1. Embedded System Design Framework for Minimizing Code Size and Guaranteeing Real-Time Requirements Insik Shin, Insup Lee, & Sang Lyul Min CIS, Penn, USACSE, SNU, KOREA

2. 2 Agenda  Background Period Calibration Method (PCM) Code size reduction technique  Design framework overview  Optimization problem formulation  Heuristic solutions and evaluations  Conclusion

3. 3 Period Calibration Method (PCM)  Design methodology that transforms real- time system requirements into real-time task scheduling parametersreal- time system requirements real-time task scheduling parameters  Example Example  Drawback : it may not generate schedulable solutions  R. Gerber et al. “Guaranteeing End-to-End Timing Constraints by Calibrating Intermediate Processes”, RTSS ’94.

4. 4 Code Size Reduction Technique  Code size is a critical design factor for many embedded systems.  Reduced bit-width instructions  ARM microprocessor normal mode : 32-bit instruction set Thumb mode : 16-bit instruction set code size can be reduced by 30%, while # of instructions can increase by 40%.

5. 5 Code Size vs Execution Time Tradeoff  A program contains both 16/32 bit instructions in functions or basic blocks.  Compile-time tradeoff between code size (s) and execution time (e) of a task s e

6. 6 Tradeoff Function  Tradeoff function for each task  i s = f i (e) (linear or discrete) s e A B

7. 7 Embedded Real-Time System Design  Problem: design a system satisfying real- time system requirements while minimizing the total code size of the task system Task 1Task 2Task n … X1 X2 Y1 11 22 d1 33 d2 44 F(Y1|X1)=30, F(Y1|X2)=25, C(Y1|X1,X2) = 4, u(Y1)=40, l(Y1)=30 Real-time System Requirements Tradeoff

8. 8 Design Framework  Goal : deriving task code size and scheduling parameters while minimizing the system code size and guaranteeing real-time requirements X1 X2 Y1 11 22 d1 33 d2 44 F(Y1|X1)=30, F(Y1|X2)=25, C(Y1|X1,X2) = 4, u(Y1)=40, l(Y1)=30 Real-time System Requirements PCM 0510 Task Scheduling Parameters 0510 Task 1Task 2Task n … Tradeoff Design Framework

9. 9 Design Framework Overview Real-Time System Requirements Task Code Size Feasibility Constraints Task Exec. Time Min. Task Exec. Time PCM Task Scheduling Parameters Task Tradeoff Feasibility Analysis Optimization Framework Design Framework Task Code Size & Scheduling Parameters

10. 10 Design Framework Overview Real-Time System Requirements Task Code Size Feasibility Constraints Task Exec. Time Min. Task Exec. Time PCM Task Scheduling Parameters Task Tradeoff Feasibility Analysis Optimization Framework Design Framework Task Code Size & Scheduling Parameters

11. 11 Optimization Problem Formulation  Given linear or discrete tradeoff functions and task scheduling parameters, determine task execution time solving the following optimization problem:  Optimization problem: objective: minimizing constraint: feasibility

12. 12 Feasibility Analysis  Task model : asynchronous periodic tasks with pre-period deadlines under EDF scheduling  For the task model, an exact feasibility condition is for all, where is the number of jobs of task that must be completely scheduled in [t 1, t 2 ).  Feasibility Analysis is NP-hard [Baruah ’90].

13. 13 Feasibility Analysis  Our contribution: another exact feasibility condition that can be more efficiently evaluated. for all (t 1, t 2 ) OD ALL, where OD ALL is a set of possible pair of (offset, deadline) between 0 and 2T LCM + O max.

14. 14 Optimization Framework  Optimization Problem Objective : minimizing Constraint : for all (t 1, t 2 ) OD ALL.  Complexity of optimization problem Linear tradeoff : the optimization problem can be solved through linear programming. Discrete tradeoff: we prove the problem is NP-hard and present three heuristics.

15. 15 Heuristic Algorithms  Consider the following three tasks 11 22 33 TiTi 975 eiei 212 11 22 33 05101520

16. 16 Heuristic Algorithms  Each job can increase its execution time if there is an empty slot in its execution window 11 22 33 05101520 05101520 EDF Schedule

17. 17 Heuristic Algorithms  Each job can increase its execution time if there is an empty slot in its execution window 11 22 33 05101520 05101520 EDF Schedule

18. 18 Heuristic Algorithms  Each job can increase its execution time if there is an empty slot in its execution window Cumulative amount of execution time each job can increase 11 22 33 05101520

19. 19 Heuristic Algorithms  Each job can increase its execution time if there is an empty slot in its execution window The maximum amount of execution time a task can increase is the maximum amount of execution time all of its jobs can increase together. 11 22 33 05101520

20. Heuristic Algorithms  Highest Best Reduction-Ratio First (HBRF) reduction ratio choose a task with the highest reduction ratio 11 22 05101520 eiei ii

21. 21 Heuristic Algorithms  Longest Period First (LPF) choose a task with the longest period. In general, increasing the execution time of this task has the least impact on the schedulability of task set 11 22 05101520 T1T1 T2T2

22. 22 Heuristic Algorithms  Highest Best Weighted-Reduction-Ratio First (HBWF) Weighted reduction ratio choose a task with the highest weighted reduction ratio 11 22 05101520 eiei ii T1T1 T2T2

23. 23 Evaluation of Heuristic Algorithms  Closeness to OPT S(init) – initial system code size S(alg) – system code size obtained with an heuristic algorithm S(opt) – optimal system code size Closeness to OPT

24. 24 Performance of algorithms with 8 tasks Closeness to OPT (%)

25. 25 Performance of BEST with various task numbers Closeness to OPT (%)

26. 26 Conclusion  Design framework taking advantage of the code size vs. execution time tradeoff  Future work Energy consumption is another critical design factor of embedded systems. Extends this framework so as to utilize tradeoffs among code size, execution time, and energy consumption.

27. 27 Real-Time System Requirements  Task graph Task graph dataflow & task precedence  End-to-end timing constraints End-to-end timing constraints freshness from input to output input correlation output separation

28. 28 Task Graph  Dataflow & task precedence X1 X2 Y1 11 22 d1 d2 44 X3 33 d3 d4 55 Y2 66

29. 29 End-to-end timing Constraints  Freshness from input to output: F(Y1|X1)  Input correlation : C(Y1|X1,X2)  Output separation : u(Y1), l(Y1) X1 X2 Y1 11 22 d1 d2 44

30. 30 Example – System Requirements X1 X2 Y1 11 22 d1 d2 44 X3 33 d3 d4 55 Y2 66 F(Y1|X1)=30, F(Y1|X2)=30, F(Y2|X2)=20, F(Y2|X3)=15 C(Y1|X1,X2)=3, C(Y2|X2,X3)=4 l(Y1)=21, u(Y1)=32, l(Y2)=29, u(Y2)=41 e1=2, e2=2, e3=1, e4=3, e5=2, e6=3

31. 31 Example – Solution Process 1. deriving the period of each task minimizing utilization ( ) 2. deriving the offset and deadline of each task 3. deriving the fixed priority of each task

32. 32 Example – Task Scheduling Parameters 11 22 33 44 55 66 period2613392639 offset00021013 deadline211213261315 priority123456

33. 33 Real-Time Task Scheduling Parameters  Period (T i )  Offset (O i )  Deadline (D i )  Fixed priority  Execution time (e i )