# Bus dilemma, The

Peter Jordan alerted me earlier today to a New York Times article about whether you should wait for a bus or start walking.  He suggested that it might be one for me. (Or “one 4 u”, should I say.)  Oddly, the article bears the title “Bus-wait Formula, The”.  Either it’s incomplete in some way, or some form of iTunes-esque artists algorithm has been run against it putting the The (not The The) at the end.

The overall outcome of the scientific study is that you should stay put, unless your journey distance is short, and the buses are infrequent.  No shit.

The formula is relatively straightforward to establish.  Here’s my maths.

Let’s say the expected time until the next bus is x, that your walking journey time is y, and the bus journey time is z.  (To get rid of a variable, you could measure z instead as a fixed fraction of y, if you know the comparative speed of the bus and walking.)

If you walk, you’ll take y time to get to your destination.  If you wait for the bus, you will take on average x + z.  So if the expected wait time is less than the walking time less the bus journey time, then wait; else walk.

The dilemma is largely taken away from you in London, with the digital read-outs that adorn many bus stops—although I’ve once or twice debated whether to walk a little further to the bus stop with the read-out, or head for the closer, read-out-free bus stop.

A more difficult dilemma each day is which 87 bus stop to head to having walked down the north side of Horseferry Road on to Millbank.  Should I turn left, against the bus’s direction of travel, running to the stop if I see the bus approaching?  Or should I instead turn right down Millbank, running instead to the subsequent stop should I see the bus.  This evening, I solved the dilemma.  Turning left into Millbank, the 87 was already at the bus stop.  So I turned on my heels, traversed many lanes of traffic and sprinted to the subsequent bus stop and catching the bus my a comfortable margin, aided in part by the slow progress of the bus due to traffic.  Which means there’s no benefit in heading for the earlier bus-stop.

Must’ve been a slow news day at the NYT.

3 Responses to “Bus dilemma, The”

1. Peter on October 3rd, 2009 00:04

What about the probability that the second bus will be late given the first one is? Part of the strategy assumes that a road blockage is preventing all buses.

2. SLATFATF on October 9th, 2009 16:18

Or, what is the benefit of getting out 5 mins earlier. Given the number of times one has to run for a bus only to just miss it surely you just leave 5 mins ealier, don’t tell the bus company and get the previous bus. Cheat fate! But don’t let on.

3. Dan on October 10th, 2009 13:59

Five minutes earlier than what? Than you would otherwise have left? When was that? And by leaving five minutes earlier each day, surely that becomes your new default time, so you need to leave another five minutes’ earlier…