Worstcase response time analysis of realtime tasks under fixedpriority scheduling with deferred preemption
 Reinder J. Bril,
 Johan J. Lukkien,
 Wim F. J. Verhaegh
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Abstract
Fixedpriority scheduling with deferred preemption (FPDS) has been proposed in the literature as a viable alternative to fixedpriority preemptive scheduling (FPPS), that obviates the need for nontrivial resource access protocols and reduces the cost of arbitrary preemptions.
This paper shows that existing worstcase response time analysis of hard realtime tasks under FPDS, arbitrary phasing and relative deadlines at most equal to periods is pessimistic and/or optimistic. The same problem also arises for fixedpriority nonpreemptive 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 nonempty, right semiopen intervals. It is shown that the critical instant, longest busy period, and worstcase 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 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 worstcase response time analysis for FPDS is expressed in terms of known worstcase 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.
 Title
 Worstcase response time analysis of realtime tasks under fixedpriority scheduling with deferred preemption
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

RealTime Systems
Volume 42, Issue 13 , pp 63119
 Cover Date
 200908
 DOI
 10.1007/s112410099071z
 Print ISSN
 09226443
 Online ISSN
 15731383
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Leveli active period
 Leveli busy period
 Worstcase response time
 Worstcase occupied time
 Periodic tasks
 Fixedpriority scheduling
 Deferred preemption
 Realtime systems
 Industry Sectors
 Authors

 Reinder J. Bril ^{(1)}
 Johan J. Lukkien ^{(1)}
 Wim F. J. Verhaegh ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven (TU/e), Den Dolech 2, 5600 AZ, Eindhoven, The Netherlands
 2. Philips Research Laboratories, High Tech Campus 11, 5656 AE, Eindhoven, The Netherlands