Worst-case response time analysis of real-time tasks under fixed-priority scheduling with deferred preemption

Abstract

Fixed-priority scheduling with deferred preemption (FPDS) has been proposed in the literature as a viable alternative to fixed-priority pre-emptive scheduling (FPPS), that obviates the need for non-trivial resource access protocols and reduces the cost of arbitrary preemptions. This paper shows that existing worst-case response time analysis of hard real-time tasks under FPDS, arbitrary phasing and relative deadlines at most equal to periods is pessimistic and/or optimistic. The same problem also arises for fixed-priority nonpre-emptive scheduling (FPNS), being a special case of FPDS. This paper provides a revised analysis, resolving the problems with the existing approaches. The analysis is based on known concepts of critical instant and busy period for FPPS. To accommodate for our scheduling model for FPDS, we need to slightly modify existing definitions of these concepts. The analysis assumes a continuous scheduling model, which is based on a partitioning of the timeline in a set of non-empty, right semi-open intervals. It is shown that the critical instant, longest busy period, and worst-case response time for a task are suprema rather than maxima for all tasks, except for the lowest priority task. Hence, that instant, period, and response time cannot be assumed for any task, except for the lowest priority task. Moreover, it is shown that the analysis is not uniform for all tasks, i.e. the analysis for the lowest priority task differs from the Real-Time Syst (2009) 42: 63-119 analysis of the other tasks. These anomalies for the lowest priority task are an immediate consequence of the fact that only the lowest priority task cannot be blocked. To build on earlier work, the worst-case response time analysis for FPDS is expressed in terms of known worst-case analysis results for FPPS. The paper includes pessimistic variants of the analysis, which are uniform for all tasks, illustrates the revised analysis for an advanced model for FPDS, where tasks are structured as flow graphs of subjobs rather than sequences, and shows that our analysis is sustainable.

Exact comparison of fixed priority and EDF scheduling based on speedup factors for both pre-emptive and non-pre-emptive paradigms

“…Subsequent research by Bril et al (2009) has refined exact analysis of FP-NP, correcting issues of both pessimism and optimism, and extending the schedulability tests to co-operative scheduling where each task is made up of a number of non-pre-emptive regions.…”

“…Further, the minimum possible amount of time 8 ∆ prior to this simultaneous release, a lower priority task k  is released, and this task has the longest execution time of any such lower priority task. George et al (1996) and Bril et al (2009) showed that for fixed priority non-pre-emptive scheduling, the longest response time of a task i  occurs for some job of that task within the priority level-i busy period starting at a ∆-critical instant. Lemma 3 in (Bril et al 2009) states that the worstcase length of a priority level-i busy period i A is given by the minimum solution to the following fixed point iteration:…”

Adaptive Mixed Criticality Scheduling with Deferred Preemption

“…In general, all jobs in the busy-period at the task's priority level need to be checked to see which gives the largest response time. The analysis used by Davis and Bertogna [15] follows the approach introduced by Bril [10], [11].…”

“…(2)) with the framework given by the series of equations (5) to (11). Hence, for the LO-criticality mode, (7) becomes:…”

Using non-preemptive regions and path modification to improve schedulability of real-time traffic over priority-based NoCs

“…Saksena and Wang 2000;Wang and Saksena 1999); (2) executing certain parts of a task in a nonpreemptive manner (e.g. Bril et al 2009;Bertogna et al 2011a, b;Davis and Bertogna 2012); (3) a combination of the two former approaches (e.g. Bril et al 2012).…”