Then they opened their APIs, and now I have a half dozen apps to choose from that will show the approximate time until the next bus from a particular line will reach any given stop.
(Not always 100% accurate, but useful enough to know when to wait indoors for 5 min if it's raining, or pick another line/choose to walk because of delays.)
That's all speculation though.
It's a tricky one, because they have big concerns about over-promising (e.g. the bus could be stuck behind an accident instead, in which case guessing that it's 5 minutes away because of past behaviour will really annoy people) so in some situations they err on the side of caution.
But they are unable to get rid of all of the corner cases. E.g. a bus that moves rapidly for a short stretch, then gets "stuck", will often appear, disappear, appear, disappear, with much less progress in time estimates than elapsed time should indicate.
The thing is, the team working on it has a huge amount of gathered info on how to give these predictions in a way that tries to minimise surprise and avoid making promises that cause problems for people. E.g. often it's better to take a bus off the list so people who are in a hurry will grab a taxi, rather than "promise" the bus will be there in just another few minutes. They still get it wrong too often, but I really don't envy them trying to get the right balance between promising too much and too little.
I don't know about London, I've seen some systems where the stops had "live-updating signs" but only provided the time of the next official passage. And while I wasn't clear, my bug is not just stop signage but phone access as well (that's most useful when e.g. it's raining cats and dogs and you want to avoid waiting in the rain at uncovered bus stops)
Apps like 'Transit' also (accurately) show the current GPS location of the bus as it approaches, and it updated every minute (I believe)
http://reisapi.ruter.no/Help/Api/GET-StopVisit-GetDepartures...
>Returns a List of StopVisits (departures) from a Stop. If no time parameter is supplied, departures in realtime will be returned.
Consider that e.g. in London the old route indicators on the buses used odometers. Which worked for telling you were along the route a bus was. Most of the time. But didn't tell you how long it takes until the bus reaches the next stop other than on average, as it would tell you nothing about traffic etc.
Today London buses don't use just GPS to replace it either, because that's nowhere near good enough. See the "Tracking" section here [1].
Even with all the extra data, and a lot number crunching, in London it's a challenge to get it to withing a few minutes during rush hour.
So, sure, if you're dealing with simple, small systems with little congestion, you can simplify.
We had that, through GPS + GPRS (or SMS?), back in 2001-2 in a small city I was living in Europe. Complete with full (flash based) website map of where each bus is.
I used it to get out of the tech park/institute I worked at and into the bus stop outside at the very last minute (since bus timetables where completely unreliable).
Displaying the actual bus status, though, is huge progress.
On some bus routes (and/or outside of peek times) you can pay a cash fare on the buss, but even that is still a single-use paper RFID card that should be tapped on and off. These sales are in the extreme minority though - the elderly require an electronic card to get their discount IIRC.