One- and Two-Seat Rides

All large urban rail networks rely on transfers – there are too many lines for direct service between any pair of stations. However, transfers are still usually undesirable; there is a transfer penalty, which can be mitigated but not eliminated. This forces the planners who design urban and suburban rail systems to optimize: too many transfers and the trips are too inconvenient, too few and the compromises required to avoid transfers are also too inconvenient. How do they do it? And why?

Of note, the strategies detailed below are valid for both urban rail and suburban commuter rail systems. Multi-line commuter rail networks like the RER and the Berlin S-Bahn tend to resemble urban rail in their core and work in conjunction with the rest of the urban rail network, and therefore strategies for reducing the onerousness of transferring work in much the same way for both kinds of systems. Suburban strategies such as timing half-hourly trains to meet connecting buses are distinct and outside the scope of this post.

Transfer penalties

Passengers universally prefer to avoid transfers between vehicles, keeping everything else constant. The transportation studies literature has enough studies on this pattern that it has a name: transfer penalty. The transfer penalty consists of three elements:

  • Walking time between platforms or bus curbs
  • Waiting time for the connecting train or bus
  • An independent inconvenience factor in addition to the extra time

One meta-study of this topic is by Iseki-Taylor-Miller of the Institute for Transportation Studies. There’s a bewildering array of different assumptions and even in the same city the estimates may differ. The usual way this is planned in elasticity estimates is to bundle the inconvenience factor into walking and waiting times; passengers perceive these to be more onerous than in-vehicle time, by a factor that depends on the study. Iseki-Taylor-Miller quote a factor as low as 1.4-1.7 and Lago-Mayworm-McEnroe’s classic paper, sourced to a Swedish study, go up to 3; Teulings-Ossokina-de Groot suggest it is 2, which is the figure I usually use, because of the convenience of assuming worst-case scenario for waiting time (on average, the wait is half the headway).

The penalty differs based on the quality of station facilities, and Fan-Guthrie-Levinson investigate this for bus shelter. However, urban rail estimates including those in the above meta-studies are less dependent on station facilities, which are good in all cases.

Mitigating the transfer penalty

Reducing the transfer penalty for riders can be done in three ways, if one believes the model with a constant penalty factor (say 2):

  • Reducing the number of transfers
  • Reducing walking time between platforms
  • Reducing waiting time for trains

All three are useful strategies for good urban rail network planning, and yet all three are useful only up to a point, beyond which they create more problems than they solve.

Reducing transfers

The most coherent network planning principle for reducing passengers’ need to transfer is to build radial rail networks. Such networks ideally ensure each pair of lines intersects once in or near city center, with a transfer, and thus there is at most one transfer between any pair of stations. A circumferential line may be added, creating some situations in which a three-legged trip is superior in case it saves a lot of time compared with the two-legged option; in Moscow, the explicit purpose of the Circle Line is to take pressure off the congested passageway of the central transfer connecting the first three lines.

In general, the most coherent radial networks are those inherited from the Soviet tradition of metro building; the London Underground, which influenced this tradition in the 1920s, is fairly radial itself, but has some seams. It’s important in all cases to plan forward and ensure that every pair of lines that meets has a transfer. New York has tens of missed connections on the subway, and Tokyo has many as well, some due to haphazard planning, some due to an explicit desire to build the newer lines as express relief lines to the oversubscribed older lines.

On a regional rail network, the planning is more constrained by the need to build short tunnels connecting existing lines. In that case, it’s best to produce something as close to a coherent radial network with transfers at all junctions as possible. Through-running is valuable here, even if most pairs of origins and destinations on a branched commuter line trunk still require a transfer, for two reasons. First, if there is through-running, then passengers can transfer at multiple points along the line, and not just at the congested city center terminus. And second, while through-running doesn’t always cut the transfer for suburb-to-suburb trips, it does reliably cut the transfer for neighborhood-to-suburb trips involving a connection to the metro: a diameter can be guaranteed to connect with all radial metro lines, whereas a radius (terminating at city center) will necessarily miss some of them, forcing an extra transfer on many riders.

Reducing walking time

The ideal transfer is cross-platform, without any walking time save that necessary to cross a platform no more than 10-15 meters wide. Some metro building traditions aim for this from the outset: London has spent considerable effort on ensuring the key Victoria line transfers are cross-platform and this has influenced Singapore and Hong Kong, and Berlin has accreted several such transfers, including between the U- and S-Bahn at Wuhletal.

However, this is not always viable. The place where transfers are most valuable – city center – is also where construction is the most constrained. If two lines running under wide streets cross, it’s usually too costly to tilt them in such a way that the platforms are parallel and a cross-platform transfer is possible. But even in that case, it’s best to make the passageways between the platforms as short as possible. A cruciform configuration with stairs and an elevator in the middle is the optimum; the labyrinthine passageways of Parisian Métro stations are to be avoided.

Reducing waiting time

The simplest way to reduce waiting time is to run frequently. Passengers’ willingness to make untimed transfers is the highest when frequency is the highest, because the 2-minute wait found on such systems barely lengthens one’s trip even in the worst case, when one has frustratingly just missed the train.

Radial metro networks based on two- rather than one-seat rides pair well with high frequency. Blog supporter and frequent commenter Threestationsquare went viral last month when he visited Kyiv, a Soviet-style three-line radial system, and noted that due to wartime cuts the trains only run every 6-7 minutes off-peak; Americans amplified this and laughed at the idea that base frequency could be so high that a train every 7 minutes takes the appellation “only.”

When frequency is lower, for example on a branch or at night, cross-platform transfers can be timed, as is the case in Berlin. But these are usually accidental transfers, since the core city center transfers are on frequent trunks, and thus the system is only valuable at night. Moreover, timed transfers almost never work outside cross-platform transfers, which as noted above are not always possible; the only example I’m aware of is in Vienna, where a four-way transfer with stacked parallel platforms is timed.

This is naturally harder on a branched commuter rail system. In that case, it’s possible to set up the timetable to make the likeliest origin-destination pairs have short transfer windows, or even one-seat rides. However, in general transfers may require a wait as long as the system’s base clockface intervals, which is unlikely to be better than 20 minutes except on the busiest trunks in the largest cities; even Paris mixes 10-, 15-, and occasionally 20- and 30-minute intervals on RER branches.

24 comments

  1. Luke

    I’d asked a question somewhat tangential to this on Twitter ages ago, and never got an answer, but it seems like it should be significant for network planning. You often emphasize the importance of radial lines over tangential, diametric, or circumferential lines, but that all suggests a monocentric city geography. What about polycentric cities? Going further, for public transit planning, at what distance of geographic analysis is a city considered to be mono- or polycentric? You often highlight Tokyo as a strongly monocentric city, yet Shinjuku, Shibuya, Chiyoda, and Minato are all both significant in terms of employment and are at least ~2.5km away from each other. Tokyo’s rail lines all obviously converge on each other near these areas, yet it feels like a stretch to call these all one center. Is it because they are close enough to one another relative to the catchment area of the entire Greater Tokyo railway network?

    If so, I then have questions for other cities. Seoul springs to mind: it’s generally regarded as a polycentric city, as Jongno, Yeouido, and Gangnam are quite far apart (4-9 km, depending on the side of the triangle) yet the subway clearly converges on Seoul, as a whole, in the scope of Sudogwon. At what distance for a regional transit network is a region considered polycentric vs. monocentric?

    To make my query fit this post better: what is the strength of the transfer penalty relative to total travel distance? Someone going from Chiba to Kawasaki seems likely to be less bothered over a multi-seat ride (though it can be done with a single transfer) than someone going from Cheongnyangni to Seocho (can be a single transfer onto the circumferential Line 2, but could be 3 or more using radial lines)

    • Alon Levy

      The transfer penalty in most studies is just an extra trip time with additional weight. So if I’m walking 4 minutes between platforms and waiting an average of 2 minutes for my connecting train, it counts as 6*(penalty factor) extra minutes in the model, say 12 minutes if the penalty factor is 2.

      You’re absolutely right that the pure radial model assumes monocentricity. Polycentric cities are more complex and radial networks work differently there. I wrote about this in the context of rivers here; Seoul’s situation fits this as well, with Gangnam anchoring the wrong side of the river. In this case, it’s good to have some lines crossing each other multiple times, to ensure there’s a coherent network feeding the wrong-side centers.

    • Eric2

      ” all suggests a monocentric city geography. What about polycentric cities?”

      If the centers are far from each other, you generally go for a radial network around each of the centers, with the lines in the two networks combining or crossing each other in an intelligent way. Sort of how lots of NYC subway lines converge in downtown Brooklyn before making their way to Manhattan. Or how La Defense (Paris) is building a north-south metro line to supplement its east-west metro and RER lines, forming an overall radial network which overlays Paris’s radial network.

      “at what distance of geographic analysis is a city considered to be mono- or polycentric? ”

      Another way of asking this question is “at what distance do you need to build a direct line to CBD2, as opposed to relying on the existing line to CBD1 plus a short transfer?” There is no single answer to this, you will have to draw the lines on a map and see what pencils out. Obviously, the closer your two CBDs are to each other, the less likely you are to want to build a line to CBD2 which roughly duplicates the first line’s route to CBD1, unless the first line is over capacity.

      Regarding Tokyo, Seoul, or any other specific city – there are going to be factors like overbuilt legacy infrastructure, or geographic constraints, which mean that the actual network you see is not the theoretically optimal one.

      • Alon Levy

        The Métro is not radial, and has many origin-destination pairs that require a three-legged trip. It is sort of a grid, but like all grids is not complete enough to avoid the three-legged trip problem, which is especially onerous for such a short-distance system. The transfers in Paris also require a lot of walking between platforms, and the big stations (like Châtelet or Nation) are the worst, as are all Métro-RER transfers.

        • Eric2

          Notice that I said Paris, while you said Métro. Once you take away the RER, the Métro itself has less of an obvious structure. But despite the Métro’s messiness, in general it is indeed radial. Except for lines 2/6 which together form a circumferential, every line connects the “city core” (which I define as the area roughly in between the legacy rail terminals) to outlying districts. This radial aspect is getting stronger by the year as a number of lines (4, 11, 14, etc) are being extended to the suburbs. And within that “city core” area, there is a focus around the Auber area where 7-8 metro lines converge, with the network being sparser away from this center-of-the-center.

  2. brw12

    One thing I’ve noticed, in both the Boston and NYC systems, is a consistent gap between the number of scheduled subway trains and buses and the actual, observed number. I’m not sure how much this has to do with staffing/maintenance/train readiness (a longtime problem, even before the pandemic) and how much with the cascading effects of oversubscription (crowded trains and platforms have to spend much longer in the station/stop, and so many trains end up clustered behind the most clogged train, unable to move past it into the underserved gap in front of it; this can be mitigated by less empty trains “going express” and passing the lead train, which is something the NYC system had an aggressive policy of doing in the 1990s and early 2000s, but (in my observation) noticeably stopped doing in the 2010s.

    • Matthew Hutton

      Wouldn’t you need much clearer announcements and maps etc on the train if you were going to do that?

      I’m not sure given the complexity of the network that it’s even possible without pissing off occasional users a lot.

    • Tiercelet

      Are you sure? The solution I remember seeing most was “make the late front train skip stops on the local track until it caught up its schedule”–and given the congestion on express tracks at rush hour, it seems like it’d be hard to slot a local onto them to skip a leading train on an ad-hoc basis. But I may not have been paying good attention, and wasn’t as much of a rush-hour commuter back then.

      Having a late local skip stops isn’t a great plan, since it manages to a) annoy 80% of the passengers, b) make the station delay worse as you wait for most of the passengers to alight onto a platform that’s by definition already crowded, and c) reproduce the exact same crowding problem on the next train, so it’d make sense to avoid it unless absolutely necessary. But seems more doable than finding a slot for a trailing train to leapfrog it, no?

  3. Sarapen

    Are there cross cultural comparisons of accepted wait times? Presumably not every culture shares the exact same ideas on convenience and don’t react the exact same way to the transfer penalty.

  4. Allan Rosen

    The transfer penalty between modes and between buses is far greater than transfer between rail lines if they are across the platform and timed to meet and may be weather protected. In NYC, the transfer penalty often includes a fare penalty as well.

  5. Tonami Playman

    I’ve noticed that despite the heavy use of phased plans where multiple lines are planned together, Indian metros tend to prioritize cost of construction over convenient transfers. A perfect example is Hyderabad, where the current 3 line network was planned and built simultaneously with a soviet triangle. There’s a missed opportunity of not providing cross-platform or stacked platform transfers between the 3 interchange stations at Ameerpet (between red & blue lines), MGBS (between red & green lines), and Parade Ground(between green 7 blue lines). At Ameerpet and MGBS, the stations are parallel to each other, but at Parade Ground, it would be a little more challenging.

    Delhi metro does have a few asymmetric cross-platform transfers where two parallel lines with side platform stations have the adjacent side platforms connected to form a single Island platform and 2 side platforms. This allows for cross-platform transfer for 1 of 4 possible transfers vs 2 of 4 for a single station symmetric cross-platform transfer.

    Bengaluru also has a missed opportunity at RV Road station, where they’re going with the Delhi-style asymmetric cross-platform instead of a more convenient symmetric cross-platform or stacked platform layout.

    Chennai metro is the exception where effort was made to have stacked platforms at the two interchanges on the current network at Alandur & Central.

  6. gault8121

    With the new regional connector in LA merging these lines into two, how much time will be saved in transfer penalty costs? Additionally, with the proposed new line configuration, sending the Pasadena/Asuza line down to Long Beach, rather than to Santa Monica, seems like it would create a higher transfer penalty relative to the other configuration given the population density of Western L.A. Is it actually a greater number of one-seat rides to send East L.A. line to Santa Monica and Pasadena to Long Beach? This seems like it wouldn’t be the case, and I can’t find anything that justifies why this configuration makes sense.

    • Alon Levy

      So, usually the straight way to do it – north-south and east-west, as currently planned in LA – works best for reducing the number of transfers. The reason is that Long Beach-Eastside would miss the connections to north-south Westside lines, like the planned but deferred South Vermont line (which apparently is going to be a bus instead). In general, future radial lines are guaranteed to intersect with existing radial lines, but not with non-radial ones that bend the wrong way.

      But the problem with this line of thinking is that Los Angeles is not building a radial transit network. The Green Line has no connection to the Purple and Expo Lines, and the Regional Connector isn’t going to change this; only if the line is extended as a Sepulveda line will there be a connection, and in that case it still wouldn’t matter what the line pairing is via the Regional Connector. So the north-south-and-east-west principle is still useful but loses most of its value.

      The question then is whether it’s valuable to instead pair lines in a different way. You’re right that West LA has more jobs than Long Beach – the Blue Line as I understand it has more traffic than Expo but it’s more directional. The questions then become:

      1. Is it more valuable to connect Pasadena to West LA jobs than to connect the Eastside to West LA jobs?
      2. How valuable is the connection to Union Station for either Long Beach or the Westside?

      • Sascha Claus

        There other things to consider when pairing lines, like technical compatibility (pairing light rail and metro won’t work) and capacity: connecting one end with 10min interval to the other end with 15min interval doesn’t work well, too. Or one end that has 2-car trains with an end needs 3-car trains.
        You could spend the money to operate the lesser side with overcapacity, or you can find another pairing that fits better.

        • Matthew Hutton

          Is it a big deal to run 3 car trains that aren’t full on the whole line?

          • Henry Miller

            You need to build all your stations long enough for that extra car. Longer platforms make the station more expensive to build, and also mean you have to buy more land.

            You could maybe cheap out by just not opening the doors for the one car, but you still need to have space for that car on the tracks (if you have any switches at the station they need to have enough room for this car). Locals will figure out that the one car can’t be used, but you will still have confusion from new riders who are surprised that they can’t get off.

          • Sascha Claus

            Is it a big deal to run 3 car trains that aren’t full on the whole line?

            Having the empty cars turn around earlier means you need fewer cars and less energy. The size of that deal depends on the amount of money you can and want afford to spend.

  7. Phake Nick

    I think this cannot be generalized and must take into account differences in individual situations.
    For example, after through running on new track in Hong Kong in a service called Tuen Ma Line, passengers along northern section of East Rail Line have two options to reach Kwun Tong, a single transfer at Kwun Tong, or double transfer via Tai Wai then Diamond Hill.
    The new double transfer option become surprisingly more popular than the original single transfer option even though the original estimate were considered aggressive, neither of the transfer offer cross platform interchange and passengers must went through station hall, as well as relative low frequency of the new Tuen Ma Line at about 7 minutes headway off peak, and even the door to door time across both options are similar.
    Some think part of the success can be attributed to that the single transfer at Kowloon Tong involve a long walking corridor crowded with people, and the involving trains at transfer station would already have high load factor that it would be unpleasant to get on and hard to guarantee passengers can get on the first train they reach in during peak hour, while the new service isn’t extremely crowded

    • Luke

      I think what this emphasizes is the important of not having missed connections. That way, you can have a two-seat ride act as a relief for a more crowded one-seat ride along the same corridor. If the time penulty for the two-seat ride is essentially null–whether due to platform or train crowdedness or an unnecessarily labyrnthine stations for the one-seat ride origin/destination–you’ve basically doubled the service frequency between two ares; if the penulty is small, then people can choose depending on whether they’re more time sensitive or other variables are more important. Ceteris paribus, people will choose a one-seat ride, but of course life isn’t that way, so offering other options is valuable.

  8. Borners

    Alon, how much does the search for 1-seat rides justify Japanese/Korean reverse branch subway through-running? Its not the only reason for it (relieving terminal capacity was the original one), but it clearly does work given the ridership on Tokyo and Seoul’s systems.

  9. Martin Pagel

    Yes, great headways reduce the transfer headache. One reason why urban gondolas (Mexico City, Haifa, Medellin, La Paz, Toulouse…) make great feeders as they provide hyper frequency – you never have to wait (unless due to overcrowding) Typically the gondola station is right next or above the rail station and therefore easy to reach.

  10. Mark N.

    Something of extreme importance that greatly contributes to the ease or difficulties of transfers is having a logical and easily understood signage system. Although you criticize the long walks that the Parisian Metro requires, what I have always loved about it — from a tourist standpoint — is how easy it is to figure out the way to the next transfer. (For a resident I could see how the distance would be annoying!). I’ve been using Stuttgart’s U-Bahn for many years (teeny-tiny compared to the Metro), and I still spend a few minutes nearly every time wandering around Station Charlottenplatz trying to find my connection platform. To me good signage makes up A LOT for of other weaknesses in a system.

    Something else which I have always found admirable about the Metro, in addition to its sheer density of stops, is in fact its divergence from a radial system. I’ve always thought of it more as a “spaghetti” system. From my albeit small amount of experience using it (again, just as a tourist), I have always been impressed with how uncomplicated it is to get from one area to another on the far side of the centre while avoiding a transfer at a large station like Châtelet. Subjectively, it just seemed like there was nearly always some simple combination of transfers to get from any Point A to any Point B.

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