There was an interesting discussion on Twitter a few hours ago about stop consolidation on the subway in New York. Hayden Clarkin, the founder of TransitCon, brings up the example of 21st Street on the G in Long Island City. The stop is lightly-used and very close to Court Square, which ordinarily makes it a good candidate for removal, a practice that has been done a handful of times in the city’s past. However, the spacing is irregular and in context this makes the stop’s removal a lower-value proposition; in all likelihood there should not be any change and trains should keep calling at the station as they do today.
What is 21st Street?
The G train, connecting Downtown Brooklyn with Long Island City directly, makes two stops in Queens today: Court Square, at the southern end of the Long Island City business district, and 21st Street, which lies farther south. Here is a map of the area:
At closest approach, the platforms of 21st are 300 meters away from those of Court Square on the G; taking train length into account, this is around 400 meters (the G runs short trains occupying only half the platform). Moreover, Court Square is a more in-demand area than 21st Street: Long Island City by now near-ties Downtown Brooklyn as the largest job center in the region outside Manhattan, and employment clusters around Queens Plaza, which used to be one stop farther north on the G before the G was curtailed to Court Square in order to make more room for Manhattan-bound trains at Queens Plaza. Court Square is still close to jobs, but 21st Street is 400 meters farther away from them, with little on its side of the neighborhood.
Stop spacing optimization
Subways cannot continuously optimize their stop spacing the way buses can. Building a new bus stop costs a few thousand dollars, or a few ten thousand if you’re profligate. Building a new subway stop costs tens of millions, or a few hundred million if you’re profligate. This means that the question of subway stop optimization can only truly be dealt with during the original construction of a line. Subsequently, it may be prudent to build a new stop but only at great expense and usually only in special circumstances (for example, in the 1950s New York built an infill express station on the 4 and 5 trains at 59th, previously a local-only station, to transfer with the N, R, and W). But deleting a stop is free; New York has done it a few times, such as at 18th Street on the 6 trains or 91st on the 1. Is it advisable in the case of 21st?
The answer has to start with the formula for stop spacing. Here is my earliest post about it, in the context of bus stops. The formula is,
The factor of 4 in the formula depends on circumstances. If travel is purely isotropic along the line, then the optimum is at its minimum and the factor is 2. The less isotropic travel is, the higher the factor; the number 4 is when origins are purely isotropic, which reflects residential density in this part of New York, but destinations are purely anisotropic and can all be guaranteed to be at distinguished nodes, like business centers and transfer points. Because 21st Street is a residential area and Court Square is a commercial area and a transfer point, the factor of 4 is justified here.
Walk speed is around 1.33 m/s, the walk penalty is typically 2, the stop penalty on the subway is around 45 seconds, and the average unlinked trip on the subway is 6.21 km; the formula spits out an optimum of 863 m, which means that a stop that’s 400 meters from nearby stops should definitely be removed.
But there’s a snag.
The effect of irregular stop spacing
When the optimal interstation is 863 meters, the rationale for removing a stop that’s located 400 meters from adjacent stations is that the negative impact of removal is limited. Passengers at the stop to be removed have to walk 400 meters extra, and passengers halfway between the stop and either of the adjacent stops have no more walking to do because they can just walk to the other stop; the average extra walk is then 200 meters. The formula is based on minimizing overall travel time (with a walk penalty) assuming that removing a stop located x meters from adjacent stops incurs an extra walk of x/2 meters on average near the station. Moreover, only half of the population lives near deleted stops, so the average of x/2 meters is only across half the line.
However, this works only when stop spacing is regular. If the stop to be removed is 400 meters from an adjacent stop, but much farther from the adjacent stop on the other side, then the formula stops applying. In the case of 21st Street, the next stop to the south, Greenpoint Avenue, is 1.8 km away in Brooklyn, across an unwalkable bridge. Removing this stop does not increase the average walk by 200 meters but by almost 400, because anywhere from 21st south in Long Island City the extra walk is 400. Moreover, because this is the entire southern rim of Long Island City, this is more than just half the line in this area.
In the irregular case, we need to halve the factor in the formula, in this case from 4 to 2 (or from 2 to 1 if travel is isotropic). Then the optimum falls to 610; this already takes into account that 21st Street is a weaker-demand area than Court Square, or else the factor in the formula would drop by another factor of 2. At 610 meters, the impact of removing a stop 400 meters from an adjacent stop is not clearly positive. In the long run, it is likely counterproductive, since Long Island City is a growth area and demand is likely to grow in the future.
Does this generalize?
In New York, this situation occurs at borough boundaries, and also at the state boundary if more service runs between the city and New Jersey. For example, in retrospect, it would have been better for the east-west subway lines in Manhattan to make a stop at 1st or 2nd Avenue, only 300-500 meters from the typical easternmost stop of Lexington. The L train does this, and if anything does not go far enough – there’s demand for opening a new entrance to the 1st Avenue stop (which is one of the busiest on the line) at Avenue A, and some demand for a likely-infeasible infill stop at Avenue C. These are all high-density areas, but they’re residential – most people from Queens are not going to 2nd Avenue but to Lex and points west, and yet, 2nd would shorten the walk for a large group of residential riders by around 400 meters, justifying its retrospective inclusion.