‘Transit stupidity’ is inevitable, say mathematicians

In the Ars Technica “Weird Science” roundup, they link to a report that should interest any and all denizens of public transit:

A bus pulls up at a stop that’s so densely packed with commuters that they practically explode out when the doors are opened. Less than a minute later, it’s followed by a pair of nearly empty busses, running along the same route. Apparently, that’s a mathematical inevitability, termed the “Equal Headway Instability.”

The authors of this paper create a model that can reproduce the equal headway problem, and then try various solutions under the assumption that the current behavior seriously annoys commuters. Unfortunately, none of their solutions—minimum and maximum waiting times at stops, limited boarding, etc.—work well under all conditions, and the authors recognize that having commuters watch an unfilled bus pull away is also going to piss them off. The solutions, not surprisingly, are basic commute manners: stand away from the doors, let people out first, and don’t pile into an overstuffed bus. Conductors have been saying all of that for years—good luck getting impatient commuters to go along.

This reminds me of something I read the purported to prove (again, mathematically) that queues and lineups were, basically, backwards. Instead of first-come, first-serve (so, the person who has been waiting longest in line gets served first), the authors suggested that the people who had been waiting the least amount of time get served first. That would mean that the people who were not willing to wait (and therefore apparently desired what they were waiting for the least) had the least chance of clogging up the queue. It’s counterintutive, and it just seems unfair, but they mathematicians swear that it works.