Dependency Graph Approach for Multiprocessor Real-Time Synchronization

Abstract

Over the years, many multiprocessor locking protocols have been designed and analyzed. However, the performance of these protocols highly depends on how the tasks are partitioned and prioritized and how the resources are shared locally and globally. This paper answers a few fundamental questions when realtime tasks share resources in multiprocessor systems. We explore the fundamental difficulty of the multiprocessor synchronization problem and show that a very simplified version of this problem is N P -hard in the strong sense regardless of the number of processors and the underlying scheduling paradigm. Therefore, the allowance of preemption or migration does not reduce the computational complexity. For the positive side, we develop a dependency-graph approach, that is specifically useful for framebased real-time tasks, in which all tasks have the same period and release their jobs always at the same time. We present a series of algorithms with speedup factors between 2 and 3 under semi-partitioned scheduling. We further explore methodologies and tradeoffs of preemptive against non-preemptive scheduling algorithms and partitioned against semi-partitioned scheduling algorithms. The approach is extended to periodic tasks under certain conditions.

Scheduling of Real-Time Tasks With Multiple Critical Sections in Multiprocessor Systems

“…Whether there exists a polynomial-time algorithm with a constant approximation ratio for the general F M ||C max or J M ||C max problem remained open until 2011, when Mastrolilli and Svensson [29] showed that F M ||C max (and hence J M ||C max ) does not admit any polynomial-time approximation algorithm with a constant approximation ratio. Moreover, they also showed that the lower bound on the Chen et al in [11] M ≥ n + 1, any scheduling paradigm approximation ratio is very close to the existing upper bound provided by Goldberg et al [18].…”

“…Chen et al [11] showed that a special case of the MMSS makespan problem is N P -hard in the strong sense when a task has only one critical section and M is sufficiently large. The following theorem shows that the MMSS schedulability problem is N P -complete when there are only two critical sections per task and the critical sections are with unit execution time.…”

“…Since our approach is an extension of the DGA by Chen et al [11], and Shi et al [36], our implementation is based on the source code the authors provided online [35], i.e., it is implemented under the plug-in Partitioned EDF with synchronization support (PSN-EDF), called P-DGA-JS, and the plug-in Global EDF with synchronization support (GSN-EDF), denoted G-DGA-JS.…”

“…http://www.rtems.org/ time systems has been the design and analysis of resource sharing protocols, where the protocols decide the order in which the new incoming requests access the shared resources dynamically. Contrarily, the Dependency Graph Approaches (DGA), that was proposed by Chen et al [11] in 2018, pre-computes the order in which tasks are allowed to access resources, and consists of two individual steps: 1) A dependency graph is constructed to determine the execution order of the critical sections guarded by one binary semaphore or mutex lock. 2) Multiprocessor scheduling algorithms are applied to schedule the tasks by respecting the constraints given by the constructed dependency graph(s).…”

“…Chen et al [11] showed significant improvement against existing protocol-based approaches from the empirical as well as from the theoretical perspective, and demonstrated the practical applicability of the DGA by implementing it in LITMUS RT [5], [9]. However, the original dependency graph approaches presented in [11] has two strong limitations: 1) the construction in the first step allows only one critical section per task, and 2) the presented algorithms can only be applied for frame-based real-time task systems, i.e., all tasks have the same period and release their jobs always at the same time. The latter has been recently removed by Shi et al [36], who applied the DGA after unrolling the jobs in the hyper-period.…”