Discussion: Scheduling

1. Discussion: Scheduling Haibo Zeng Amit Mahajan EE 249, Fall 2002

2. Outline • Problem: multi-program scheduling on a single processor • Optimum fixed priority scheduler – rate monotonic scheduling • Optimum dynamic scheduling algorithm – deadline driven scheduling • Mixed scheduling algorithm EE 249, Fall 2002

3. Introduction • Environment: • hard-real-time vs. soft-real-time • Scheduling: • Preemptive and priority driven • Fixed priority vs. dynamic EE 249, Fall 2002

4. Assumption of environment • A1: The requests for all tasks with hard deadlines are periodic • A2: Task deadline is its next request • A3: The tasks are independent • A4: Run-time for each task is constant • A5: Nonperiodic tasks have no deadlines EE 249, Fall 2002

5. Outline • Problem: multi-program scheduling on a single processor • Optimum fixed priority scheduler – rate monotonic scheduling • Optimum dynamic scheduling algorithm – deadline driven scheduling • Mixed scheduling algorithm EE 249, Fall 2002

6. Rate Monotonic Scheduling • According to their request rates only • Higher request rates, higher priorities • Optimum fixed priority scheduling: feasible if any feasible fixed priority assignment exists • Proof: • Use the concept critical instant to analyze the case of scheduling two tasks EE 249, Fall 2002

7. RMS (cont’d) • Proof: • Use the concept critical instant to analyze the case of scheduling two tasks • Result: assign higher priorities to task with shorter request period; independent of their run-times. • Generalize this result to m tasks EE 249, Fall 2002

8. RMS (cont’d) • Available Processor Utilization can be as low as: • Analysis: • Right hand side of the inequality is monotonic decreasing with m EE 249, Fall 2002

9. RMS (cont’d) • Question: • Why utilization factor can’t reach 100%? • Answer: • Processor idle time: example • Question: • How to relax the utilization bound? • Answer: • For i=1,2,…,m-1, • Better choice: dynamic priority assignment EE 249, Fall 2002

10. Outline • Problem: multi-program scheduling on a single processor • Optimum fixed priority scheduler – rate monotonic scheduling • Optimum dynamic scheduling algorithm deadline driven scheduling • Mixed scheduling algorithm EE 249, Fall 2002

11. Deadline Driven Scheduling • According to their request rates: earliest deadline first (EDF) • No processor idle time before overflow • Schedulable iff processor use is less than 1 • Optimum scheduling algorithm: feasible if any feasible assignment exists EE 249, Fall 2002

12. Outline • Problem: multi-program scheduling on a single processor • Optimum fixed priority scheduler – rate monotonic scheduling • Optimum dynamic scheduling algorithm – deadline driven scheduling • Mixed scheduling algorithm EE 249, Fall 2002

13. Mixed scheduling algorithm • Nice for many applications • Interrupt hardware: fixed priority scheduler • Other software tasks: dynamic priority scheduler • Scheduling algorithm • K tasks of shortest periods: RMS • Remaining slower paced tasks: EDF EE 249, Fall 2002

14. Mixed scheduling algorithm (cont’d) • Comparison with RMS and EDF: • Still can’t reach 100% utilization • But much better than RMS • Example with 3 tasks • T1=3, T2=4, T3=5 • C1=1, C2=1, C3=1(rate-monotonic), 2(mixed) • RMS: U = 1/3 + 1/4 + 1/5 = 78.3% • Mixed scheduling algorithm: U = 1/3 + 1/4 + 2/5 = 98.3% EE 249, Fall 2002

15. Questions • Overhead we ignored? • Dynamic scheduling • Preemption • If programs are nonterminating, how about the resources? • Are the assumptions about environment always fine? • If A1 or A4 don’t hold, what do we do? • Is A3 suitable for embedded systems? EE 249, Fall 2002