Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling

  • Authors:
  • Lars Lundberg;Håkan Lennerstad

  • Affiliations:
  • Department of Systems and Software, School of Engineering, Blekinge Institute of Technology, Ronneby, Sweden 372 25;Department of Systems and Software, School of Engineering, Blekinge Institute of Technology, Ronneby, Sweden 372 25

  • Venue:
  • Real-Time Systems
  • Year:
  • 2007

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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 驴 驴7 驴 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 驴 驴7驴 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 驴 驴.The results are based on a utilization function u(x) = 2(1 驴 x)/(2 + 驴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.