Jarrett has been pushing the idea of frequent bus network maps for some time now. I think they're definitely worth trying. In his latest post, he invited transit planners to comment on the idea. One concern was that if you choose an arbitrary headway like twelve or fifteen minutes, in some systems you have almost nothing on the map, and in others it's still too crowded.
The thing to do, I think, is to keep in mind that you're just trying to present the most frequent routes, and "most frequent" is relative to your system. I would suggest just starting with the ten most frequent routes. If the map is still too crowded, then drop a few routes; if it's too sparse, add a few, until you get the right information density. Conduct a few interviews with your target demographic, or throw a draft at a focus group, to see if you've got it right.
A challenge I see, that I don't recall anyone else raising, is how to represent corridors where multiple less-frequent routes work together to provide frequent service, for example on Fifth Avenue in Manhattan. On corridors like this, you often find people who take advantage of the frequent service but do not use the less-frequent branches. This could be handled with line thickness, so that the frequent corridor is thicker than the branches. That's the best thing I could think of; I'd be interested to know if anyone else has a better idea.
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You can have a policy that says that low-frequency branches do not exist on the frequent map. You can also add lower-frequency branches in dashed or dotted lines, but that doesn't tell people much: "This line comes infrequently, but if you get on it, this is where you can do." Without hearing from other people, I'd lean toward the first solution.
Your scenario raises a related issue: in such cases of overlapping bus lines, how can system planners be encouraged to schedule for the most even-possible distribution of rides in the shared corridor, rather than letting buses from the overlapping lines "bunch up" as a side effect of "regular" scheduling on each of the individual lines? And how can signage on the shared corridor make clear what the mean-time-to-wait is and how far the shared corridor will carry you?
Actually, the interlining issue raises another problem: in Manhattan, there are many buses that aren't high-frequency but always share their corridor with other buses, leading to high frequency within a corridor. For example, if you use a 7.5-minute standard, then no route that uses 125th, 3rd/Lex, or Amsterdam is frequent, but the corridors themselves are frequent due to interlining.
The issue here is that if you draw all those corridors as frequent, then you may run into problems of depicting the low-frequency connections. Amsterdam and 125th may be frequent, but that doesn't mean that the Amsterdam-125th combined route is frequent.
You could just add a yellow highlight to the street segments with high frequency. This would illustrate it pretty easily, although it would have to be truly scheduled as high-frequency, as buses could be scheduled to arrive at the same time, which wouldn't be very frequent.
TriMet's frequent service map has one such example of two interlined busses provide frequent service over a significant corridor, but the individual routes do not: the 54 and 56 interlining between Raleigh Hills and downtown. The way it is depicted on the map is with a thick line with both numbers, and in the came color; and the two branches given in thin lines. Both lines are labeled as frequent service on their route pages; but the individual timetable pages don't make it explicit that only the duplex of the two lines is frequent.
(There are other segments of the system where two lines overlap for short stretches and provide service over the overlapped section that is technically "frequent"; but the remainder of these are insignificant and not marketed or documented as frequent service).
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