Optimal schedules for periodically recurring events

Abstract Two periodically recurring events are to be scheduled in order to get optimal solutions for three types of objective functions: the first objective is the minimization of the maximum time between two adjacent events (e.g. minimization of maximal waiting time). In the second case the expectation value of the average waiting time is minimized and in the third case we maximize the minimal time between two adjacent events. It is shown that there exists a schedule which simultaneously optimizes these three objectives. Moreover generalizations to more than two events are discussed, in particular for the third objective function, and relations to a packing problem for residue classes are pointed out.