Scheduling Periodic Tasks in a Hard Real-Time Environment

  • Friedrich Eisenbrand
  • Nicolai Hähnle
  • Martin Niemeier
  • Martin Skutella
  • José Verschae
  • Andreas Wiese
Conference paper

DOI: 10.1007/978-3-642-14165-2_26

Volume 6198 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Eisenbrand F., Hähnle N., Niemeier M., Skutella M., Verschae J., Wiese A. (2010) Scheduling Periodic Tasks in a Hard Real-Time Environment. In: Abramsky S., Gavoille C., Kirchner C., Meyer auf der Heide F., Spirakis P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg

Abstract

We give a rigorous account on the complexity landscape of an important real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks τi = (ci,pi) on a minimum number of identical machines and to compute offsets ai for the tasks such that no collision occurs. A task τi releases a job of running time ci at each time \(a_i + k\cdot p_i, \, k \in {\mathbb N}_0\) and a collision occurs if two jobs are simultaneously active on the same machine. Our main results are as follows: (i) We show that the minimization problem cannot be approximated within a factor of n1 − ε for any ε> 0. (ii) If the periods are harmonic (for each i,j one has pi |pj or pj |pi), then there exists a 2-approximation for the minimization problem and this result is tight, even asymptotically. (iii) We provide asymptotic approximation schemes in the harmonic case if the number of different periods is constant.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Friedrich Eisenbrand
    • 1
  • Nicolai Hähnle
    • 1
  • Martin Niemeier
    • 1
  • Martin Skutella
    • 2
  • José Verschae
    • 2
  • Andreas Wiese
    • 2
  1. 1.EPFLLausanneSwitzerland
  2. 2.TU BerlinGermany