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Real-Time Systems

, Volume 35, Issue 2, pp 135–151 | Cite as

Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling

  • Lars Lundberg
  • Håkan Lennerstad
Article

Abstract

We provide a constant time schedulability test for an on-line multiprocessor server handling aperiodic tasks. Dhall's effect is avoided by dividing the tasks in two priority classes based on task utilization: heavy and light. We prove that if the load on the multiprocessor server stays below U threshold = 3 − √7 ≈ 35.425%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. The same number 35.425% is also a threshold for a task to be characterized as heavy.

The bound U threshold = 3 − √7≈ 35.425% is easy-to-use, but not sharp if we know the number of processors in the multiprocessor system. Assuming the server to be equipped with m processors, we calculate a formula for the sharp bound U threshold (m), which converges to U threshold from above as m → ∞.

The results are based on a utilization function u(x) = 2(1 − x)/(2 + √2+2x). By using this function, the performance of the multiprocessor server can in some cases be improved beyond U threshold(m) by paying the extra overhead of monitoring the individual utilization of the current tasks.

Keywords

Multiprocessor Scheduling Aperiodic Dhalls effect Optimal threshold Synthetic utilization 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Systems and Software, School of EngineeringBlekinge Institute of TechnologyRonnebySweden

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