How is such a task?

You should read about the problems the scheduling theory.

If we assume that any transfer can only look as a whole — it will be the task of the applications (=activity-selection problem).
Solved by a greedy algorithm like this. Presume the priority of transmission and solves the classical problem about the orders: take the one that ends early, then one that ends early, and does not contradict available In the "window" with the same algorithm put less of a priority, etc.

If you believe that you can throw a used transmission. Upon the occurrence of a higher priority transfer switch to it.

Don't know what the name of this task.

Solved sorting time of events and their enumeration: in each moment we must decide to "stay / switch".

There is a priority of the current transfer (if it is not the end). And there are priorities other gear at this point (especially interested in the beginning).