Fast and Tight Response-Times for Tasks with Offsets

  • Authors:
  • Jukka Maki-Turja;Mikael Nolin

  • Affiliations:
  • Mälardalen Real-Time Research Centre (MRTC);Mälardalen Real-Time Research Centre (MRTC)

  • Venue:
  • ECRTS '05 Proceedings of the 17th Euromicro Conference on Real-Time Systems
  • Year:
  • 2005

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Abstract

In previous work, we presented a tight approximate response-timeanalysis for tasks with offsets. While providing a tight boundon response times, the tight analysis exhibits similarly longexecution times as does the traditional methods for calculatingresponse-times for tasks with offsets. The existing method for fastanalysis of tasks with offsets is not applicable to the tight analysis. In this paper we extend the fast analysis to handle the distinguishing trait of the tight analysis; continuously increasing interference functions. Furthermore, we provide anotherspeedup; by introducing pessimism in the modelling of interferenceat certain points, we speed up the convergence of the numericalsolving for response-times without increasing the pessimism of theresulting responsetimes. The presented fast-and-tight analysis isguaranteed to calculate the same response-times as the tight analysis, and in a simulation study we obtain speedups of more than two orders of magnitude for realistically sized tasks sets compared to the tight analysis. We also demonstrate that the fast-and-tightanalysis has comparable execution time to that of the fast analysis.Hence, we conclude that the fast-and-tight analysis is the preferredanalysis technique when tight estimates of response-times are needed,and that we do not need to sacrifice tightness for analysis speed;both are obtained with the fast-and-tight analysis.