Open Problem Resolved: The "Two" in Existing Multiprocessor PI-Blocking Bounds Is Fundamental

Authors Shareef Ahmed , James H. Anderson

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Shareef Ahmed
  • University of North Carolina at Chapel Hill, NC, USA
James H. Anderson
  • University of North Carolina at Chapel Hill, NC, USA

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Shareef Ahmed and James H. Anderson. Open Problem Resolved: The "Two" in Existing Multiprocessor PI-Blocking Bounds Is Fundamental. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


The goal of a real-time locking protocol is to reduce any priority-inversion blocking (pi-blocking) a task may incur while waiting to access a shared resource. For mutual-exclusion sharing on an m-processor platform, the best existing lower bound on per-task pi-blocking under suspension-oblivious analysis is a (trivial) lower bound of (m-1) request lengths under any job-level fixed-priority (JLFP) scheduler. Surprisingly, most asymptotically optimal locking protocols achieve a per-task pi-blocking upper bound of (2m-1) request lengths under JLFP scheduling, even though a range of very different mechanisms are used in these protocols. This paper closes the gap between these existing lower and upper bounds by establishing a lower bound of (2m-2) request lengths under global fixed-priority (G-FP) and global earliest-deadline-first (G-EDF) scheduling. This paper also shows that worst-case per-task pi-blocking can be arbitrarily close to (2m-1) request lengths for locking protocols that satisfy a certain property that is met by most (if not all) existing locking protocols. These results imply that most known asymptotically optimal locking protocols are almost truly optimal (not just asymptotic) under G-FP and G-EDF scheduling.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • Real-Time Systems
  • Real-Time Synchronization
  • Multiprocessors


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