If the sequential aspect is important (i.e. FIRST request must go to FIRST available schedule), then I think a cursor will be faster than any of the alternatives. But make it one cursor (for the requests). Don't use a cursor to find the first available schedule. And if it ruuns slow, check if the query to find the first available schedule is efficient. Having a column RemainingTime in the Schedules table can help, having an index on (ScheduleType, RemainingTime) may help even more - but check that the overhead of updating this column when adding a session to a schedule doesn't hurt performance more it helps the search query.

If, on the other hand, you are looking for an algorithm to pack as many sessions in the available schedules, read my series of blog posts about "bin packing" (google for "bin packing Hugo Kornelis") - especially part 5. It's not exactly the same, but hopefully close enough to give you some pointers. The trick I used to speed up the process is to use a loop that in each iteration assigns all available schedulers a session. Maybe you can work that into your situation? However, this will totally change the order in which sessions are assigned to schedulers, so you can't use this if the order matters.