Thanks for the replies so far. A few examples from Bluestar, as I started the thread.
The Totton side in particular seems to have somewhat unpredictable interworking. There are some common patterns, e.g. the 11 and 12 interworking, and the 8 interworking with one of the two 4s per hour, but there are plenty of exceptions. The 9 is often self-contained but in some half-hours interworks with other Totton routes. All of the Totton routes, except the 17 (double-decker only) appear to be a mixture of single- and double-deckers.
The 4 is probably the most "random" as it interworks with a range of different routes as well as occasionally working out again as a 4, is operated by both single- and double-deckers, and for extra points it gets some Empress Road as well as Totton workings. Wide range of vehicles too.
The Empress Road side has more in the way of self-contained routes, plus the 10, 13 and 14 which generally interwork on a particular pattern (4 workings do 10-14-13-10-repeat while 3 do the 13 and 14 alternately). However from around 1pm the pattern is disrupted and becomes more "random". Later in the afternoon some interworking of this group of routes with the 20 occurs, which means single-deckers appearing on some 20 journeys and double-deckers on some 13 and 14 journeys.
There is also occasional interworking between the 3 and 16.
That said, Bluestar seem to change, or at least tweak, their workings around 6 times a year, after every school holiday and half-term - so some details may change again after the Easter holidays.
Singles do appear on the 120 as well - albeit sporadically, so I assume that's more of an ad-hoc arrangement when not enough deckers are available.
There doesn't seem to be a way of finding out what type of vehicle is allocated to a particular working (unless it's in open data?) so often it's a case of just inferring it from bustimes based on what it is the majority of the time.
That said there is one Bluestar working (working S25, involving the 20, 14, 15 and 16) which I can't figure out as it seems to be almost 50:50. For example, last week, double-deck Mon-Wed and single-deck Thurs-Fri. Other weeks have a similar mix.
ADL Enviro200 MMC
bustimes.org