While waiting for the AATA's mobile ridetrak system to go back online (it's been down for two weeks now due to a series of unfortunate events), I've been thinking about how to model the network of bus and pedestrian routes so that you could say some useful things about the goodness of a given route network for a particular task at a particular time of day. What I'm after is understanding just how far I can reasonably go from where I am to somewhere else useful based on bus routes, my willingness or ability to walk, and the minute by minute information about how late the bus is.
Frankly, this is a complex set of questions to answer, especially if you're unwilling to wait outside for the bus and if you're willing to ride unfamiliar buses to new destinations. Most people figure out how a single route does between two places at two particular times, sorting through the commuter problem and coming up with a rough rule of thumb that depends on the bus being more or less predictably late. By the time you sort through all of the details to get somewhere new, the bus might have gone by.
Some observations, numbered, probably requiring each of them to have more details.
1. Always carry a paper schedule. If the bus computer system is down again, or your phone is out of battery, a piece of paper no matter how confusing is probably better than nothing.
2. Some places are better to wait than others. The cost of being wrong about a bus when you're at the Blake Transit Center is small, because there's a warm place to wait and because there are six buses an hour that go to or near enough to my house to be reasonable to get on. Contrairiwise, missing a bus by 1 minute on some routes might mean you would wait for an hour (or more).
3. Close by stops might really be far away. This is a function of pedestrian access - if you need to cross a busy street to get to a stop, it might take two, three, or five minutes to cross between lights and perhaps even a 20 minute hike if you look at the worst pedestrian crossing (Washtenaw at Platt). A naive pedestrian distance measure is going to be wrong.
4. All roads lead to downtown. With a few exceptions, the Ann Arbor route system is about getting people to the center of Ann Arbor. You'll have a lot better luck getting anywhere if you go downtown first and use it as the base of operations. I looked at "optimal routes" from home to some places nearby and the best way to get there was a 20+ minute walk, and there are too many destinations where the trip by bus is 40+ minutes for what is a 10 minute drive.
5. The University bus system, although frequent, is not integrated with the AATA system. This is most notable when you look at Google Transit to plan a trip and notice that it doesn't ever put you on a UM bus. Many of the UM buses run frequently enough during my time to use them that no schedule is necessary, but you have to always be prepared to do a transfer of a random, maximum time if you're switching lines.
The model that I had in mind for looking at this whole system was to make a big graph, with each node on the graph being a plausible location to be at and the edges being the time to go to the next node. There would be a pedestrian network reflecting the sidewalks and bus stops, and a bus network overlaid on top of it where if you were on the bus you could move from node to node but if you weren't on the bus you'd have to wait. Some nodes would be warm (cafes, libraries) and some would be cold and slushy (most bus stops).
This graph becomes the playing board for a big urban game. You and all of the other players start at various points on the board, and each minute you take a turn either walking to a next node, staying still where you are, or riding on a bus. The winner after 60 turns is the person who managed to get the highest score - whether it be maximum minutes on a bus, maximum distance from origin, maximum distance walking, interesting destinations reached, or any other measure you'd like to score. Minus points for wet boots. Double minus points for missing the kids pickup from day care.
As you can see from thinking about this game a little bit, you can play a lot more effectively if you know where all of the buses are. Instead of getting negative points for the boot-minutes you spend shivering at the stop, you can accumulate credits indoors until the last minute necessary to get outside. Knowing that an infrequent bus is close by lets you get bonus points for going to stops that are close by but not often served, and it lets you avoid missed connections where the schedule says you can get from one line to another but you won't make that connection when the outbound line is late.
I'm collecting a bunch of links about this on delicious - see http://delicious.com/vielmetti/where-is-my-fracking-bus for my idiosyncratic collection, and more generally if you are looking at transportation literature a key term is automatic vehicle location. Route planning sits on top of that, and the best current summary of the state of the world is from Andrew Turner's summary of the state of transit routing in 2008.