A pre-order relation for exact schedulability test of sporadic tasks on multiprocessor Global Fixed-Priority scheduling

Abstract

International audienceIn this paper we present an exact schedulability test for sporadic real-time tasks scheduled by the Global Fixed Priority (G-FP) Fully Preemp-tive Scheduler on a multiprocessor system. The analysis consists in mod-eling the system as a Linear Hybrid Automaton (LHA), and in performing a reachability analysis for states representing deadline miss conditions. To mitigate the problem of state space explosion, we propose a pre-order relationship over the symbolic states of the model: states that are simulated by others can be safely eliminated from the state space. We also formulate the concept of decidability interval with respect to a set of constrained-deadline sporadic tasks on multiprocessor. The decidability interval is a bounded time interval such that, if a deadline miss occurs in the schedule, then it is possible to find a configuration of arrival times for the tasks such that the deadline miss happens within the bounded interval. Vice versa, if no configuration of arrival times produces a deadline miss in the bounded interval, then no deadline miss is ever possible in the schedule. Hence we prove that the schedulability analysis problem is decidable, and we provide a formula for computing the decidability interval. To our knowledge, this is the first time such a time interval is proposed for sporadic tasks running on multiprocessor. The proposed schedulability analysis has been implemented in a software tool. For the first time we assess the pessimism of the state-of-the-art approximate schedulability test through experiments. Moreover, we show * This paper has been accepted by the Real Time Systems Journal. This is the submitted version, the final accepted version is avaliable at the journal's web site

On the Trade-offs between Generalization and Specialization in Real-Time Systems

“…Consider, for example, global and partitioned multiprocessor scheduling. Some exact schedulability tests for global static-priority [63], [65] and global EDF [12], [19], [39] scheduling are known, but their scalability is such that they cannot be applied to anything more than toy examples (from an industrial perspective). When sufficient schedulability tests are used, the current state-of-the-art analyses for global scheduling, both for static-priority [31], [40], [41], [63] and EDF [11], [13], [64], stem from the seminal work by Baker [10], which leads to an interference upper bound with a multiplicative factor of 1/m in the resulting tests, where m is the number of processors.…”

Schedulability Analysis of Distributed Multicore Avionics Systems with UPPAAL

“…They adopt a dynamic server algorithm, separating each server from the rest of the system, and thereby enabling component-based scheduling analysis. This method is subsequently applied to a multicore global scheduling system and extended with a weak simulation in [25] to reduce the state space of complex models. The approaches of [26,27] use TA to describe a hierarchical scheduling system, while both of them are limited to periodic tasks isolated from each other.…”

On the ineffectiveness of 1/m-based interference bounds in the analysis of global EDF and FIFO scheduling

“…the state-of-the-art) and exact test for G-FP by relying on accurate statespace pruning. Sun and Lipari [44,45] proposed an exact analysis for G-FP by modeling the system as a linear hybrid automaton. The authors identified a pre-order relationship over the symbolic states of the model to mitigate the problem of state space explosion.…”

“…Also, their corresponding schedulability problems have been proven to be PSPACE-complete by Geeraerts et al [27]. To date, all the techniques that allow implementing exact schedulability tests for G-FP [44,45] and G-EDF [3,27,14] suffer from severe scalability issues, and many of them can produce a result in a reasonable amount of time only when the task parameters belong to fairly limited ranges (e.g., see the experimental results in [17]).…”