FPZL Schedulability Analysis

Abstract

Abstract-This paper presents the Fixed Priority until Zero Laxity (FPZL) scheduling algorithm for multiprocessor realtime systems. FPZL is similar to global fixed priority preemptive scheduling; however, whenever a task reaches a state of zero laxity it is given the highest priority. FPZL is a minimally dynamic algorithm, in that the priority of a job can change at most once during its execution, bounding the number of pre-emptions. Polynomial time and pseudopolynomial time sufficient schedulability tests are derived for FPZL. These tests are then improved by computing upper bounds on the amount of execution that each task can perform in the zero laxity state. An empirical evaluation shows that FPZL is highly effective, with a significantly larger number of tasksets deemed schedulable by the tests derived in this paper, than by state-of-the-art schedulability tests for Earliest Deadline until Zero Laxity (EDZL) scheduling.

FPSL, FPCL and FPZL schedulability analysis

“…These papers were initially published in Japanese, with an English language version of (Takeda et al, 2009) subsequently made available in May 2010 as a technical report (Kato et al, 2010). Independently, Davis and Burns (2011a) developed schedulability analysis for FPZL, initially published as a technical report in April 2010 (Davis and Burns, 2010b). The analysis given for FPZL by Davis and Burns (2011a) is applicable to constrained-deadline tasksets with no restrictions on the priority ordering which may be used; whereas the analysis given for RMZL by Kato et al, (2010) is limited to implicit-deadline tasksets with task priorities assigned in Rate Monotonic priority order.…”

“…Independently, Davis and Burns (2011a) developed schedulability analysis for FPZL, initially published as a technical report in April 2010 (Davis and Burns, 2010b). The analysis given for FPZL by Davis and Burns (2011a) is applicable to constrained-deadline tasksets with no restrictions on the priority ordering which may be used; whereas the analysis given for RMZL by Kato et al, (2010) is limited to implicit-deadline tasksets with task priorities assigned in Rate Monotonic priority order. As well as being more generally applicable, the FPZL analysis dominates, and significantly outperforms the RMZL schedulability test; see (Davis and Burns, 2011a) for a detailed discussion and empirical comparison.…”

“…These tests are used in Section 4 to derive polynomial time and pseudo-polynomial time sufficient schedulability tests for FPSL. These schedulability tests are a generalisation of the tests given by Davis and Burns (2011a) for FPZL, and also hold for FPCL. Section 4 also shows how the schedulability tests for FPSL can be improved by bounding the amount of execution that each task can perform once its priority has been promoted to the highest level.…”

“…These schedulability tests are a generalization of the tests given for FPZL by Davis and Burns (2011a). With FPZL, there are additional scheduling points whenever the laxity of a task reaches zero.…”

“…This sufficient schedulability test is a generalization of the equivalent test for FPZL given by Davis and Burns (2011a). It reduces to that test for FPZL by setting the laxity threshold i X for each task i τ to zero.…”