Statistics and How to Interpret Them

Here's a few of my thoughts on the MTA's Bus Performance Dashboard

So one the statistics is "Service Delivered". It basically says "the percentage of trips that are actually provided, measured at the peak load point". That last part is bolded because it does not necessarily mean that any given stop will see that percentage of its trips filled. On an express bus, the peak load point is generally the last stop before the nonstop portion (between the outer borough and Manhattan). So technically, if a trip skips a whole bunch of stops and serves the last stop before the nonstop portion, that trip counts as filled. And most likely (given that bus operators don't put up "Next Bus Please" as often as they used to), if a bus is full to capacity and bypasses the last stop, that trip (most likely) counts as filled. So pretty much, if a given trip serves any passengers on that route and passes by the peak load point, it is counted as filled. (The one thing I would wonder is, if for example, a QM5 were diverted via Fresh Meadows to cover a QM1 trip, would both trips count as filled?)

Now we get to the measure of Excess Wait Time. So let's take a route with 15 minute headways, and a stop where the rate of passenger arrival is 1 passenger per minute. If buses actually arrive evenly spaced, and the passenger arrivals follow a uniform distribution, the average wait time will be 7.5 minutes (half the headway). You will have some passengers who barely make the bus, and some who barely miss the bus, and then a lot in between. However, let's say that the buses arrive at the stop at 8:00am, 8:24am, 8:32am, 8:58am, and 9:00am. So the math works as follows:

24 passengers experienced an average 12 minute wait.
8 passengers experienced an average 4 minute wait
26 passengers experienced an average 13 minute wait
2 passengers experienced an average 1 minute wait

So cumulative wait time is (24*12)+(8*4)+(26*13)+(2*1) = 660 passenger-minutes, divided by 60 passengers = 11 minutes of average wait time. So the excess wait time at this stop would be 11-7.5 = 3.5 minutes

Notice how uneven the spacing is. 11 minutes of average wait time is the equivalent to an evenly-spaced 22 minute headway. 22/15 (or 11/7.5) = 1.467, which means effectively, the average wait time was 1.467 times longer than it was scheduled to be. But yet, after all of this math, it only shows 3.5 minutes of excess wait time. So that ratio (actual wait time/expected wait time) is just as important as the raw excess wait time numbers, because it actually captures the classic experience of "I waited 20 minutes and then 3 buses showed up at once".

Even if a line was super-frequent (say, 2 minute headways), this ratio captures the "chaos" for lack of a better term. If the effective headway is 1.467 times the scheduled headway, that means that a typical passenger experiences 1.467 times the number of scheduled passengers on the vehicle (whether it is a bus or train), or at least in the waiting area (bus stop or train station platform). And then some of them may not be able to fit into the vehicle and have to wait for the next one, so a vehicle arrival doesn't necessarily mean that the wait time ends for every single passenger in the waiting area. But then of course, you need more math to quantify that....you need to account for vehicle capacity. On the local bus or subway, it is a reasonable assumption to make that people will pack themselves onto the vehicle if necessary (I'm not condoning scheduling the service that tightly, but generally speaking, that is the behavior of passengers on those vehicles, myself included). On the express bus, the MTA schedules trips in a manner to avoid standees, but at the same time the buses can physically hold standees, so which number should you use for the capacity? Should you only take the seated capacity and when you are making the calculations, you assume that the standees would've otherwise been people who would've waited for the next bus? Or do you just go by the passenger counters/MetroCard swipes? Maybe publish both numbers?)

The one thing that does bother me on express buses is that people who let buses pass with seats in order to be at the front of the line for the next bus to get a "better seat" (on a bus that may very well end up with standees). It used to happen on the SIM8 all the time. I would get on around 7am, and maybe 2-3 people would end up letting the bus go by (at say, Christopher Lane). Then the bus would pick up people at Lambert Street and South Avenue, and continue into Manhattan with about 5 seats left. Then en-route to Manhattan around 7:30-7:40am or so, I'm seeing posts of "3 buses came with no seats". I wonder how many of those buses would've had seats if people around the 7am timeframe weren't picky about which seats they took.

Finally, the one thing (that I think may be almost impossible to quantify with official metrics, but is worth mentioning) is how many people ended up switching to a "backup option" that resulted in the trip taking longer than scheduled, but still shorter than waiting for the next bus (whether it was due to a delay or just infrequent service). If an Aspen Knolls resident checks BusTime at the time a scheduled SIM22 is supposed to arrive, finds that it is 20 minutes away and decides to take an arriving SIM25 to Arthur Kill Road/Veterans Road West and then wait 10 minutes for the S74 (as opposed to waiting 20 minutes for the SIM22 outright), is there a way to quantify the extra 10 minutes that the bus rider spent?

NYCT Track Safety Training

I figured I'd deviate a little from talking about buses to discuss one of the most fun experiences I've had in my life: The NYC Transit track safety course. Long story short, at my job we are involved with bridge inspection, so we need to learn the rules, regulations and operating procedures of all of the railroads where we need to enter on their property to inspect the bridge. There are many railroads in NYC (CSX, Long Island Railroad, Metro-North, Amtrak, NYC Transit, Staten Island Railroad, etc) and so each one has their own course on track safety. What makes NYC Transit unique is that their course involves a supervised walk on the track, to practice what you have learned.

The course starts at 7am at an old public school in Brooklyn (P.S. 248, right between the 25th Avenue station on the D line, and the Avenue U station on the N line). You fill out some paperwork (including a liability waiver...that hopefully never is actually needed...they shred it at the end of the day once everyone is back in the classroom). We watch a little introductory video on how the system works, and then the instructors (two veteran trackworkers) hand out a booklet with all of the main rules pertaining to track safety. They put up a Powerpoint where they discuss these rules (what types of locations are considered safe "clear up" locations where there is enough space to prevent you from being struck by a train, different arrangements for where the flagmen should be standing so that they can see approaching trains with enough time to warn the workers, and also so that the train can hopefully stop if necessary, how to work around the third rail, and with some stories of workers who made mistakes that unfortunately got them injured or killed. I heard they used to have much more graphic stories and pictures/videos (the most graphic one we saw was a guy whose hand got caught in a switch, but I heard they used to put out some really nasty stuff)

So then we go out for the field portion (I love how the instructors come to class all dressed with nice suits and ties, and then a few minutes later, they change into their safety gear, grab their lanterns, and lead us out to the training area). One of the things you learn quickly is that many people become complacent....the instructor literally had to remind some people to step back from the platform edge when the train was approaching