Utilization Bounds for N-Processor Rate MonotoneScheduling with Static Processor Assignment

  • Authors:

  • Dong-Ik Oh;T. P. Bakker

  • Affiliations:

  • Dept. of Computer Science, Soonchunhyang University, Asan, Korea;Department of Computer Science, Florida State University, Tallahassee, FL 32306-4530

  • Venue:
  • Real-Time Systems
  • Year:
  • 1998

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Abstract

We consider the schedulability of a set of independentperiodic tasks under fixed priority preemptive scheduling onhomogeneous multiprocessor systems. Assuming there is no taskmigration between processors and each processor schedules taskspreemptively according to fixed priorities assigned by the RateMonotonic policy, the scheduling problem reduces to assigning theset of tasks to disjoint processors in such a way that theMonotonic policy, the scheduling problem reduces to assigning theset of tasks to disjoint processors in such a way that theschedulability of the tasks on each processor can be guaranteed.In this paper we show that the worst case achievable utilizationfor such systems is between n(2^{1/2}-1) and(n+1)/(1+2^{1/(n+1)}), where n stands for the number ofprocessors. The lower bound represents 41 percent of the totalsystem capacity and the upper bound represents 50 to 66 percentdepending on n. Practicality of the lower bound is demonstratedby proving it can be achieved using a First Fit schedulingalgorithm.