Quantifying the Sub-optimality of Uniprocessor Fixed Priority Pre-emptive Scheduling for Sporadic Tasksets with Arbitrary Deadlines

This paper examines the relative effectiveness of fixed priority pre-emptive scheduling in a uniprocessor system, compared to an optimal algorithm such as Earliest Deadline First (EDF). The quantitative metric used in this comparison is the processor speedup factor, defined as the factor by which processor speed needs to increase to ensure that any taskset that is schedulable according to an optimal scheduling algorithm can be scheduled using fixed priority pre-emptive scheduling. For implicit-deadline tasksets, the speedup factor is 1/ln(2) ≈ 1.44270. For constrained-deadline tasksets, the speedup factor is 1/Ω ≈ 1.76322. In this paper, we show that for arbitrary-deadline tasksets, the speedup factor is lower bounded by 1/Ω ≈ 1.76322 and upper bounded by 2. Further, when deadline monotonic priority assignment is used, we show that the speedup factor is exactly 2.

[1]  Michael L. Dertouzos,et al.  Control Robotics: The Procedural Control of Physical Processes , 1974, IFIP Congress.

[2]  Areej Zuhily Optimality of (D-J)-monotonic Priority Assignment , 2006 .

[3]  Alan Burns,et al.  An extendible approach for analyzing fixed priority hard real-time tasks , 1994, Real-Time Systems.

[4]  Alan Burns,et al.  Applying new scheduling theory to static priority pre-emptive scheduling , 1993, Softw. Eng. J..

[5]  Alan Burns,et al.  Quantifying the sub-optimality of uniprocessor fixed-priority scheduling , 2008 .

[6]  Neil Audsley,et al.  OPTIMAL PRIORITY ASSIGNMENT AND FEASIBILITY OF STATIC PRIORITY TASKS WITH ARBITRARY START TIMES , 2007 .

[7]  Giorgio C. Buttazzo,et al.  Rate Monotonic Analysis: The Hyperbolic Bound , 2003, IEEE Trans. Computers.

[8]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[9]  James W. Layland,et al.  Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment , 1989, JACM.

[10]  Alan Burns,et al.  Sustainable Scheduling Analysis , 2006, 2006 27th IEEE International Real-Time Systems Symposium (RTSS'06).

[11]  Aloysius Ka-Lau Mok,et al.  Fundamental design problems of distributed systems for the hard-real-time environment , 1983 .

[12]  Omri Serlin,et al.  Multiprogramming for hybrid computation , 1899, AFIPS '67 (Fall).

[13]  John P. Lehoczky,et al.  The rate monotonic scheduling algorithm: exact characterization and average case behavior , 1989, [1989] Proceedings. Real-Time Systems Symposium.

[14]  Alan Burns,et al.  Optimal (D-J)-monotonic priority assignment , 2007, Inf. Process. Lett..

[15]  Theodore P. Baker,et al.  Stack-based scheduling of realtime processes , 1991, Real-Time Systems.

[16]  Robert I. Davis,et al.  Quantifying the Sub-optimality of Uniprocessor Fixed Priority Non-Pre-emptive Scheduling , 2010 .

[17]  Giorgio C. Buttazzo,et al.  Measuring the Performance of Schedulability Tests , 2005, Real-Time Systems.

[18]  Sanjoy K. Baruah,et al.  Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor , 1990, Real-Time Systems.

[19]  Sanjoy K. Baruah,et al.  Preemptively scheduling hard-real-time sporadic tasks on one processor , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.

[20]  Mathai Joseph,et al.  Finding Response Times in a Real-Time System , 1986, Comput. J..

[21]  Alan Burns,et al.  Exact quantification of the sub-optimality of uniprocessor fixed priority pre-emptive scheduling , 2009, Real-Time Systems.

[22]  John P. Lehoczky,et al.  Fixed priority scheduling of periodic task sets with arbitrary deadlines , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.