CprE 458/558: Real-Time Systems

CprE 458/558: Real-Time Systems (G. Manimaran) 1

CprE 458/558: Real-Time Systems

(m, k)-firm tasks and QoS enhancement


(m, k) firm real-time tasks

• A periodic task is said to have an (m,k)-firm guarantee if it is adequate to meet the deadlines of m out of k consecutive instances of the task, where m ≤ k.

• The adaptive QoS management problem

– Admit the tasks to satisfy at least the (m,k) guarantee

– Maximize the QoS of admitted tasks beyond the (m,k) property, at run-time, without violating (m,k) property of any of the admitted tasks.


Task model and performance index

• Task Model - firm periodic tasks [1,2]

• Tasks should meet mi deadlines for every Ki consecutive instances

• Performance Index– Dynamic Failure Rate (DFR): for a task Ti, it is the percentage

of instances of the task miss their (m,k) guarantee.– Marginal Quality Received (MQR):

• To maximize the quality of tasks during overloading, is increased as much as possible

periodptimecompckmpcT iiiiiii :.:,,,

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usedvalueactualthem

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MK-RMS Schedulability Check [2]

• Utilization-based MK-RMS-schedulability check (sufficient, but not necessary)

MKLoad <= n(21/n -1)

• Classification of mandatory and optional instances - Instances of task Ti activated at times api is mandatory if

• Optional instance is assigned the lowest priority• Mandatory instances are assigned priority as per RMS

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MK-RMS Schedulability - exact analysis [2]

• Theorem: Given such that

Let

• If , MK-RMS meets the (m,k)-firm guarantee requirement of

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Scheduling Example

Task 1

Task 2

RMS

120

120

120

(a) T1: <4,8,2,10> T2: <4,6,1,5>

Task 1

Task 2

RMS

120

120

120

(b) T1: <4,8,4,10> T2: <4,6,2,5>

Task 1

Task 2

RMS

120

120

120

(c) T1: <4,8,6,10> T2: <4,6,3,5>Task 1 misses its deadline


Example (Cont.)

• We can increase the values to increase the QoS when the system is underloaded, and decrease the values to handle overloading.

• Feedback method can be used to adjust the values.– Regulated/measured variable:– Set point: desired value of – Control variable: estimation factor, , of

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imetfDFR

DFR


Introduction (Cont.)

• Feedback control technique

Controller ActuatorsControlledRT System

Sensors

Set Points

Controlvariable

s

Measured variables

Regulated variables

+

-

disturbance


Proposed scheduling architecture [3]

PI Controller Actuator

SchedulerAdmission Controller

Submitted tasks Accepted tasks

Average Dynamic Failure Rate

CPU

Co

mp

lete

d ta

sks

+

-

Set point


Proposed scheduling architecture (Cont.)

• Admit tasks based on minimum quality requirement• The actual execution time of tasks are normally less

than or equal to the worst case execution time used in the admission test– Try to increase the quality as much as possible– Use feedback method to adjust .

• Non-zero set point is used – achieve high CPU utilization and low dynamic failure rate

• is zero with respect to – is changed with respect to the current laterDFR

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Feedback control algorithm

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Online controller design

• Initial Value of K: • Halve K when DFR fluctuate across set point

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• K– high value will lead to fluctuation– Low value will lead to a long time to reach the final value

K on-linedesign

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Control signal

Output

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Controllerparameters

Reference


Fairness measure

• All tasks use the same value of all tasks are the same

• Fairness index ( ) in terms of :

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MQR

MQRf

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tasksnofMQRaverageMQR

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• The higher the value of f for a task set, the better the fairness.


MQR performance: Load = 1.1 and MKLoad varied

– MQR decreases as MKLoad increases– ACET < WCET can be exploited to increase MQR– Feedback algo offers better MQR than non-feedback algo

Simulation studies

• Feedback algorithm vs. iterative algorithm

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Simulation studies (Cont.)

Fairness (f): – Fairness obtained by the feedback approach is higher than

that obtained by non-feedback algo (MK-RMS)


Imprecise computation - summary

• Offers scheduling flexibility to achieve graceful degradation (i.e., means to achieve predictable timing faults without violating system spec)

• Applicable only to a class of applications

• Models– Imprecise computation - monotone model– Imprecise computation – 0/1 constraint model– (m,k)-firm model


References

[1] Reference [18] in chapter 4.

[2] Overload management in real-time control applications using (m, k)-firm guaranteeRamanathan, P.; IEEE Transactions on Parallel and Distributed Systems, Volume 10, Issue 6, June 1999 Page(s):549 – 559.

[3] Suzhen Lin, Ph.D Dissertation, ISU, 2005.

CprE 458/558: Real-Time Systems

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