that to me? 🙂

          • Alon Levy

            Peak-base ratio is the ratio of service provided at rush hour to service provided not at rush hour. “Not at rush hour” can mean different things depending on time of day, but I think the most useful definition is “the lowest amount of service between the morning and afternoon rushes.” Typical metros have a peak-to-base ratio in the 1-2 range; American commuter trains start at 5 and go up from there, with one line at 24 (12 trains per hour peak, a train every 2 hours off-peak).

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  6. Eric2

    Am I correct in summarizing your thoughts as follows?
    1) If density is uniform, stop spacing should be uniform.
    2) If density is nonuniform, denser areas need more frequent stops.
    3) Every significant line should have a transfer to every other significant line. In very large cities, there are more significant lines, which forces a greater density of stops in the core to accommodate all transfers.

    My questions on this:
    2) How much more frequent? If an area has double the trip density, should it have double the stop density to equalize usage of all stops? Or is this too extreme?
    3) Is significance absolute or relative? Perhaps a tram or major bus line in a medium-sized city has the same transfer potential (relative to the population) as a metro in a large city, and thus equally justifies a transfer stop?

    • df1982

      Another question, following Eric2:
      – should stop density be higher at “destination” stations (e.g. city centres, employment zones, entertainment districts, etc.) than at “origin” stations (residential areas)? In my experience, it’s much more practical to take feeder transport (cycling, driving, local transit) from home to the local origin station, than it is from the destination station to the actual destination. The latter should be within a short walk as a rule.

      • Eric2

        I think Alon, in an old post, agreed with you that people are less likely to tolerate a transfer at the end of their trip than the beginning.

        In any case, regarding the density, I would say “estimate how many people will use it, taking feeder transport into account as we discussed, and choose stop density based on that usage number”

    • Henry Miller

      My answers.

      1. Probably, but geography is also in play. Almost all cities in the world are built near water (for good reasons I won’t go into), and that often means a river that the system needs to cross. In the middle of the river you won’t have stations. That water also tends to be a draw and so you put stations near there (but that draw also implies non uniform density).

      If your city has hills that also affects stations, people want to walk downhill so you place stations at the top and bottom and expect most people will start at one and finish at the other. The hill also is important for system design, you might be forced to not have a station in the middle of the hill because you cannot accelerate or stop except at the top or bottom (applies to those going up /down)

      2. This is a compromise and we would prefer the same stop spacing everywhere. In less dense areas you turn people away (to cars) with more density, but you can go faster drawing them back in. In dense areas you figure most people are not riding through so a few closely spaced stops get everyone to their destination faster, even though you are slower overall. If you have several dense areas with sparse areas in between you should not space stations close in the dense areas because the people who are passing through to the next don’t want to be slowed down.

      To answer your question we need to know where people are going. Total door to door trip time is what people care about. Close stop spacing in the dense area gets people there faster, but only if the stops are in reasonable places. If you serve buildings with one secure entrance you want to be next to the entrance even if that means non uniform stop spacing.

      3. This again is about compromise. To get a going fast you need distant stop spacing. Which means that you have to designate some lines as less significant and miss the transfer for them. That lowers the importance of the lesser line in two ways, it doesn’t go to the fast line so people won’t have an easy time getting to/from the fast line, and again because people who could use it as an alternative probably will prefer a different nearby line that does connect. Large cities are more likely to need this treatment, but it is about the needs of the city.

  7. Vishek

    I was looking at the situation in Chennai, which is a wide long low-lying metropolis (due to a radar tower for airport and seaport operations), thinking that metro would be too cumbersome to connect the entire city. You would need to have two or three metro system cores in order to serve the city properly, connected together through an RER system.

    I face palm when I come across third world cities build elevated “metro” systems because they’re doing it for prestige rather than actual convenience. Why not expand the suburban railway system if you have room for an elevated metro system? Build a S-Bhan instead of U-Bahn that isn’t underground!

    Generally, metro systems are very cumbersome in suburban areas. Tokyo solved this by running commuter trains into the metro system as RER trains.

    • Eric2

      Strong disagree.

      Elevated metro is just as useful as underground metro, and can be built for ~1/3 the price. That makes it a great solution for poorer large cities where the cost in terms of shadows and noise can be easily tolerated.

      In Chennai specifically (looking at a map) there appear to be about 6 rail corridors radiating from the “city center”, 3 metro and 3 suburban rail. It appears they have used all their legacy rail corridors for suburban rail, then building metro on unserved corridors. That is about the optimal solution for a megacity. I would only criticize them for putting much of their metro underground, which seems like a waste of money for a poor city.

      There is no intrinsic difference between metro and suburban rail. Both are electrified trains running on grade separate corridors. As for average distance between stops, that depends on the overall length of the line. Nearly all of the Chennai are is within 15km of the “city center”, which allows for a 15 stop long metro line with 1 stop per km, perfectly reasonable.

      Admittedly I don’t know the frequencies/fares/transfers on these 6 corridors, and it is likely that they are screwed up like they are in many Indian cities. But that is a cheap concrete-free fix.

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