real time systems real-time schedulability part i

Real Time Systems

Real-Time Schedulability

Part I

Schedulability (part 1) - 2

Outline

Timing Requirements

Concurrency and Scheduling

Scheduling Schemes

Notation

Rate Monotonic Algorithm

Utilization Bound Theorem

Examples


Timing Requirements

Where do timing requirements come from? Top-level (explicit) Requirements

assemble two widgets every second jam a hostile emitter within 250 milliseconds of it being

identified

Derived (implicit) Requirements precision: track emitter position to within 5°

leads to periodicity dependability: recover from message loss within 500

msec user-interface: respond to key press within 200 msec


Concurrency and Scheduling

concurrent systems are said to exhibit extreme non-determinism consider a simple 5 task concurrent system there are 120 possible execution permutations

for a non-preemptive system and an infinite number for a preemptive system

real-time systems must restrict this non-determinism via scheduling

define schedulability as the assessment as to whether tasks will meet their deadlines


Scheduling Schemes

a scheduling scheme provides: an algorithm for the use of system resources a way of predicting the worst case behaviour

there are two classifications of schemes static (compile-time) and dynamic (run-time)

we will only study static schemes and in particular, preemptive priority-based schemes

schemes involve: a priority assignment algorithm; and a schedulability test


Notation

C: worst-case computation time of the task T: minimum time between task releases

(period) P: priority assigned to the task N: number of tasks in the system R: worst-case response time of the task B: worst-case blocking time of the task I: interference time of the task

Define Utilization: U = C/T


Define a Simple Task Model

Assumptions: fixed set of tasks all tasks are periodic tasks are completely independent* all system overheads (context switching) are

ignored (or included in task computation times) task deadlines are equal to their periods

implies that tasks must complete before next release all tasks have a fixed worst-case execution time

Critical instant - defined as the maximum load condition when all tasks release together


Rate Monotonic Algorithm (RMA)

a priority assignment scheme for the simple task model described above such that: each task is assigned a priority based upon its

period, wherein the shorter the period, the higher the priority

Example:Task Period (T) Priority (P) A 100 3 B 25 1*

highest C 205 4 D 60 2


Utilization Bound Theorem

a set of N independent periodic tasks scheduled by the rate monotonic algorithm will always meet its deadlines, ifC1/T1 + … CN/TN N(2 1/N - 1) = URM(N)

URM(N) converges to 69% at large N

a sufficient but not necessary test i.e. we cannot say that a system with higher utilization is

not schedulable with this scheduling algorithm


RMA Example 1

Task Ci Ti Ui

A 20 100 0.2 B 30 150 0.2

C 60 200 0.3

U1 + U2 + U3 = 0.7, and is URM(3)

where URM(3) = 3*(21/3 - 1) = 0.779

Therefore these tasks will always meet their deadlines under the scheduling scheme:

P(A) = 1, P(B)=2, P(C)=3


RMA Example 1

t

C

B

A 20

30

50

20

10

30

idle idle

0 40 80 1006020 120 140 160 180 200

- task released

- task complete

Task Ci Ti Ui A 20 1000.2 B 30 1500.2 C 60 2000.3


Task Ci Ti Ui

A 12 50 0.24 B 10 40 0.25

C 10 30 0.33

U1 + U2 + U3 = 0.82, and is not URM(3)

where URM(3) = 3*(21/3 - 1) = 0.779

Therefore these tasks fail the utilization test, and by examination of their Gantt chart, it can be seen that all deadlines will not be met

RMA Example 2


RMA Example 2

t

C

B

A

0 20 40 503010 60 70

10

- task released

- task complete

10

10

10

x x - missed deadline

...10

Task Ci TiUi

A 12 500.24

B 10 400.25

C 10 300.33


RMA Example 3

Task Ci Ti Ui

A 40 80 0.5 B 10 40 0.25

C 5 20 0.25

U1 + U2 + U3 = 1.00, and is not URM(3)

again where URM(3) = 3*(21/3 - 1) = 0.779

These tasks clearly fail the utilization test, but after examination of their Gantt chart, it can be seen that all deadlines will be met ????


RMA Example 3

t

C

B

A

0 20 40 503010 60 70

5

- task released

- task complete

5

15

80

5 5 5

5

10 10

15

Task Ci Ti Ui A 40 80 0.5 B 10 40 0.25 C 5 20 0.25


Additional Points on RMA

RMA has the advantage of being stable in conditions of transient overload a subset of the tasks (those with the highest

priorities) will still meet their deadlines even in a temporary overload condition.

Completion Time Theorem for a set of independent periodic tasks, if each

task meets its first deadline when all tasks are started at the same time, then the deadlines will be met every time.


Weaknesses of RMA and U Test

utilization test is not exact sufficient, but not necessary therefore other tests must be used (besides manually

checking the timelines)

the simple task model is too restrictive only allows for periodic tasks all tasks must be independent

implies no shared resources (no mutexes)

introduce Response Time Analysis - a stronger schedulability test supports aperiodic (sporadic) tasks as well as dependence


References

[1] Burns, A. and Wellings, A., “Real-Time Systems and Programming Languages”, Chapter 13, Addison Wesley, 1997

[2] TimeSys Corp, “The Concise Handbook of Real-Time Systems”, Version 1.0, 1999

[3] www.timesys.com[4] Gomaa, H., “Software Design Methods for

Concurrent and Real-Time Systems”, Addison-Wesley, 1993.

real time systems real-time schedulability part i

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