Bounding Preemption Delay within Data Cache Reference Patterns for Real-Time Tasks

1. Harini Ramaprasad, Frank MuellerNorth Carolina State UniversityCenter for Embedded Systems Research Bounding Preemption Delay within Data Cache Reference Patterns for Real-Time Tasks

2. Motivation • Timing Analysis • Calculation of Worst Case Execution Times (WCETs) of tasks • Required for scheduling of real-time tasks • Schedulability theory requires a-priori knowledge of WCET • Estimates need to be safe • Static Timing Analysis – an efficient method to calculate WCET of a program! • Data caches introduce unpredictability in timing analysis • Data caches: • Improve Performance Significantly • Complicate Static Timing Analysis for a task

3. Preemptive scheduling • Practical Real-Time systems • Multiple tasks with varying priorities • Higher prio. task may preempt a lower prio. task at any time • Additional DC misses occur when lower prio. task restarted • WCET with preemption delay required Static Timing Analysis becomes even more complicated!

4. Data Cache Reference Patterns (Prior Work) • Data Cache Analyzer added to Static Timing Analysis framework • Enhanced Cache Miss Equations (Ghosh et al.) framework  D$miss/hit patterns for memory references • Used for loop-nest oriented code • Scalar and array references analyzed • Considers only a single task with no preemptions • Patterns fed to timing analyzer to tighten WCET estimate • Necessary terminology: • Iteration point • Represents an iteration of a loop-nest • Set of all iteration points – Iteration Space

5. Static Timing Analyzer Framework

6. Methodology • Task Schedulability  Response Time Analysis used • Steps involved in calculation of WCET with preemption delay • Calculate max. # of preemptions possible for a task • Identify placement of preemption points in iteration space • Calculate preemption delay at a certain point

7. Methodology: Analysis Phases • Phase 1: Single-Task Analysis • For every task • Calculate Base Time • Build D$ Reference Patterns assuming NO preemptions Performed once for every task • Phase 2: Preemption Delay Calculation (in task-set context) • Step 1: Identification of preemption points • Step 2: Calculation of WCET with preemption delay Performed once for a task in context of task-set

8. Phase 2: Preemption Delay Calculation • Max # of preemption points for task Ti • For every higher priority task, Tj • Find max time Tj can preempt Ti • Subtract this from time rem. before deadline of Ti • Termination • No more higher priority tasks • No time left before deadline (whichever occurs first) • Sum of gives max # of preemptions For T1: No hp task. # preemptions = 0 For T2: Trem = 100 – (2 * 8) = 84 No more hp tasks # preemptions = 2 For T3 Trem = 200 – (4 * 8) = 168 Trem = 168 – (2 * 10) = 148 No more hp tasks #preemptions = 4 + 2 = 6

9. Phase 2: Preemption Delay Calculation • Identification of preemption points • Access Chain building • Build time-ordered list of all mem. refs in task • Connect all refs accessing same D$ set to form chain • Different cache sets shown with different colors • Assign weights to every access point • Weight • # distinctly colored chains that cross the point • indicates # misses if preemption at that point • Count only chains for D$ sets used by a higher prio. task • Count only if next point in chain is a HIT

10. Phase 2: Preemption Delay Calculation • Calculation of WCET with preemption delay • Identification of worst-case preemption scenario • General Observation: • Large chunk of iter. pts. have max. preemption delay • Reason: high temporal/spatial reuse in code • Considering n highest costs gives upper bound on delay • n = max # of preemptions for task

11. Distribution of preemption costs

12. Experimental Results – Task Set 1 • Without delay, seems schedulable • Adding delay to response time  safe • Above task-set is actually unschedulable!

13. Ratios – Task Set 1 • Preemption delay calculation: • No significant change in R/WCET factor • Increase in WCET itself is significant •  pessimistic analysis

14. Spreading preemption points – key idea • Find n most expensive points • Spread them out in the iteration space

15. Related Work • S. Basumallick and K. Nilsen. Cache issues in real-time systems. in ACM SIGPLAN Workshop on Language, Compiler, and Tool Support for Real-Time Systems, 1994. • C.-G. Lee, J. Hahn, Y.-M. Seo, S. L. Min, R. Ha, S. Hong, C. Y. Park, M. Lee, and C. S. Kim. Analysis or cache-related preemption delay in Fixed-priority preemptive scheduling. IEEE Transactions on Computers, 47(6):700.713, 1998. • C.-G. Lee, K. Lee, J. Hahn, Y.-M. Seo, S. L. Min, R. Ha, S. Hong, C. Y. Park, M. Lee, and C. S. Kim. Bounding cache related preemption delay for real-time systems. IEEE Transactions on Software Engineering, 27(9):805.826, Nov. 2001. • J. Staschulat and R. Ernst. Multiple process execution in cache related preemption delay analysis. In ACM International Conference on Embedded Software, 2004. • J. Staschulat, S. Schliecker, and R. Ernst. Scheduling analysis of real-time systems with precise modeling of cache related preemption delay. In Euromicro Conference on Real- Time Systems, 2005.

16. Conclusions • Derivation of data cache reference patterns for every task • Construction of data cache access chains from these • Calculate preemption delay at a point • Determination of the max # of preemptions, n, for a given task • Context of a task set. • Identification of the worst-case scenarios of preemptions. • Current work: Choose the n most expensive points • First work addressing data cache related preemption delay

17. Thank you! • Questions?