Pinwheel Scheduling With Tow Distinct Numbers

Holte, R., L. Rosier, I. Tulchinsky and D. Varvel, Pinwheel scheduling with two distinct numbers, Theoretical Computer Science 100 (1992) 1055135. “The Pinwheel” is a real-time scheduling problem based on a problem in scheduling satellite ground stations but which also addresses scheduling preventive maintenance. Given a multiset of positive integers A = {aI, a,, _.., a,}, a schedule S for A is an infinite sequence over { 1,2, .._, n} such that any subsequence of length a, (1 1.0 cannot be scheduled. In the present paper we limit ourselves to instances in which A contains elements having only two distinct values. We prove that all such instances with d< 1.0 can be scheduled, using a scheduling strategy based on balancing. The schedule so created is not always of minimum length, however. We use a related but more complicated method to create a minimum-length cyclic schedule, and prove its correctness. The former is computationally easier to obtain but not necessarily minimal. The latter, although still obtainable in polynomial time, requires significantly more computation. In addition, we show how to use either method to produce a fast online scheduler. Thus, we have solved completely the three major problems for this class of instances.