# NYC subways probability question

I get on the subway at Forest Hills, where the E and F trains run on the same line, one after the other, alternatively, usually at least 5 minutes apart.

I need to take the E train to the World Train Center stop, but if the F train comes I take it and switch at w 4th street, where the E and F trains run on separate floors. Often, when I get off the F train and take the escalator up to the level of the E train (about 30 seconds), an E train arrives in the station within 30 seconds.

Is this E train

1. the E train that left the Forest Hills stop five minutes before my F train arrived (and I’m gaining a few minutes by this manuever)?

2. the E train that got to Forest Hills five minutes AFTER the F train I just switched off (and so I’m saving zero time by this manuever and would be better off just to wait for an E train at the Forest Hills station)?

3. sometimes 1) and sometimes 2)?

I think we’d need to know the differences in each train’s path. If the E has fewer stops and/or a more direct route, it might be the one that left Forrest Hills right after you took the F. (Meaning you’re in the ‘saving no time’ category.) If it has a longer route, then you’re probably doing the quickest thing.

It’s not really a probability question, prr, because the NY Subway trains keep to a schedule (at least in theory!), so the best strategy ought to be deterministic (or at least any MTA screw-ups should on average affect each line by the same amount).

First, let’s look at the NYC Subway Map. For those not familiar with NYC geography, the OP’s point of origin at Forest Hills / 71Av is in Queens on the right-hand (eastern) side of the map, at the lower edge of the green area marked “Flushing Meadows Park”.

The E and F trains both run on the same tracks and make the same stops until the 5th Av (@51st St) in Manhattan. Up until this stop, there’s no advantage taking either train – just take the first one that comes. Between 5th Av and W 4th St (the OP’s transfer point), however, the F takes a more direct route than the E (6th Ave rather than 8th), which is why the “take the F then transfer to E strategy” might improve the OP’s chances if the F is the first train to come along at Forest Hills.

So much for map-based theory. Let’s look at some schedules: E and F (warning: both are PDF files). In general, during weekday commute times, each train is on a 4-6 minute headway, interleaved (i.e. one or the other will come along every 2-3 minutes).

From the schedules, the E takes 32 minutes to go from Forest Hills to W 4th, whereas the F takes 30 minutes. So, if the first train that comes along is an E, the OP should just take it all the way to the WTC stop. If the first train is an F, then one could take it to W 4th and dash upstairs, but why bother? The E that comes then will be the next E from Forest Hills, not the one previous to the F taken. In the best-case scenario (4 minute headways), the E and F will go through W 4th St at exactly the same time, leaving no time for the transfer via escalator.

The above analysis breaks down if there is some kind of unusual “differential delay” between the E and F trains, i.e. between the 5th Av and the W 4th St stops (presumably due to one of the ubiquitous “track fires” that I remember from my NY-subway-riding days). If this is known in advance, or announced at some time during the trip, the OP should take the non-flammatory route (E or F) between 5th Ave and W 4th, and proceed from there.

In other words, in general the OP won’t save any time by taking the F and transferring. The decision may boil down to a simple one such as: on which train is it easier to get a seat? [Here in the SF Bay Area, I’m convinced that there’s a PhD thesis waiting for the first person to crack the optimum BART-seat-getting-strategy for the various different lines, and the same is evidently true in other cities.]

Sorry the answer’s not more exciting, pseudotriton ruber ruber.

Fellas (and I’m assuming you are both fellas), there’s this stuff called alcohol you might want to try sometime. It’s widely available, and if used judiciously, will keep you from being zombified by the endless barrage of intricate trivia that is urban life. Worked for me, anyway.

[hijack]You ever wonder how many dopers you run into on a daily basis and have no clue?[/hijack]

I think the simple answer to your question is 3) Sometimes it’s faster, sometimes not.

I too get on at 71st-Continental and due to my work location, I can take the E to Spring or the F to Broadway-Lafayette with an equidistant walk (or the R to Prince or V to B-L, but let’s concentrate on express trains for now).

The map isn’t all too clear, but the E and F only run on the same track for almost two express stops (to Jackson Heights, breaking off slightly past local stop 36th Street but before Queens Plaza). The F has one more stop in Queens then Roosevelt Island, while the E has two stops in Queens. Each then has an equal number of stops to West 4th - the F enters Manhattan slightly more north, then turns south for a more direct route; the E goes further west, then has to come back to the southeast.

It’s my observational experience that the F is faster than the E into Manhattan for two reasons:
[ul]
[li]The F skips Queens Plaza, a very slow station, and does not need to interleave with the V at this point like the E does. (True, the F stops at Roosevelt Island, but really, there are like two passengers boarding as opposed to Queens Plaza.)[/li][li]The E seems (to me) to take longer to load and unload since slightly more people ride it to get to the west side.[/li][/ul]
Likewise, when the V returns to the Broadway mainline, it’s already been interleaved once with the E and are thus are already intentionally spread apart, making interleaving with the F less of a hassle. Another observation: at Queens Plaza, I’ve seen the E and V arrive at the same time and the V is given the signal to leave first, further slowing the E down.

But the MTA schedules are a guideline at best - there are too many variables other than switching and signals such as passenger boarding times, objects on the track and such to give a definitive answer. I can’t mathematically prove it, but I’d put money on taking the F then switching to the E at West 4th saving one E train’s worth of time. (so much for general questions)

In fact, I can’t recall any of my commutes taking the same time. Going home I’ll sometimes take the V if it comes first since I get a seat

-D

Incorrect. This used to be the case, but it has changed.

Currently the E and F trains share a track from Union Turnpike (where I get on the F) to Roosevelt Ave/Jackson Heights. The E train continues on to Queens Plaza, 23rd Street/Ely Avenue/Lexington Ave (53rd St). The F splits off to 21st Street/Queensbridge, Roosevelt Island, Lexington Ave (63rd St).

My thoughts exactly. My stop is Roosevelt Ave.

Nothing to add to the GQ. Carry on.

Youv’e also got 53rd@Lexington to deal with if you’re on the E train. That’s where the E and V line crosses the #6 Lex Ave line, and hordes of folks from Queens who works on the east side are going to get off, while another horde of folks from the upper east side who work on the west side are going to get on. It ain’t pretty. Oh, and then 34th/Penn Station just as an add-on.

The F line admittedly gets the Rockefeller Center stop and the 34th/Herald Square stop, which see heavy duty, but still less so than Queens Plaza and 53rd/Lex.

I’m currently* using the Rock Center stop. It’s nothing compared to Lex/53rd. I used to go to 5th Ave to avoid that stop - the walk was a couple of extra blocks, but not as bad as that stop.

*As a consultant, I get the joy of changing office locations approximately every 6 months. This let’s me get a feel for a lot of midtown/downtown subway stops.

I’m sensing a Dopefest on the IND coming up…

Okay, so this morning, I race downstairs to catch to catch the arriving express into the city, but --too late! Bing-bong! The doors close.

It was an “E” train. As it leaves the station, a plan forms in the dim recesses of my mind. I note the number on the last car: 3686. I resolve to take the next “F” into Manhattan and change at w 4th. If this train is the train that arrives at w 4th, then (at least this one time) I’ll know that I’ve saved myself a few minutes by taking the “F” rather than waiting for the “E”.

This is not without costs. If I took an R train instead, I would have a seat, and the “R” stop downtown is actually closer to work than the “E” (though it’s a local and a little bit slower, I usually take it because I’ll get a seat.) But anything for science.

I hop the F, and stand all the way into midtown. I take the escalator at w. 4th and–sure enough–an E is arriving. The number on the last car? 3686. Yes. I have saved 4 minutes.

Please, no applause. No, stop. You’re very kind.

As I take this line every weekday, I’d have to say that the E-train that you encounter at West 4th Street is a later train. The E and F run not only the same route, but the same track till Queens Plaza. So your F train is always behind the E train till then. After that, the F train makes more stops than the E train - and there are two more stops between 34th Street and West 4th Street alone.

Unless the E train that left Forest Hills before your F train was delayed after the lines split at Queens Plaza, you’d never catch up with it. The train you catch at West 4th is definitely at least one train later and maybe two.

Not yesterday, it wasn’t.

And not this morning. Did the same experiment again, same results.

Usually, around 50th Street, the E train slows to a crawl as it has a very sharp turn. The F train, with its newer route, was better designed and does not slow as much as it turns downtown.

Also, the E train stops at Lexington and 53rd, at Times Square, and at Penn Station. These are 3 ‘long’ stops. They have more loading/unloading than the F train’s high traffic stops (Rockefeller Center and Herald Square).

Cillasi, did you miss my description of 53rd/Lex? And dasgupta’s descrip of Queens Plaza? The F train peels off towards Roosevelt Island prior to the Queens Plaza stop, enters Manhattan at the latitude of 63rd St and then turns downtown on 6th Ave, avoiding those two heavy-traffic / long-stop stations.

I’ve seen it take upwards of 10 minutes just to get the 53rd/Lex exiting passengers off the train and a sufficient percent of them up the narrow escalators and stairs to allow the folks wishing to get on to even get within viewing distance of the train. It’s like that old Barnum & Bailey clown routine with the little car except in reverse.

MTA guys with flashlights wait until the one at the front of the train can see the flashlight of the guy at the back of the train and vice versa, and that’s after the boarding crowd has managed to eel through and past the horded of disembarking folks and pile in, and the departing platform throng has oozed at least a foot away from the closing doors. (They hate to take off with elbows and umbrellas snagged in the works).

10 minutes may be an exaggeration, except as a one-off situation. The flashlight signals are side-to-side - passengers still exiting/entering, and up-and-down - close doors. Lastly, it is not that they hate to take off with elbows and whatnot hanging out. It’s that a properly operating train can’t leave without all the doors closed. Personally, I think more than a few operators/conductors would like to set a few examples of people cramming into a car that they can’t fit into. Certainly wouldn’t hurt their on-time percentages.