A few months back, I did a post about estimating the time required for the different routes I take to work, looking at the question of whether it’s better to take a shorter route with a small number of slow traffic lights, or a longer route with a bunch of stop signs. This was primarily conceived as a way to frame a kinematics problem, but I got a bunch of comments of the form “Aren’t you an experimentalist? Where’s the data?”
Well, here it is:
This is a histogram plot showing the number of times my morning commute fell into a given ten-second bin over the last couple of months. The blue bars are for the main-road route, with four traffic lights, the red bars are for the back-road route with nine stop signs, and the green bars are a “hybrid” route which takes the main road a bit more than half the way to campus, then cuts onto some side streets to skip the last two traffic lights, replacing them with two stop signs and shortening the distance by a fairly trivial amount.
I didn’t do this previously, because it was kind of a pain in the ass– I had to remember to start the stopwatch app on my phone when I pulled out of the driveway, stop it when I got to work, and record the time and route. As I am emphatically not a morning person, this was not that easy, which is why there are only 35-ish useful data points from 40 weekdays of class.
I think, though, that all the major factors were controlled here. I was teaching five days a week at 9am, so all of the recorded trips are between 8:00 and 9:00 am. I parked in exactly the same lot every day, and close to the same spot within the lot. I strictly alternated routes for most of this time, so each sample has roughly the same number of each day of the week. There was no really dramatic variation in the level of traffic on the drive– the very slowest point came when I got stuck behind a garbage truck for part of the trip, but that’s about it.
(I could’ve doubled the data by timing my drive home as well, but my departure time varied from day to day, and I often needed to run some other errands on the way home, so it would be harder to get clean data.)
So, what’s the lesson, here? The times for the three routes were pretty similar, as you would expect given the short distances involved. The main-road route took 350 ± 28 s, the back-street route 380 ± 24 s, and the hybrid route 316 ± 22 s. The distributions aren’t terribly well separated, but it’s pretty clear that the hybrid is the best of the lot, with the back-street route the worst.
How did my toy model do? The model time for the main-road route was 210s, and the back-road was 300s, which isn’t all that bad, considering how grossly simplified the model was. The difference between the averages is smaller in reality than in the model, reflecting the fact that when I get stopped at a light, I usually have to sit for a while, whereas the stop signs don’t produce as much delay. The distribution of times might be slightly wider for the main-road route (which you would expect given the probabilistic aspect of the lights), but the data aren’t nearly good enough to say anything definite.
So, anyway, there you have it: the definitive scientific analysis of my morning commute. Expect it to appear in print once somebody starts a Journal of Overanalyzing Everyday Tasks.
(And just to head things off: If you are planning to leave a comment chastising me for driving a five-minute commute rather than walking, you are welcome to bike or walk over here every day and entertain SteelyKid for an hour to make up the productive time I would lose to walking. If you’re not available to babysit, don’t bother with that comment.)