Dimishing Returns for Frequency Enhancements

I was reading this post on Cap'n Transit's blog.

One of the commenters posted:

a route that is by mistake operating at a profit is under-providing, and should have its schedule extended or frequency increased until it gets back down to break-even.

Typically, when a transit line increases either frequency or extended hours, that tends to increase ridership. It would be an open question if ridership was rising fast enough to cover the cost of increased operations. Beyond a certain frequency, I would tend to expect not. But I would anticipate that bumping frequency from 30 minutes to 15 minutes would more then double ridership.

The rule of thumb I've learned is that at 15 minute service, you start attracting more unscheduled trips, where someone will show up at the bus stop, and wait for a bus to come. It would be amazing to have some data to show under what conditions increases in frequency show diminishing returns. If ever.

*I've never seen any study data for this. (If anyone knows of any, please drop me a line.) It would be great to see a case comparison before-and-after study of a transit line's increased or decreased frequency. Sadly, changes to transit schedules or routes are rarely done in isolation for a single transit line. They tend to be done en-masse, making it difficult to disaggregate the effect. The Federal New Starts has made this even more difficult, as upgrades to frequency on a single bus line tend to occur as part of a general upgrade to BRT status, which includes a number of other improvements.