The Transit User's Problem

The New York Times Magazine recently published Year in Ideas 2008. Many interesting ideas were profiled, the more exotic of which include never-ending bubble wrap and spray-on condoms. Amongst the economics ideas, my favourite is the Bus-Wait Formula:

You arrive at the bus stop to catch the ride to work, but the bus isn’t
there. Your destination isn’t very far, so you think, Hmm, maybe I should just
walk. But then you might find yourself halfway between stops when the bus whips
past, which would be deeply annoying. What to do? Should you walk or should you
wait?

This question has plagued commuters for years, but this year three
undergraduate students at Harvard and Cal Tech decided to resolve it. “We were
sick of sitting at a bus stop, not seeing the bus and torturing ourselves over
whether we should start walking,” says Scott Kominers, a Harvard student
studying math, economics and ethnomusicology. So Kominers and his co-authors,
Justin Chen and Robert Sinnott, drew up the problem as a classic game theory
dilemma, began crunching the numbers and, three pages later, had their answer:
You should probably wait — and whatever you do, don’t second-guess
yourself.

Buses, after all, are usually punctual and move much faster than you.
If you start walking and catch the bus halfway through your journey, you might
consider yourself fortunate — but even then you won’t have gotten to your
destination any faster. What’s more, Kominers — like a good economist — points
out that waiting allows you to “optimize” your time, because you could get some
work done while hanging out at the bus stop. There’s also a practical problem
with walking, because people who decide to walk usually pause at each stop to
see if a bus is coming, which drags their journey out. “You think you’re not
slowing down if you stop, but you’re adding a bunch of time each time,” Kominers
adds.

Mind you, their equation breaks down in extreme cases. If your journey is
relatively short — less than a mile — and you suspect the next bus is half an
hour away, they calculate that you should walk. (Though you should walk
decisively, without dallying at each stop along the way.) But since most trips
involve more-punctual buses and longer journeys, waiting is, far more
frequently, the winning strategy. Or as Kominers concludes with some delight,
“Laziness almost always works.”

This is an interesting problem that I have encountered on a practical level many times in my life, especially since I often have short transfers on my transit journeys. Some comments on the methodology:

(a) The authors suggest that the way to optimize your time is by waiting at the bus stop and getting some work done. How might the analysis change if the benefits of exercise are also considered?

(b) The model should also incorporate the likelihood that the next scheduled bus will simply fail to show up. I was a transit user in Winnipeg for several years and know first hand that during periods of intemperate weather (read: deep freeze), the probability of a bus break-down is much higher. Transit users will consider this when taking decisions. Especially since walking is a more efficient method of maintaining body temperature than standing still.