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Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling

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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 − √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.

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Authors and Affiliations

  1. Department of Systems and Software, School of Engineering, Blekinge Institute of Technology, 372 25, Ronneby, Sweden

    Lars Lundberg & Håkan Lennerstad

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  1. Lars Lundberg
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  2. Håkan Lennerstad
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Correspondence to Lars Lundberg.

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Lars Lundberg is currently a full professor in computer systems engineering at Blekinge Institute of Technology, Sweden. He received his Ph.D. in Computer Engineering 1993 at Lund University, Sweden. His research interests include real-time systems, high performance computing, and software engineering. Lars is the author or coauthor of more than 100 peer reviewed articles in international journals and conferences.

Håkan Lennerstad is currently an associate professor in mathematics at Blekinge Institute of Technology, Sweden. He recieved his Ph.D. in mathematics 1990 at Chalmers Institute of Technology, Sweden. His interests include partial differential equations and combinatorics that appear from essential computer science scenarios. Hehas also been active in philosophy of mathematics and mathematics didactics.

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Lundberg, L., Lennerstad, H. Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling. Real-Time Syst 35, 135–151 (2007). https://doi.org/10.1007/s11241-006-9005-y

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  • DOI: https://doi.org/10.1007/s11241-006-9005-y

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