New Response Time Bounds for Fixed Priority Multiprocessor Scheduling

Abstract

Recently, there have been several promising techniques developed for schedulability analysis and response time analysis for multiprocessor systems based on over-approximation. This paper contains two contributions. First, to improve the analysis precision, we apply Baruah's window analysis framework [6] to response time analysis for sporadic tasks on multiprocessor systems where the deadlines of tasks are within their periods. The crucial observation is that for global fixed priority scheduling, a response time bound of each task can be efficiently estimated by fixed-point computation without enumerating all the busy window sizes as in [6] for schedulability analysis. The technique is proven to dominate theoretically state-of-the-art techniques for response time analysis for multiprocessor systems. Our experiments also show that the technique results in significant performance improvement compared with several existing techniques for multiprocessor schedulability analysis. As the second main contribution of this paper, we extend the proposed technique to task systems with arbitrary deadlines, allowing tasks to have deadlines beyond the end of their periods. This is a non-trivial extension even for single-processor systems. To our best knowledge, this is the first work for multiprocessor systems in this setting, which involves sophisticated techniques for the characterization and computation of response time bounds.

FPSL, FPCL and FPZL schedulability analysis

“…Bertogna and Cirinei (2007) adapted this approach to iteratively compute an upper bound on the response time of each task, using the upper bound response times of other tasks to limit the amount of interference considered. Guan et al (2009) extended the response time analysis of Bertogna and Cirinei (2007) for global FP scheduling, using ideas from Baruah (2007). Burns (2009, 2010a) showed that priority assignment is fundamental to the effectiveness of global FP scheduling.…”

“…Burns (2009, 2010a) showed that priority assignment is fundamental to the effectiveness of global FP scheduling. They proved that the optimal priority assignment algorithm of Audsley (1991Audsley ( , 2001) is applicable to some of the sufficient tests developed for global FP scheduling, including the simple response time test of Andersson and Jonsson (2000) and the deadline-based test of Bertogna et al (2009), but not to others such as the response time tests of Bertogna and Cirinei (2007), and Guan et al (2009). Leung (1989) considered global Least Laxity First (LLF), referred to in that paper as the Slack Time algorithm.…”

“…Guan et al (2009) showed that if task k τ is schedulable in an interval of length L, then an upper bound on the interference over the interval due to a higher priority task i τ without a carry in job is given by:…”

“…We note that using the RTA test, task schedulability needs to be determined in priority order, highest priority first, as upper bounds on the response times of higher priority tasks are required for computation of the interference term ) Guan et al (2009) showed that at most m-1 higher priority tasks with carry-in jobs may contribute interference in the worst-case, and used this result to improve the RTA test as follows: Guan et al (2009) showed that if task i τ does not have a carry-in job, then the interference term is given by (5). The difference between the two interference terms ( (10) and (5)) is then given by:…”

Cluster scheduling for real-time systems: utilization bounds and run-time overhead

“…With the emergence of multicore processors, there is a reviving interest in the multiprocessor real-time scheduling problem and many results have been reported recently (Andersson et al 2008;Baruah and Baker 2008;Davis and Burns 2009a;Devi and Anderson 2005;Guan et al 2009Guan et al , 2010Kato and Yamasaki 2007;Levin et al 2010).…”