General Schedulers for the Pinwheel Problem Based on Double-Integer Reduction

The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance) A=(a/sub 1/, . . . a/sub n/), the problem is to find an infinite sequence (schedule) of symbols from (1,2, . . . n) such that there is at least one symbol i within any interval of a/sub i/ symbols (slots). Not all instances A can be scheduled; for example, no 'successful' schedule exists for instances whose density is larger than 1. It has been shown that any instance whose density is less than 2/3 can always be scheduled. Two new schedulers are proposed which improve this 2/3 result to a new 0.7 density threshold. These two schedulers can be viewed as a generalization of the previously known schedulers, i.e. they can handle a larger class of pinwheel instances including all instances schedulable by the previously known techniques. >