Utilization Bounds for Multiprocessor Rate-Monotonic Scheduling

  • Authors:
  • J. M. López;M. García;J. L. Díaz;D. F. García

  • Affiliations:
  • Departamento de Informática, Universidad de Oviedo, Gijón 33204, Spain chechu@atc.uniovi.es;Departamento de Informática, Universidad de Oviedo, Gijón 33204, Spain manuel@atc.uniovi.es;Departamento de Informática, Universidad de Oviedo, Gijón 33204, Spain jdiaz@atc.uniovi.es;Departamento de Informática, Universidad de Oviedo, Gijón 33204, Spain daniel@atc.uniovi.es

  • Venue:
  • Real-Time Systems
  • Year:
  • 2003

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Abstract

In this paper, we extend Liu and Layland’s utilization bound for fixed priority scheduling on uniprocessors to homogeneous multiprocessor systems under a partitioning strategy. Assuming that tasks are pre-emptively scheduled on each processor according to fixed priorities assigned by the Rate-Monotonic policy, and allocated to processors by the First Fit algorithm, we prove that the utilization bound is (n−1)(21/2−1)+(m−n+1)(21/(m−n+1)−1), where m and n are the number of tasks and processors, respectively. This bound is valid for arbitrary utilization factors. Moreover, if all the tasks have utilization factors under a value α, the previous bound is raised and the new utilization bound considering α is calculated. Finally, simulation provides the average-case behavior.