You mentioned that the intervals are disjoint, but are they adjacent? I've had success with maintaining a "coalescing interval set" structure, where adjacent intervals are merged into a single interval. It's very, very efficient for lookups, and not terrible for insertion / removal of intervals. At the very least it might work as a view for your read-heavy processes.
You mentioned shop scheduling below as well. If your intervals represent booked time, you could also insert 'unavailable' time into the coalesced set, so that, when fully booked, the interval set is reduced to a single interval.
You mentioned shop scheduling below as well. If your intervals represent booked time, you could also insert 'unavailable' time into the coalesced set, so that, when fully booked, the interval set is reduced to a single interval.