1. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 1 André M. van Renssen, Stefan J. Geuns, Joost P.H.M. Hausmans, Wouter Poncin, and Reinder J. Bril Technische Universiteit Eindhoven (TU/e) The Netherlands On utilization bounds for a periodic resource under rate monotonic scheduling

2. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 2 Overview Scheduling model (recap) Utilization bound for RM (Shin and Lee, 2003) Example refuting existing bound Alternative approach Conclusion

3. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 3 Scheduling model (recap) Single processor; Periodic task model (Liu and Layland, 1973): –set W of m independent periodic tasks  1,  2, …,  m ; –characteristics of task  i : (release) period p i ; computation time e i ; (relative) deadline equal to period; arbitrary phasing. Rate monotonic (RM) scheduling of tasks; Periodic resource model Γ (Shin and Lee, 2003): –period Π ; –(guaranteed) allocation time Θ.

4. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 4 Utilization bound for RM Theorem (Shin and Lee, 2003): Given a periodic resource Γ(Π,Θ), a utilization bound UB Γ (RM) of the RM scheduling algorithm for a set of m periodic workloads is where p* is the shortest period of W.

5. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 5 Example refuting existing bound TaskPeriod p Computation time e 11 1001 22 1501 Periodic resource: Γ(60,10) Conclusion: Existing utilization bound is optimistic!

6. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 6 Alternative approach Model unavailability as a Deferrable Server –Period Π ; –Computation time Π–Θ ; –(Activation jitter Θ ). Utilization bound (Lehoczky, Sha, and Strosnider, 1987):

7. ECRTS/WiP, July 2009 André M. van Renssen, a.m.v.renssen@student.tue.nl TU/e, Mathematics & Computer Science 7 Conclusion Presentation and poster: –example refuting existing utilization bound; –alternative approach based on unavailability of the periodic resource; –reuse of existing bounds. Paper: –additional errors in existing bounds; –future work.