1. Non-Preemptive Fixed-Priority Uniprocessor Scheduling where the Execution Time of a Job Depends on the Scheduling of Jobs that Executed Before it Björn Andersson, Dionisio de Niz and Sagar Chaki Software Engineering Institute Carnegie Mellon University

2. Processor Memory

3. Processor Cache Memory Memory

4. Sensor Processor Cache Memory Memory

5. Sensor Processor Cache Memory Memory Signature of a known object

6. Sensor time Job A Read sensor Compare sensor readings with signature …… Processor Cache Memory Memory Signature of a known object

7. Sensor time Job B Read sensor Compare sensor readings with signature …… Processor Cache Memory Memory Signature of a known object

8. Sensor time Job A Read sensor Compare sensor readings with signature …… Job B Read sensor Compare sensor readings with signature …… Processor Cache Memory Memory Signature of a known object

9. Sensor time Job A Read sensor Compare sensor readings with signature …… Job B Read sensor Compare sensor readings with signature …… Processor Cache Memory Memory Signature of a known object

10. Sensor time Job A Read sensor Compare sensor readings with signature …… Job B Read sensor Compare sensor readings with signature …… The execution time of Job B depends on whether Job A executes before Job B. Processor Cache Memory Memory Signature of a known object

11. Sensor time Job A Read sensor Compare sensor readings with signature …… Job B Read sensor Compare sensor readings with signature …… How can we model such systems? Processor Cache Memory Memory Signature of a known object

12. Example of Task Set in the New Model n=3, T 1 =50, D 1 =11,T 2 =150, D 2 =14,T 3 =500, D 3 =500, nhistories 1 =2nhistories 2 =2nhistories 3 =1 C 1 1 =5, historylength 1 1 =0C 2 1 =5, historylength 2 1 =0C 3 1 =5, historylength 3 1 =0 C 1 2 =4, historylength 1 2 =1, historyitem 1 2,1 =2C 2 2 =4, historylength 2 2 =1, historyitem 2 2,1 =1

13. Example of Task Set in the New Model n=3, T 1 =50, D 1 =11,T 2 =150, D 2 =14,T 3 =500, D 3 =500, nhistories 1 =2nhistories 2 =2nhistories 3 =1 C 1 1 =5, historylength 1 1 =0C 2 1 =5, historylength 2 1 =0C 3 1 =5, historylength 3 1 =0 C 1 2 =4, historylength 1 2 =1, historyitem 1 2,1 =2C 2 2 =4, historylength 2 2 =1, historyitem 2 2,1 =1

14. Example of Task Set in the New Model n=3, T 1 =50, D 1 =11,T 2 =150, D 2 =14,T 3 =500, D 3 =500, nhistories 1 =2nhistories 2 =2nhistories 3 =1 C 1 1 =5, historylength 1 1 =0C 2 1 =5, historylength 2 1 =0C 3 1 =5, historylength 3 1 =0 C 1 2 =4, historylength 1 2 =1, historyitem 1 2,1 =2C 2 2 =4, historylength 2 2 =1, historyitem 2 2,1 =1 Example of Schedule 11 time 22 33 33 22 051015 11

15. Example of Task Set in the New Model n=3, T 1 =50, D 1 =11,T 2 =150, D 2 =14,T 3 =500, D 3 =500, nhistories 1 =2nhistories 2 =2nhistories 3 =1 C 1 1 =5, historylength 1 1 =0C 2 1 =5, historylength 2 1 =0C 3 1 =5, historylength 3 1 =0 C 1 2 =4, historylength 1 2 =1, historyitem 1 2,1 =2C 2 2 =4, historylength 2 2 =1, historyitem 2 2,1 =1 Example of Schedule 11 time 22 33 33 22 051015 11 The execution time of this job of task  2 is 4.

16. Open Questions OP1. Is it possible to create an algorithm, with pseudo-polynomial time- complexity, which computes R i ? OP2. How to create an optimal priority assignment scheme.

17. Thanks!