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Pinwheel scheduling with two distinct numbers

  • Robert Holte
  • Louis Rosier
  • Igor Tulchinsky
  • Donald Varvel
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 379)

Abstract

“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 = {a1, a2, ..., a n }, a schedule S for A is an infinite sequence over {1, 2, ..., n} such that any subsequence of length a i (1 ≤ in) contains at least one i. Schedules can always be made cyclic; that is, a segment can be found that can be repeated indefinitely to form an infinite schedule. Interesting questions include determining whether schedules exist, determining the minimum cyclic schedule length, and creating an online scheduler. The “density” of an instance is defined as \(d = \sum\nolimits_{i = 1}^n {1/a} _i\). It has been shown that any instance with d > 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.

Keywords

Schedule Problem Schedule Algorithm Integer Linear Programming Schedule Strategy Periodic Maintenance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    R. Holte, A. Mok, L. Rosier, I. Tulchinsky, D. Varvel, “The Pinwheel: A Real-Time Scheduling Problem,” Proceedings of the 22nd Hawaii International Conference on System Science, pp. 693–702, Kailua-Kona, January 1989.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Robert Holte
    • 1
  • Louis Rosier
    • 1
  • Igor Tulchinsky
    • 1
  • Donald Varvel
    • 1
  1. 1.Department of Computer SciencesThe University of Texas at AustinAustin

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