The pinwheel: a real-time scheduling problem

Some satellites transmit a piece of information for a set duration, then proceed with another piece of information. A ground station receiving from several such satellites and wishing to avoid data loss faces a real-time scheduling problem. The pinwheel is a formalization of this problem. Given a multiset A of integers=( a₁, a₂, . . ., a_n ), a successful schedule S is an infinite sequence over {1, 2, . . ., n} such that any subsequence of a_i (1⩽i⩽n) consecutive entries (slots) contains at least one i. The pinwheel decision problem concerns whether a useful representation of the corresponding schedule exists. Several results thus far established for these problems are reported