courseware scheduling uniprocessor real-time systems jan madsen informatics and mathematical...

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Scheduling Uniprocessor Real-Time Systems

Jan Madsen

Informatics and Mathematical ModellingTechnical University of Denmark

Richard Petersens Plads, Building 321DK2800 Lyngby, Denmark

[email protected]

Jan Madsen 2SoC-MOBINET courseware

Rate-monotonic scheduling

Real-time scheduling with provable properties [Liu and Layland 73]

Each process is independent and given a unique priority A process may be preempted by a higher-priority process All processes have a deadline equal to their period and a

fixed WCET Context switching overhead is ignored


RMS

The critical instance for a process occurs when the process and all higher-priority processes are released simultaneously

si ciai di = Ti

Must guarantee that all processes meet their deadlines, independent of order of releases

pi pi


RMS example

50

40

30

p3

p2

p1

0 20 30 40 50 6010

Ti Ci

p1 50 12

p2 40 10

p3 30 10


Rate-monotonic priority assignment

Each process is given a unique priority where 1 is the highest

Prioritize according to Ti’s, with shortest-period process given highest priority Fixed-priority scheme Independent of ci’s

This priority assignment is optimal

No fixed priority scheme does it better!


RMS example (cont.)

Ti Ci priority

p1 50 12 3

p2 40 10 2

p3 30 10 1


CPU utilization under RMS

Given N independent processes, utilization U

N

i i

i

T

cU

1

121 NNU ( )

%3.69)12((lim 1

N

NN

• Least upper bound for utilization


RMS example (cont.)

Ti Ci priority U

p1 50 12 1

p2 40 10 2

p3 30 10 3

121 33U ( ) = 0.78

0.24

0.25

0.33

0.82


RMS example (cont.)

p3

p2

p1

50

40

30

0 20 30 40 50 6010


RMS

The utilization-based schedulability test is sufficient but not necessary If the test is passed it is schedulable If the test is not passed, it may be schedulable

If all processes meet their first deadline then they will meet all future one


Response time analysis

Highest-priority process

r = c Other processes will suffer interference from

higher-priority processes

ri = ci + ii

Maximum interference occur at a critical instance


Response time analysis

cjTj

RiciRi)(ihpj

Processes with higher-priority than pi

number of releases of process pj during [0, Ri )

each release will impose an interference of cj

cjciihpj

Tj

win

)(wi

n 1


Response time analysis example

Ti Ci priority

p1 7 3 1

p2 12 3 2

p3 20 5 3

w10 3

w20 3

73

w21 3 + 3 = 6

76

w22 3 + 3 = 6

R1=3

R2=6


Earliest-Deadline-First Scheduling

Dynamic priority scheme changes priorities during execution based on

initiation times can achieve higher CPU utilization than RMS, i.e.

100% Priority policy:

process with closest deadline gets highest-priority


EDF example

Ti Ci

p1 3 1

p2 4 1

p3 5 2

p1

p2

p3

0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16

123

312

231

231

123

213

123


RMS example

50

40

30

p3

p2

p1

0 20 30 40 50 6010

Ti Ci

p1 50 12

p2 40 10

p3 30 10


RMS example scheduled using EDF

40

30

50

p3

p2

p1

0 20 30 40 50 6010 80 90 100 11070

Ti Ci

p1 50 12

p2 40 10

p3 30 10


Comparing RMS and EDF

Higher CPU utilization with EDF Easier to ensure that deadlines will be satisfied

with RMS RMS easier to implement


Overload conditions

When not all processes can meet their deadlines EDF may result in domino effect

First process missing its deadline may cause all subsequent processes to miss their deadlines

Accociate value wi of importance with each process Use Ti/wi as priority (similar to shortest-process-first)


More realistic model assumptions

Shared resources Data dependencies Context switching Cache effects Power reduction


Shared resources

Scheduling processes without considering resource requirements may cause priority inversion

example, p1 highest-priority process

p1{r1}

p2 {r1}deadlock!


Shared resources

When there are mutual exclusion constraints, it is impossible to find a totally on-line optimal runtime scheduler [Mok83]

Priority ceiling protocol (PCP) a way to bound priority inversion blocking of processes that may cause them temporary priority increase of process

PCP prevents deadlocks


t1 t2

Data dependencies

p1 p3

p2

di

t1 10

t2 8

ci

p1 2

p2 1

p3 4

p1

p2

p3


Context switching

ci di

p1 3 5

p2 2 10

p2

p1

0 4 6 8 102

p2

p1

0 4 6 8 102


Cache effects

ci average ci

p1 2 1.5

p2 1 0.75

p3 1 0.75

p3

p2

p1

p1

p2

p1

p3

p2

p1

p3

p2

p1

p3

p2LRU

cache policy: least-recently-used


Cache effects

ci average ci

p1 2 1.5

p2 1 0.75

p3 1 0.75

p1

p2

p1

p3

p1

p3

p1

p2

p1

p3

p1

p3

p2

p1

cache policy: keep p1 in cache


Power reduction

Power management policy Takes time to power-down/up Techniques:

event/request based predictive probabilistic


Power reduction

p3

p2

p1 r1 r1

r1

r1

p3

p2

p1 r1

r1

r1 idle

r1 idle r1 idle

courseware scheduling uniprocessor real-time systems jan madsen informatics and mathematical...

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