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Discussion: Scheduling

Haibo ZengAmit Mahajan

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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

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Introduction Environment:

hard-real-time vs. soft-real-time Scheduling:

Preemptive and priority driven Fixed priority vs. dynamic

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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

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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

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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

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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

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RMS (cont’d) Available Processor Utilization can

be as low as:

Analysis: Right hand side of the inequality is

monotonic decreasing with m

)12(/ /1

1

mm

iii mTCU

%3.692ln)12( /1lim

m

m

m

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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

iim TkT

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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

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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

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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

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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

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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%

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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?