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.
 Audsley NC, Burns A, Richardson MF, Wellings AJ (1991) Hard realtime scheduling: The deadline monotonic approach. In: Proc of the 8th IEEE workshop on realtime operating systems and software (RTOSS), May 1991, pp 133–137
 Baeten, JCM, Middelburg, CA (2002) Process algebra with timing. Springer, Berlin
 Baruah S (2005) The limitedpreemption uniprocessor scheduling of sporadic systems. In: Proc of the 17th Euromicro conference on realtime systems (ECRTS), July 2005, pp 137–144
 Baruah S, Burns A (2006) Sustainable schedulability analysis. In: Proc of the 27th IEEE realtime systems symposium (RTSS), December 2006, pp 159–168
 Baruah SK, Mok AK, Rosier LE (1990a) Preemptively scheduling hardrealtime sporadic tasks on one processor. In: Proc of the 11th IEEE realtime systems symposium (RTSS), December 1990, pp 182–190
 Baruah, SK, Rosier, LE, Howell, RR (1990) Algorithms and complexity concerning the preemptive scheduling of periodic, realtime tasks on one processor. RealTime Syst 2: pp. 301324 CrossRef
 Bril RJ (2004) Realtime scheduling for media processing using conditionally guaranteed budgets. PhD thesis, Technische Universiteit Eindhoven (TU/e), The Netherlands. http://alexandria.tue.nl/extra2/200412419.pdf
 Bril RJ (2006) Existing worstcase response time analysis of realtime tasks under fixedpriority scheduling with deferred preemption is too optimistic. Technical report CS 0605, Department of Mathematics and Computer Science, Technische Universiteit Eindhoven (TU/e), The Netherlands, February 2006
 Bril RJ, Verhaegh WFJ, Lukkien JJ (2004) Exact worstcase response times of realtime tasks under fixedpriority scheduling with deferred preemption. In: Proc of the workinprogress (WiP) session of the 16th Euromicro conference on realtime systems (ECRTS), Technical report from the University of NebraskaLincoln, Department of Computer Science and Engineering (TRUNLCSE20040010), June 2004, pp 57–60
 Bril RJ, Lukkien JJ, Davis RI, Burns A (2006) Message response time analysis for ideal controller area network (CAN) refuted. In: Proc of the 5th international workshop on real time networks (RTN), July 2006, pp 13–18
 Bril RJ, Lukkien JJ, Verhaegh WFJ (2007) Worstcase response time analysis of realtime tasks under fixedpriority scheduling with deferred preemption revisited. In: Proc of the 19th Euromicro conference on realtime systems (ECRTS), July 2007, pp 269–279
 Burns, A Preemptive priority based scheduling: An appropriate engineering approach. In: Son, S eds. (1994) Advances in realtime systems. PrenticeHall, Englewood Cliffs, pp. 225248
 Burns, A (2001) Defining new nonpreemptive dispatching and locking policies for Ada. Proc of the 6th AdaEurope international conference, May 2001. Springer, Berlin, pp. 328336
 Burns A, Wellings AJ (1997) Restricted tasking models. In: Proc of the 8th international realtime Ada workshop, pp 27–32
 Burns A, Nicholson M, Tindell K, Zhang N (1993) Allocating and scheduling hard realtime tasks on a pointtopoint distributed system. In: Proc of the 1st workshop on parallel and distributed realtime systems, April 1993, pp 11–20
 Buttazzo, GC (2005) Hard realtime computing systems—predictable scheduling algorithms and applications. Springer, Berlin
 Davis, RI, Burns, A, Bril, RJ, Lukkien, JJ (2007) Controller area network (CAN) schedulability analysis: refuted, revisited and revised. RealTime Syst 35: pp. 239272 CrossRef
 George L, Rivierre N, Spuri M (1996) Preemptive and nonpreemptive realtime uniprocessor scheduling. Technical report 2966, Institut National de Recherche en Informatique et en Automatique (INRIA), France, September 1996
 González Harbour M, Klein MH, Lehoczky JP (1991) Fixedpriority scheduling with varying execution priority. In: Proc of the 12th IEEE realtime systems symposium (RTSS), December 1991, pp 116–128
 Gopalakrishnan R, Parulkar GM (1996) Bringing realtime scheduling theory and practice closer for multimedia computing. In: Proc of the ACM Sigmetrics conference on measurement & modeling of computer systems, May 1996, pp 1–12
 Hermant JF, Leboucher L, Rivierre N (1996) Realtime fixed and dynamic priority driven scheduling algorithms: theory and practice. Technical report 3081, Institut National de Recherche en Informatique et en Automatique (INRIA), France, December 1996
 Hooman J (1991) Specification and compositional verification of realtime systems. PhD thesis, Technische Universiteit Eindhoven (TU/e), The Netherlands
 Joseph, M, Pandya, P (1986) Finding response times in a realtime system. Comput J 29: pp. 390395 CrossRef
 Klein, MH, Ralya, T, Pollak, B, Obenza, R, González Harbour, M (1993) A practitioner’s handbook for realtime analysis: guide to rate monotonic analysis for realtime systems. Kluwer Academic, Dordrecht
 Koymans, R (1990) Specifying realtime properties with metric temporal logic. RealTime Syst 2: pp. 255299 CrossRef
 Lee, S, Lee, CG, Lee, M, Min, SL, Kim, CS (1998) Limited preemptible scheduling to embrace cache memory in realtime systems. Proc of the ACM Sigplan workshop on languages, compilers and tools for embedded systems (LCTES), June 1998. Springer, Berlin, pp. 5164
 Lehoczky JP (1990) Fixed priority scheduling of periodic task sets with arbitrary deadlines. In: Proc of the 11th IEEE realtime systems symposium (RTSS), December 1990, pp 201–209
 Liu, JWS (2000) Realtime systems. PrenticeHall, Englewood Cliffs
 Liu, CL, Layland, JW (1973) Scheduling algorithms for multiprogramming in a realtime environment. J ACM 20: pp. 4661 CrossRef
 Mok AKL (1983) Fundamental design problems of distributed systems for the hardrealtime environment. PhD thesis, Massachusetts Institute of Technology. http://www.lcs.mit.edu/publications/pubs/pdf/MITLCSTR297.pdf
 Mok AK, Poon WC (2005) Nonpreemptive robustness under reduced system load. In: Proc of the 26th IEEE realtime systems symposium (RTSS), December 2005, pp 200–209
 Regehr J (2002) Scheduling tasks with mixed preemption relations for robustness to timing faults. In: Proc of the 23rd IEEE realtime systems symposium (RTSS), December 2002, pp 315–326
 Sha, L, Rajkumar, R, Lehoczky, JP (1990) Priority inheritance protocols: an approach to realtime synchronisation. IEEE Trans Comput 39: pp. 11751185 CrossRef
 Simonson J, Patel JH (1995) Use of preferred preemption points in cachebased realtime systems. In: Proc of the IEEE international computer performance and dependability symposium (IPDS), April 1995, pp 316–325
 Spuri M (1996) Analysis of deadline scheduled realtime systems. Technical report 2772, Institut National de Recherche en Informatique et en Automatique (INRIA), France, January 1996
 Tindell K, Burns A (1994) Guaranteeing message latencies on controller area network (CAN). In: Proc of the 1st international CAN conference, September 1994, pp 1–11
 Tindell K, Hansson H, Wellings AJ (1994) Analysing realtime communications: Controller area network (CAN). In: Proc of the 15th IEEE realtime systems symposium (RTSS), December 1994, pp 259–263
 Tindell, K, Burns, A, Wellings, AJ (1995) Calculating controller area network (CAN) message response times. Control Eng Pract 3: pp. 11631169 CrossRef
 Wang Y, Saksena M (1999) Scheduling fixedpriority tasks with preemption threshold. In: Proc of the 6th international conference on realtime computing systems and applications (RTCSA), December 1999, pp 328–335
 Weisstein EW (2003) CRC Concise Encyclopedia of Mathematics. Chapman & Hall/CRC, London
 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
 20090801
 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