I thought this was cute. Though we are called 'Teachers-Teaching-on-call' here, the idea is the same...
Our system in Coquitlam calls starting at 5PM Sunday - Thursday evening and starting at 5:30am Monday - Friday. We also now hace advance call-outs so during those times it isn't just calls for the next day/same day but up to 10 days. This is nice for planning ahead, though has some problems if you accept a future call out as it may mean you can't get an earlier call that extends for longer periods / until further notice.
Every district has slightly different rules and methods of call outs, but those early morning calls are probably my least favourite thing... though they do mean work and for a TTOC, work is always a good thing!