An EDF-based Scheduling Algorithm for Real-time Reconﬁgurable

Sporadic Tasks

Hamza Gharsellaoui

, Mohamed Khalgui

and Samir Ben Ahmed

1,2

INSAT Institute, University of Carthage, Tunis, Tunisia

FST Faculty, University of Tunis El Manar, Tunis, Tunisia

Keywords:

EDF-based Scheduling Algorithm, Real-time Reconﬁgurable Sporadic Tasks, Intelligent Agent, Automatic

Reconﬁgurations.

Abstract:

This paper deals with the problem of scheduling the mixed workload of both homogeneous multiprocessor

on-line sporadic and off-line periodic tasks in a hard reconﬁgurable real-time environment by an optimal

EDF-based scheduling algorithm. Two forms of automatic reconﬁgurations which are assumed to be applied

at run-time: Addition-Removal of tasks or just modiﬁcations of their temporal parameters: WCET and/or

deadlines. Nevertheless, when such a scenario is applied to save the system at the occurrence of hardware-

software faults, or to improve its performance, some real-time properties can be violated at run-time. We

deﬁne an Intelligent Agent that automatically checks the system’s feasibility after any reconﬁguration scenario

to verify if all tasks meet the required deadlines after a reconﬁguration scenario ψ

(h ∈ 1..M, we assume

that we have M reconﬁguration scenarios), was applied on a multiprocessor embedded system in the case of

shared memory. Indeed, if the system is unfeasible, then the Intelligent Agent dynamically provides precious

technical solutions for users to send sporadic tasks to idle times, by modifying the deadlines of tasks, the

worst case execution times (WCETs), the activation time, by tolerating some non critical tasks m among n

according to the (m,n) ﬁrm and a reasonable cost, by sending some tasks from their current processors to

be scheduled in other processors, or in the worst case by removing some soft tasks according to prediﬁned

heuristic. We implement the agent to support these services in order to demonstrate the effectiveness and the

excellent performance of the new optimal algorithm in normal and overload conditions.

1 INTRODUCTION

Nowadays, due to the growing class of portable

systems, such as personal computing and commu-

nication devices, embedded and real-time systems

contain new complex software which are increasing

by the time. This complexity is growing because

many available software development models don’t

take into account the speciﬁc needs of embedded

and systems development. The software engineering

principles for embedded system should address

speciﬁc constraints such as hard timing constraints,

limited memory and power use, predeﬁned hardware

platform technology, and hardware costs. On the

other hand, the new generations of embedded control

systems are adressing new criteria such as ﬂexibility

and agility (H. Gharsellaoui and BenAhmed, 2012).

For these reasons, there is a need to develop tools,

methodologies in embedded software engineering

and dynamic reconﬁgurable embedded control sys-

tems as an independent discipline. Each system is a

subset of tasks. Each task is caracterized by its worst

case execution times (WCETs) C

p,ψ

, an offset (re-

lease time) a

p,ψ

, a period T

p,ψ

and a deadline D

p,ψ

for each reconﬁguration scenario ψ

, (h ∈ 1..M, we

assume that we have M reconﬁguration scenarios)

and on each processor p, (p ∈ 1..K, we assume that

we have K identical processors numbered from 1 to

K), and n real-time tasks numbered from 1 to n that

composed a feasible subset of tasks entitled ξ

old

and

need to be scheduled. The general goal of this paper

is to be reassured that any reconﬁguration scenario

changing the implementation of the embedded

system does not violate real-time constraints: i.e. the

system is feasible and meets real-time constraints

even if we change its implementation and to cor-

rectly allow the minimization of the response time

of this system after any reconﬁguration scenario

(H. Gharsellaoui and BenAhmed, 2012). To obtain

this optimization (minimization of response time),

377

Gharsellaoui H., Khalgui M. and Ben Ahmed S..

An EDF-based Scheduling Algorithm for Real-time Reconﬁgurable Sporadic Tasks.

DOI: 10.5220/0004432003770388

In Proceedings of the 8th International Joint Conference on Software Technologies (ICSOFT-EA-2013), pages 377-388

ISBN: 978-989-8565-68-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

we propose an intelligent agent-based architecture in

which a software agent is deployed to dynamically

adapt the system to its environment by applying

reconﬁguration scenarios. A reconﬁguration scenario

means the addition, removal or update of tasks

in order to save the whole system on the occurrence

of hardware/software faults, or also to improve its

performance when random disturbances happen at

run-time. Sporadic task is described by minimum in-

terarrival time P

p,ψ

which is assumed to be equal to

its relative deadline D

p,ψ

, and a worst-case execution

time (WCET) C

p,ψ

for each reconﬁguration scenario

and on each processor p. A random disturbance is

deﬁned in the current paper as any random internal

or external event allowing the addition of tasks that

we assume sporadic or removal of sporadic/periodic

tasks to adapt the system’s behavior. Indeed, a hard

real-time system typically has a mixture of off-line

and on-line workloads and assumed to be feasible

before any reconﬁguration scenario ψ

. The off-line

requests support the normal functions of the system

while the on-line requests are sporadic tasks to

handle external events such as operator commands

and recoveryactions which are usually unpredictable.

For this reason and in this original work, we propose

a new optimal scheduling algorithm based on the

dynamic priorities scheduling Earliest Deadline First

(EDF) algorithm principles on each processor p

and for each dynamic reconﬁguration scenario ψ

in order to obtain the feasibility of the system at

run-time, meeting real-time constraints and for the

optimization of the response time of this system.

Indeed, many real-time systems rely on the EDF

scheduling algorithm in the case of uni-processor

scheduling theory. This algorithm has been shown

to be optimal under many different conditions. For

example, for independent, preemptable tasks, on a

uni-processor, EDF is optimal in the sense that if any

algorithm can ﬁnd a schedule where all tasks meet

their deadlines, then EDF can meet the deadlines

(Dertouzos, 1974).

According to (Brocal V., 2011), a hyperperiod

is deﬁned as HP = [ζ, 2 ∗ LCM + ζ], where LCM

is the well-known Least Common Multiple of the

tasks periods and ζ is the largest task offset. This

algorithm, in our original paper assumes that spo-

radic tasks span no more than one hyperperiod of the

periodic tasks HP

(p,ψ

)

= [ζ

(p,ψ

)

,2*LCM + ζ

(p,ψ

)

where LCM

p,ψ

is the well-known Least Common

Multiple of tasks periods and (ζ

p,ψ

) is the largest

task offset of all tasks τ

p,ψ

for each reconﬁguration

scenario ψ

on each processor p. The problem is

to ﬁnd which solution proposed by the agent that

reduces the response time. To obtain these results,

the intelligent agent calculates the residual time R

p,ψ

before and after each addition scenario and calculates

the minimum of those proposed solutions in order to

obtain Resp

p,ψ

optimal noted Resp

p,ψ

opt

. Where

Resp

p,ψ

opt

is the minimum of the response time of

the current system under study given by the following

equation: Resp

p,ψ

opt

= min(Resp

p,ψ

k,1

, Resp

p,ψ

k,2

Resp

p,ψ

k,3

, Resp

p,ψ

k,4

, Resp

p,ψ

k,5

, Resp

p,ψ

k,6

, Resp

p,ψ

k,7

To calculate these previous values Resp

p,ψ

k,1

Resp

p,ψ

k,2

, Resp

p,ψ

k,3

, Resp

p,ψ

k,4

, Resp

p,ψ

k,5

, Resp

p,ψ

k,6

and Resp

p,ψ

k,7

, we proposed a new theoretical con-

cepts R

p,ψ

, S

p,ψ

, s

p,ψ

, f

p,ψ

and L

p,ψ

for the

case of real-time sporadic operating system (OS)

tasks. Where R

p,ψ

is the residual time of task σ

p,ψ

denotes the ﬁrst release time of task σ

p,ψ

is the last release time of task σ

p,ψ

, f

p,ψ

denotes the estimated ﬁnishing time of task σ

p,ψ

and L

p,ψ

denotes the laxity of task σ

p,ψ

for each

reconﬁguration scenario ψ

and on each processor p.

A tool RT-Reconﬁguration is developed at INSAT

institute in university of Carthage, Tunisia, to support

all the services offered by the agent. The minimiza-

tion of the response time is evaluated after each

reconﬁguration scenario ψ

and on each processor p

to be offered by the agent.

The organization of the paper is as follows.

Section 2 introduces the related work of the proposed

approach and gives the basic guarantee algorithm. In

Section 3, we present the new approach with deadline

tolerance for optimal scheduling theory. Section 4

presents the performance study, showing how this

work is a signiﬁcant extension to the state of the

art of EDF scheduling and discusses experimental

results of the proposed approach research. Section

5 summarizes the main results and presents the

conclusion of the proposed approach and describes

the intended future works.

2 BACKGROUND

We present related works dealing with reconﬁgura-

tions and real-time scheduling of embedded systems.

Today, real-time embedded systems are found in

many diverse application areas including; automotive

electronics, avionics, telecommunications, space

systems, medical imaging, and consumer electronics.

In all of these areas, there is rapid technological

progress. Companies building embedded real-time

systems are driven by a proﬁt motive. To succeed,

they aim to meet the needs and desires of their cus-

ICSOFT2013-8thInternationalJointConferenceonSoftwareTechnologies

378

tomers by providing systems that are more capable,

more ﬂexible, and more effective than their competi-

tion, and by bringing these systems to market earlier.

This desire for technological progress has resulted

in a rapid increase in both software complexity and

the processing demands placed on the underlying

hardware (Brocal V., 2011). To address demands for

increasing processor performance, silicon vendors

no longer concentrate wholly on the miniaturisation

needed to increase processor clock speeds, as this

approach has led to problems with both high power

consumption and excessive heat dissipation. Instead,

there is now an increasing trend towards using

multiprocessor platforms for high-end real-time

applications (Brocal V., 2011).

For these reasons, we will use in our work the

case of real-time scheduling on homogeneous multi-

processor platforms. Before presenting our original

contribution, we will present some deﬁnitions below.

According to (H. Gharsellaoui and BenAhmed,

2012), each periodic task is described by an initial

offset a

(activation time), a worst-case execution

time (WCET) C

, a relative deadline D

and a period

According to (Buttazzo and Stankovic, 1993),

each sporadic task is described by minimum in-

terarrival time P

which is assumed to be equal to

its relative deadline D

, and a worst-case execution

time (WCET) C

. Hence, a sporadic task set will

be denoted as follows: Sys

= {σ

, D

) }, i =

1 to m. Reconﬁguration policies in the current

paper are classically distinguished into two strate-

gies: static and dynamic reconﬁgurations. Static

reconﬁgurations are applied off-line to modify

the assumed system before any system cold start,

whereas dynamic reconﬁgurations are dynamically

applied at run-time, which can be further divided

into two cases: manual reconﬁgurations applied

by users and automatic reconﬁgurations applied by

intelligent agents (H. Gharsellaoui and BenAhmed,

2012), (X. Wang and L, 2011). This paper focuses

on the dynamic reconﬁgurations of assumed mixture

of off-line and on-line workloads that should meet

deadlines deﬁned according to user requirements.

The extension of the proposed algorithm should be

straightforward, when this assumption does not hold

and its running time is O(n + m) (T. Tia, 1994).

To illustrate the key point of the proposed dy-

namically approach, we assume that there are K

identical processors numbered from 1 to K, and n

real-time tasks numbered from 1 to n that composed

a feasible subset of tasks entitled ξ

old

and need to be

scheduled. At time t and before the application of the

reconﬁguration scenario ψ

, each one of the tasks of

old

is feasible, e.g. the execution of each instance in

each processor is ﬁnished before the corresponding

deadline and the tasks are not assumed to be arranged

in any speciﬁc order.

Every processor p assigns a set of periodic tasks

= {τ

, τ

,...,τ

}. This allocation is made with

an allowance algorithm at the time of the design,

for example by using one of the well known tech-

niques: ﬁrst-ﬁt (FF), next-ﬁt (NF), best-ﬁt (BF),

worst-ﬁt (WF). These tasks are independent and can

be interrupted at any time. Every task τ

has an

execution time (Worst Case Execution Time) C

, one

period T

, a deadline D

which is assumed to be

less than or equal to its period, e.g. D

≤ T

. Every

task instance k has to respect its absolute deadline,

namely the k

authority of the task τ

, named τ

i,k

must be completed before time D

i,k

= (k-1)T

+ D

We express all the measures of time (e.g. periods, the

deadlines, the calculations) as being multiple of the

tick of the processor clock. Every processor p will

execute its tasks in local by using EDF, it means that

the priorities P

of periodic tasks are dynamic and the

scheduler guarantees that every instance of every task

will run before its deadline. These tasks are handled

by a global scheduler (GS), which assigns them to

processors by using the state informations of the

local schedulers. Moreover, under EDF scheduling,

a task will ﬁt on a processor as long as the total

utilization of all tasks assigned to that processor does

not exceed unity (the total utilization factor = 1).

Finally, for reasons of simplicity, we assume that all

the overheads of context exchange, scheduling of

tasks, the preemption of the tasks and the migration

cost of the tasks are equal to zero.

We assume now the arrival at run-time of a sec-

ond subset ξ

new

which is composed of m real-time

tasks at time t

= t + ∆t). We have a system

Current

Sys

) composed of n+m tasks. In this case a

reconﬁguration scenario ψ

is applied. The reconﬁg-

uration of the system Sys

means the modiﬁcation

of its implementation that will be as follows at time t

= Current

Sys

) = ξ

old

∪ ξ

new

Where ξ

old

is a subset of old tasks which are not

affected by the reconﬁguration scenario ψ

(e.g. they

implement the system before the time t

), and ξ

new

subset of new tasks in the system. We assume that an

updated task is considered as a new one at time t

When the reconﬁguration scenario ψ

is applied at

time t

, two cases exist:

• If tasks of ξ

= ξ

old

∪ ξ

new

are feasible, then no

AnEDF-basedSchedulingAlgorithmforReal-timeReconfigurableSporadicTasks

379

reaction should be done by the agent,

• Otherwise, the agent should provide different so-

lutions for users in order to re-obtain the system’s

feasibility.

2.1 State of the Art

Nowadays, several interesting studies have been pub-

lished to develop reconﬁgurable embedded control

systems. In (C. Angelov and Marian, 2005) Marian

et al. propose a static reconﬁguration technique for

the reuse of tasks that implement a broad range of

systems. The work in (M. N. Rooker and Ebenhofer,

2007) proposes a methodology based on the human

intervention to dynamically reconﬁgure tasks of

considered systems. In (Al-Saﬁ and Vyatkin, 2007),

an ontology-based agent is proposed by Vyatkin et al.

to perform system reconﬁgurations according to user

requirements and also the environment evolution.

Window-constrained scheduling is proposed in (West

and Schwan, 1999), which is based on an algorithm

named dynamic window-constrained scheduling

(DWCS). The research work in (P. Balbastre and

Crespo, 2002) provides a window-constrained-based

method to determine how much a task can increase its

computation time, without missing its deadline under

EDF scheduling. In (P. Balbastre and Crespo, 2002),

a window-constrained execution time can be assumed

for reconﬁgurable tasks in n among m windows of

jobs. In the current paper, a window constrained

schedule is used to separate old and new tasks that

assumed sporadic on each processor p and after each

reconﬁguration scenario ψ

. Old and new tasks are

located in different windows to schedule the system

with a minimum response time. In (X. Wang and

L, 2011), a window constrained schedule is used to

schedule the system with a low power consumption.

In the following, we only consider periodic and spo-

radic tasks. Few results have been proposed to deal

with deadline assignment problem. Baruah, Buttazo

and Gorinsky in (H. Gharsellaoui and BenAhmed,

2012) propose to modify the deadlines of a task set

to minimize the output, seen as secondary criteria of

this work. So, we note that the optimal scheduling

algorithm based on the EDF principles and on the

dynamic reconﬁguration scenario ψ

is that we

propose in the current original work in which we

give solutions computed and presented by the intel-

ligent agent for users to respond to their requirements.

Running Example 1:

To illustrate the key point of the proposed dynamic

reconﬁguration approach, we consider ξ = Sys

Sys

a set of 5 characterized tasks, shown in Table 1

as a motivational example. Sys

= τ

, τ

, and Sys

= σ

, σ

, and σ

. τ

and τ

are periodic tasks and

all the rest (σ

, σ

, and σ

) are sporadic tasks. Each

task can be executed immediately after its arrival and

must be ﬁnished by its deadline. First, at time t, Sys

is feasible because the processor utilization factor U

= 0.30 ≤ 1. We suppose after, that a reconﬁguration

scenario is applied at time t1 to add 3 new sporadic

tasks σ

, σ

, and σ

. The new processor utilization

becomes U = 1.21 > 1 time units. Therefore the

system is unfeasible. In the following tables (table

1 and table 2), the ﬁrst column represents the task

identiﬁer, the second column represents the release

time, the third column represents the deadline of

each task which is less than or equal to its period in

these examples of real time tasks, the fourth column

represents the period and the ﬁve column represents

the worst case execution time (WCET) of each task.

∗

is the inter-arrival time.

Table 1: The characteristics of the 5 tasks.

Task a

= P

∗

A 0 10 10 2

B 0 20 20 2

C 5 15 - 5

D 5 8 - 4

E 11 12 - 1

Running Example 2:

In this section, we demonstrate the performance of

our proposed approach for both periodic synchronous

and asynchronous, and sporadic tasks. The simula-

tion runs on our tool RT-Reconﬁguration and proved

by the real-time simulator Cheddar (J. Legrand,

2004) with a task set composed of old tasks (ξ

old

)

and new tasks (ξ

p,ψ

new

) on the processor p for each

reconﬁguration scenario ψ

. We illustrate with a

simpliﬁed example to ease the understanding of our

approach. The task set considered for this example

is given in table 2 and is composed of 10 tasks. The

sum of utilization of all tasks is given in table 2 and

is equal to 426.1%. We have 3 identical processors

in our system to schedule these tasks. In this case,

we assume that each task’s deadline is less than

or equal to its period. The worst case execution

times, deadlines, and the time periods of all tasks are

generated randomly. In this experiment, the system

runs for time units equal to hyper-period of periodic

tasks.

In this experiment, our task set example is ini-

tially implemented by 5 characterized old tasks

(ξ

old

= {τ

; τ

}). These tasks are fea-

sible because the processor utilization factor U =

1.19 ≤ 3. These tasks should meet all required

ICSOFT2013-8thInternationalJointConferenceonSoftwareTechnologies

380

deadlines deﬁned in user requirements and we have

Feasibility(Current

old

(t)) ≡ True.

Firstly, tasks are partitioned; task τ

is partioned on

ﬁrst processor, τ

and τ

are partitioned on processor

2 while task τ

and τ

are partitioned on processor

3. We have three sets of local tasks. As there is only

one task on ﬁrst processor then task τ

utilization

factor is the same as the ﬁrst processor 1 utilization

factor ( u

1,0

= 0.285 ≤ 1) while utilization factors of

processor 2 and processor 3 are calculated as follows:

2,0

∑

(2)

i=1

= 0.372 < 1,

3,0

∑

(2)

i=1

= 0.533 < 1,

We suppose that a ﬁrst reconﬁguration scenario

(h = 1) is applied at time t

to add 5 new

tasks ξ

new

= {τ

; τ

}. The new pro-

cessor utilization becomes U

= 4.261 > 3

time units. Therefore the system is unfeasible.

Feasibility(Current

(t1)) ≡ False. Indeed, if the

number of tasks increases, then the overload of the

system increases too. Our optimal earliest deadline

Table 2: Task Parameters.

Task C

= P

∗

2 9 7

3 21 20

2 9 9

2 13 10

3 15 9

14 21 19

10 24 16

8 18 18

13 16 17

5 11 12

ﬁrst (OEDF) algorithm is based on the following

Guarantee Algorithm which is presented by Buttazo

and Stankovic in (Buttazzo and Stankovic, 1993).

Indeed, OEDF algorithm is an extended and ame-

liorate version of Guarantee Algorithm that usually

guarantee the system’s feasibility.

2.2 Guarantee Algorithm

The dynamic, on-line, guarantee test in terms of resid-

ual time, which is a convenient parameter to deal

with both normal and overloadconditionsis presented

here.

Algorithm GUARANTEE(ξ; σ

)

begin t = get current time();

= 0;

= t;

Insert σ

in the ordered task linked list;

ξ`= ξ

;

k = position of σ

in the task set ξ`;

for each task σ

`such that i ≥ k do {

= R

i−1

+ (d

- d

i−1

) - c

;

if (R

< 0) then return (”Not Guaranteed”);

}

return (”Guaranteed”);

end

3 NEW APPROACH WITH

DEADLINE TOLERANCE

In this section we will present some preliminaries

concepts and we will describe our contribution after.

In (Buttazzo and Stankovic, 1993), Buttazo and

Stankovic present the Guarantie Algorithm without

the notion of deadline tolerance, and then we will ex-

tend the algorithm in our new proposed approach by

including tolerance indicator and task rejection pol-

icy. For this reason, and in order to more explain these

notions we will present some preliminaries.

3.1 Preliminaries

ξ denotes a set of active sporadic tasks σ

ordered by

increasing deadline in a linked list, σ

being the task

with the shortest absolute deadline.

denotes the arrival time of task σ

, i.e., the time at

which the task is activated and becomes ready to exe-

cute.

denotes the maximum computation time of task

, i.e., the worst case execution time (WCET) needed

for the processor to execute task σ

i,k

without interrup-

tion.

denotes the dynamic computation time of task σ

i.e., the remaining worst case execution time needed

for the processor, at the current time, to complete task

i,k

without interruption.

denotes the absolute deadline of task τ

, i.e., the

time before which the task should complete its execu-

tion, without causing any damage to the system.

denotes the relative deadline of task σ

, i.e., the

time interval between the arrival time and the abso-

lute deadline. S

denotes the ﬁrst start time of task σ

i.e., the time at which task σ

gains the processor for

the ﬁrst time. s

denotes the last start time of task σ

i.e., the last time, before the current time, at which

task σ

gained the processor.

denotes the estimated ﬁnishing time of task σ

, i.e.,

the time according to the current schedule at which

task σ

should complete its execution and leave the

AnEDF-basedSchedulingAlgorithmforReal-timeReconfigurableSporadicTasks

381

system.

denotes the laxity of task σ

, i.e., the maximum

time task σ

can be delayed before its execution be-

gins.

denotes the residual time of task σ

, i.e., the length

of time between the ﬁnishing time of σ

and its abso-

lute deadline. Baruah et al. (S. Baruah and Shasha,

1991) present a necessary and sufﬁcient feasibility

test for synchronoussystems with pseudo-polynomial

complexity. The other known method is to use re-

sponse time analysis, which consists of computing

the worst-case response time (WCRT) of all tasks in a

system and ensuring that each task WCRT is less than

its relative deadline. To avoid these problems, and to

have a feasible system in this paper, our proposed tool

RT-Reconﬁguration can be used. For this reason, we

present the following relationships among the param-

eters deﬁned above:

= a

+ D

(1)

= d

- a

- C

(2)

= d

- f

(3)

= t + c

; f

= f

i−1

+ c

∀ i > 1 (4)

The basic properties stated by the following lemmas

and theorems are used to derive an efﬁcient O(n+m)

algorithm for analyzing the schedulability of the spo-

radic task set whenever a new task arrives in the sys-

tems.

Lemma 1. Given a set ξ = {σ

, σ

, ...,σ

} of ac-

tive sporadic tasks ordered by increasing deadline in a

linked list, the residual time R

of each task σ

at time

t can be computed by the following recursiveformula:

= d

- t - c

(5)

= R

i−1

+ (d

− d

i−1

) - c

. (6) (Buttazzo and

Stankovic, 1993)

Proof. By the residual time deﬁnition (equation 3) we

have:

= d

- f

By the assumption on set ξ, at time t, the task σ

execution and cannot be preempted by other tasks in

the set ξ, hence its estimated ﬁnishing time is given

by the current time plus its remaining execution time:

= t + c

and, by equation (3), we have:

= d

- f

= d

- t - c

For any other task σ

, with i > 1, each task σ

will

start executing as soon as σ

i−1

completes, hence we

can write:

= f

i−1

+ c

(7)

and, by equation (3), we have:

= d

- f

= d

- f

i−1

- c

- (d

i−1

- R

i−1

) - c

= R

i−1

+ (d

- d

i−1

) - c

and the lemma follows.

Lemma 2. A task σ

is guaranteed to complete

within its deadline if and only if R

≥ 0 (Buttazzo and

Stankovic, 1993).

Theorem 3. A set ξ = {σ

, i = 1 to m} of m

active sporadic tasks ordered by increasing deadline

is feasibly schedulable if and only if R

≥ 0 for all σ

∈ ξ, (Buttazzo and Stankovic, 1993).

In our model, we assume that the minimum inter-

arrival time P

of each sporadic task is equal to its

relative deadline D

, thus a sporadic task σ

can be

completely characterized by specifying its worst

case execution time C

and its relative deadline D

Hence, a sporadic task set will be denoted as follows:

ξ = {σ

, D

)}, i = 1 to m.

3.2 Feasibility Analysis for Tasks

By considering real-time tasks and as we mentioned

before, the schedulability analysis should be done

in the hyperperiod HP

(p,ψ

)

= [ζ

(p,ψ

)

, 2*LCM +

(p,ψ

)

], where LCM

p,ψ

is the well-known Least

Common Multiple of tasks periods and (ζ

p,ψ

) is the

largest task offset of all tasks τ

p,ψ

for each reconﬁg-

uration scenario ψ

on each processor p.

Let n + m be the number of tasks respectively in ξ

old

and ξ

new

. By assuming unfeasible system at time t

and every processor p will execute its tasks in local by

using EDF, the following formula is satisﬁed:

∑

n+m

i=1

> K, where K is the number of identical

processors.

Our proposed algorithm provides guarantees to both

old and new tasks in each processor p if and only if,

∑

n− j

i=1

p,ψ

∑

n+m

i=n− j+1

p,ψ

≤ 1

where

∑

n− j

i=1

p,ψ

denotes sum of utilization factor of n old

tasks in processor p for each reconﬁguration scenario

and,

∑

n+m

i=n− j+1

p,ψ

denotes sum of utilization factor

of new arrival m tasks to the processor p for each

reconﬁguration scenario ψ

We propose, for each reconﬁguration scenario ψ

to add the tasks of ξ

old

to a linked list L

old

that we

sort on the increasing order of their utilization factor

values. Let j

be the ﬁrst j tasks of L

old

Approach for each j

∈ [0, n]. When we add

the ﬁrst j

(p,ψ

)

tasks of L

(p,ψ

)

old

to ξ

(p,ψ

)

new

, there are

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382

three different solutions exist for the feasibility of

the system. In such case, if j

= 0, then no tasks

to be added to ξ

new

. After each reconﬁguration

scenario ψ

, the agent suggests the new parameters

for new tasks. After that, the agent selects tasks from

linked list which are sorted on their utilization factor

p,ψ

(p,ψ

)

(p,ψ

)

) with respect to this order to execute

on the processor p. Tasks from linked list are moved

to be inserted and executed with new tasks. Whenever

an old task is moved from linked list to current ready

list composed of new tasks, parameters (WCET,

periods/deadlines) are recalculated and presented by

the agent to the user for each reconﬁguration scenario

. In this case, addition of old task, neither causes

new tasks to miss their deadlines nor misses its own

deadline.

3.3 Contribution: An Algorithm for

Feasibility Testing with Respect

to Sporadic Task Systems

In the current paper, we suppose that on each

processor p, each system ξ

(p)

can be automatically

and repeatedly reconﬁgured at each reconﬁguration

scenario ψ

. ξ

(p)

is initially considered as ξ

(p,0)

and

after the h

reconﬁguration ξ

(p)

turns into ξ

(p,ψ

)

where h ∈ 1..M. We deﬁne VP

p,ψ

and VP

p,ψ

two

virtual processors to virtually execute old and new

sporadic tasks, implementing the system after the

reconﬁguration scenario for each processor p. In

(p,ψ

)

, all old tasks from ξ

(p,ψ

h−1

)

are executed by

the newly updated VP

(p,ψ

)

and the added sporadic

tasks are executed by VP

(p,ψ

)

. The proposed

intelligent agent is trying to minimize the response

time Resp

p,ψ

opt

of ξ

(ψ

)

after each reconﬁguration

scenario ψ

and for each processor p.

For example, after the ﬁrst addition scenario,

(p,0)

turns into ξ

(p,1)

. ξ

(p,1)

is automatically decom-

posed into VP

(p,1)

and VP

(p,1)

for old and new tasks

with the processor utilization factors UVP

(p,1)

and

UVP

(p,1)

respectively on each processor p.

Formalization

We assume in this work a system ξ

(p)

to be composed

of a mixture of n

(p)

periodic and m

(p)

sporadic

tasks on each processor p. An assumed system

(p,ψ

h−1

)

= {τ

(p)

, τ

(p)

,...,τ

(p)

} turns after a reconﬁg-

uration scenario to ξ

(p,ψ

)

= {τ

(p)

, τ

(p)

,...,τ

(p)

n+1

(p)

n+2

,...,σ

(p)

n+m

} by considering that m

new sporadic

tasks are added to ξ

(p,ψ

h−1

)

. After each addition, the

tasks are logically divided into two subsets. One

contains the so called new sporadic tasks which are

added to the system, and the rest of tasks taken from

(p,ψ

h−1

)

are considered as old tasks to form the sec-

ond subset. After any addition scenario, the response

time can be increased and/or some old/new tasks miss

their deadlines. When a reconﬁguration scenario

is automatically applied at run-time, the proposed

agent logically decomposes the physical processor

of ξ

(p,ψ

)

into two virtual processors VP

(p,ψ

)

and

(p,ψ

)

with different utilization factors UVP

(p,ψ

)

and UVP

(p,ψ

)

to adapt the system to its environment

with a minimum response time. For more explaining,

after any reconﬁguration scenario and in order to

keep only two virtual processors in the system ξ

(p)

the proposed intelligent agent automatically merges

(p,ψ

h−1

)

and VP

(p,ψ

h−1

)

into VP

(p,ψ

)

and creates

also a new VP

(p)

named VP

(p,ψ

)

, to adapt old and

new tasks, respectively. The VP

(p,ψ

)

is assumed

to be a located logical pool in idle periods ofVP

(p,ψ

)

For example, we assume that k = 1 and we re-

streint in this case to a uni-processor system, and

we have 2 initial tasks τ

and τ

in an assumed

system sys

p=1

with ξ

(1,0)

= ξ

(0)

= { τ

, τ

}. First,

we add {σ

, σ

and σ

} to ξ

(0)

that automatically

turns into ξ

(ψ

)

= {τ

, τ

, σ

and σ

}. In ξ

(1)

=1), subset {τ

, τ

} is considered as old tasks to be

executed by VP

(ψ

)

, whereas subset {σ

, σ

and σ

}

is considered as new sporadic tasks to be executed by

(ψ

)

. VP

(ψ

)

is located in idle periods of VP

(ψ

)

We propose thereafter, the arrival of new sporadic

tasks σ

and σ

to be added to ξ

(ψ

)

that evolves into

(ψ

)

= {τ

, τ

, σ

and σ

}. VP

(ψ

)

and

(ψ

)

are automaticlly merged into VP

(ψ

)

where

subset {τ

, τ

, σ

and σ

} is considered as old

tasks to be executed by this virtual processor. In this

case, subset {σ

, σ

} is executed by the second newly

created virtual processor VP

(ψ

)

which is located in

idle periods of VP

(ψ

)

After each addition scenario, the proposed in-

telligent agent proposes to modify the virtual

processors, to modify the deadlines of old and new

tasks, the WCETs and the activation time of some

tasks, to send some tasks from processor i to another

processor j, or to removesome soft tasks as following:

• Solution 1: Moving some arrival tasks to be

scheduled in idle times for each reconﬁguration

AnEDF-basedSchedulingAlgorithmforReal-timeReconfigurableSporadicTasks

383

scenario ψ

and on each processor p. (idle times are

caused when some tasks complete before its worst

case execution time) (S1)

• Solution 2: maximize the d

p,ψ

for each re-

conﬁguration scenario ψ

and on each processor p

(S2)

By applying equation (3) that notices:

= d

- f

, we have:

p,ψ

= d

p,ψ

- t - C

p,ψ

Or, to obtain a feasible system after a reconﬁguration

scenario

, the following formula must be enforced:

p,ψ

≥ 0 on each processor p.

By this result we can write: d

p,ψ

inew

- t - C

p,ψ

≥

0, where d

p,ψ

inew

= d

p,ψ

+ θ

p,ψ

So, d

p,ψ

+ θ

p,ψ

- t - C

p,ψ

≥ 0 ⇒

p,ψ

≥ t + C

p,ψ

- d

p,ψ

• Solution 3: minimize the c

for each recon-

ﬁguration scenario ψ

and on each processor p

(S3)

By applying equation (3) that notices:

= d

- f

, we have:

p,ψ

= d

p,ψ

- t - C

p,ψ

Or, to obtain a feasible system after a reconﬁguration

scenario, the following formula must be enforced:

p,ψ

≥ 0.

By this result we can write: d

p,ψ

- t - C

p,ψ

inew

≥ 0,

where C

p,ψ

inew

= C

p,ψ

+ β

p,ψ

So, d

p,ψ

- t - C

p,ψ

- β

p,ψ

≥ 0 ⇒ d

p,ψ

- t - C

p,ψ

≥

p,ψ

⇒ β

p,ψ

≤ d

p,ψ

- t - C

p,ψ

• Solution 4: Enforcing the release time to

come back: a

p,ψ

→ a

p,ψ

inew

→ (a

p,ψ

inew

= a

p,ψ

+ ∆

p,ψ

for each reconﬁguration scenario ψ

and on each

processor p (S4)

By applying equation (1) that notices:

= a

+ D

, we have:

p,ψ

= a

p,ψ

+ D

p,ψ

- t - C

p,ψ

Or, to obtain a feasible system after a reconﬁguration

scenario, the following formula must be enforced:

p,ψ

≥ 0 ⇒ a

p,ψ

+ D

p,ψ

- t - C

p,ψ

≥ 0.

By this result we can write:

p,ψ

inew

+ D

p,ψ

- t - C

p,ψ

≥ 0, where a

p,ψ

inew

p,ψ

+ ∆

p,ψ

So, we obtain: a

p,ψ

+ ∆

p,ψ

t + D

p,ψ

- t - C

p,ψ

≥ 0.

⇒ ∆

p,ψ

t ≥ t + C

p,ψ

- a

p,ψ

- D

p,ψ

• Solution 5: Tolerate some non critical Tasks

among (n + m)

(according to the (m,n) ﬁrm

model), on each processor p for a reasonable cost,

and for each reconﬁguration scenario ψ

(S5)

= {τ

, D

, m

, I

), i = 1ton

= 1, it tolerates missing deadline,

= 0, it doesn’t tolerate missing deadline,

= H, Hard task,

= S, Soft task,

• Solution 6: Migration of some tasks from a

processor source i in order to be scheduled on another

processor destination j for each reconﬁguration

scenario ψ

(S6)

The agent proceeds now as a sixth solution to migrate

some tasks of ξ

p,ψ

new

and ξ

old

on the processor p

for each reconﬁguration scenario ψ

. Indeed, the

agent is responsible for allocating the tasks to the K

computing processors in an optimal way.

Run-time task migration can be deﬁned as the

Figure 1: The Task Migration Sequence.

relocation of an executing task from its current

location, the source processor i, to a new location,

the destination processor j (i 6= j; i,j = 1..K) that must

belong to the inclusion set. We need by inclusion

set in paper, the set of processors in which tasks can

be scheduled after any reconﬁguration scenario ψ

when a migration request has done and in this case

all the relevant state information of that migration

is transferred to the new processor. Otherwise,

it is called exclusion set. This allows the OS to

e.g., minimize energy savings and response time

of the whole system. It also enables processors

management by moving tasks away from processors

with a high amount of workload or which have their

utilization factors > 1. The architectural differences

between the source processor i and destination source

processor j are masked by capturing and transferring

the logical task state, shown by ﬁgure 1. In order to

relocate a task, the intelligent agent notiﬁes the task

by means of a migration request signal

(1)

. Whenever

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384

that signaled task reaches a migration point (MP), it

checks if there is a pending migration request or the

destination processor j belongs to the exclusion group

of the current migrated task for each reconﬁguration

scenario ψ

. In such case of these two reasons, all the

relevant state information of that migration point is

transferred to the intelligent agent

(2)

. Consequently,

the intelligent agent will instantiate the same task on

a different processor. The new task instantiation will

be initialized using the state information previously

captured by the intelligent agent

(3)

. Finally, the task

resumes execution at the corresponding migration

point (MP).

One of the main issues in homogeneous (we suppose

before that all the processors are identical) task

migration is the overhead incurred by checking for a

pending migration request during normal execution

(i.e. when there is no pending migration request).

Especially since a task requires frequent migration

points in order to reduce the reaction time. The

reaction time (Figure 1) is the time elapsed between

selecting a task for migration and the selected task

reaching the next migration point. In order to mini-

mize the checking overhead during normal execution,

further denoted as migration initiation, we propose a

novel technique for the new generation of embedded

systems, that uses the inclusion and exclusion group

informations of each task for each reconﬁguration

scenario ψ

in order to reduce the area search feasi-

blity of such systems and to minimize the reaction

time and consequently the response time will be

minimized too.

• Solution 7: Removal of some non critical tasks (to

be rejected) for each reconﬁguration scenario ψ

and

on each processor p (S7)

= {τ

, D

, m

, I

), i = 1 to n

p,ψ

= 1, it tolerates missing deadline,

p,ψ

= 0, it doesn’t tolerate missing deadline,

p,ψ

= H, Hard task,

p,ψ

= S, Soft task,

For every solution the corresponding response time

is:

Resp

p,ψ

k,1

= the response time calculated by the ﬁrst

solution,

Resp

p,ψ

k,2

= the response time calculated by the

second solution,

Resp

p,ψ

k,3

= the response time calculated by the third

solution,

Resp

p,ψ

k,4

= the response time calculated by the fourth

solution,

Resp

p,ψ

k,5

= the response time calculated by the ﬁfth

solution,

Resp

p,ψ

k,6

= the response time calculated by the sixth

solution,

Resp

p,ψ

k,7

= the response time calculated by the

seventh solution,

We deﬁne now, Resp

p,ψ

optimal noted Resp

p,ψ

opt

according to the previous seven solutions calculated

by the intelligent Agent (Solution 1, Solution 2,

Solution 3, Solution 4, Solution 5, Solution 6 and

Solution 7) by the following expression:

Resp

p,ψ

opt

= min(Resp

p,ψ

k,1

, Resp

p,ψ

k,2

, Resp

p,ψ

k,3

Resp

p,ψ

k,4

, Resp

p,ψ

k,5

, Resp

p,ψ

k,6

and Resp

p,ψ

k,7

) (the

minimum of the seven values). So, the calculation of

Resp

p,ψ

opt

allows us to obtain and to calculate the

minimizations of response times values and to get

the optimum of these values. In conclusion, we can

deduce that by arrival of ξ

new

tasks at run-time and

the whole system become unfeasible, the following

formula based on (A.K.MOK, 1983) is satisﬁed for

each reconﬁguration scenario ψ

∑

(n+m)

i=1

> K, where K is the number of

identical processors.

Then, after the reconﬁguration scenario ψ

was

applied at run-time to the whole system by the

inteligent agent, our proposed algorithm provides

guarantees to both old and new tasks if and only if,

we have in each processor p for each reconﬁguration

scenario ψ

∑

(n+m)

(p,ψ

)

i=1

(p,ψ

)

(p,ψ

)

≤ 1, in each processor p for each

reconﬁguration scenario ψ

Moreover, we have calculated R

(p,ψ

)

opt

min(R

(p,ψ

)

k,1

, R

(p,ψ

)

k,2

, R

(p,ψ

)

k,3

, R

(p,ψ

)

k,4

, R

(p,ψ

)

k,5

(p,ψ

)

k,6

and R

(p,ψ

)

k,7

); so we obtain also:

∑

(n+m)

(p,ψ

)

i=1

(p,ψ

)

(p,ψ

)

< 1, in each processor p for each

reconﬁguration scenario ψ

with 1 ≤ p ≤ K, 1 ≤ h ≤

Now by adding the following formulas, we have:

∑

(n+m)

(1,ψ

)

i=1

(1,ψ

)

(1,ψ

)

< 1,

∑

(n+m)

(2,ψ

)

i=1

(2,ψ

)

(2,ψ

)

< 1,

... < ...

AnEDF-basedSchedulingAlgorithmforReal-timeReconfigurableSporadicTasks

385

∑

(n+m)

( j,ψ

)

i=1

( j,ψ

)

( j,ψ

)

< 1,

... < ...

∑

(n+m)

(K,ψ

)

i=1

(K,ψ

)

(K,ψ

)

< 1,

⇒

∑

(n+m)

i=1

< 1 + 1+ 1+ ... + 1

{z }

Ktimes

⇒

∑

(n+m)

i=1

< K.

This work, concentrates on the context of sys-

tems containing a set of tasks which is not feasible.

The reconﬁguration was applied in order not only

to obtain the system’s feasibility, but also to get the

performance of the system by reducing the response

time of the processes to be tolerated in interactive

environment in order to minimize the response time

of the studied reconﬁgurable embedded system at

run-time for each reconﬁguration scenario ψ

and in

each processor p.

We can observe that our proposed approach provides

an optimal global scheduling algorithm which sched-

ules tasks according to EDF in each processor p for

each reconﬁguration scenario ψ

. All tasks meet their

deadlines after a reconﬁguration scenario ψ

was

applied at run-time. We can also observe, that our

proposed algorithm selects tasks to migrate from one

processor source i to another processor destination

j in an optimal way such that overall utilization of

task set is minimum. Parameters of tasks i.e., period,

deadline and worst case execution time, are generated

randomly. We have illustrated that our proposed al-

gorithm outperforms other scheduling multiprocessor

algorithms and a number of scheduling events are

much lower than appearing in others.

3.4 The General OEDF Scheduling

Strategy

When dealing with the deadline tolerance factor m

each task has to be computed with respect to the

deadline tolerance factor m

Algorithm GUARANTEE(ξ; σ

)

For each h in [1..M] Do

begin t = get current time();

p,ψ

= 0;

p,ψ

= t;

Insert σ

in the ordered task list;

p,ψ

`= ξ

p,ψ

;

k = position of σ

in the task set ξ

p,ψ

for each task σ

p,ψ

`such that i ≥ k do

{

p,ψ

= R

p,ψ

i−1

+ (d

p,ψ

- d

p,ψ

i−1

) - c

p,ψ

;

if (R

p,ψ

≥ 0) then

{

return (”Guaranteed”);

}

else return

(”You can try by using solution 1, or,

You can try by using solution 2, or,

You can try by using solution 3, or,

You can try by using solution 4, or,

You can try by using solution 5, or,

You can try by using solution 6, or,

You can try by using solution 7 !”);

}

• Compute(Resp

p,ψ

k,1

);

• Compute(Resp

p,ψ

k,2

);

• Compute(Resp

p,ψ

k,3

);

• Compute(Resp

p,ψ

k,4

);

• Compute(Resp

p,ψ

k,5

);

• Compute(Resp

p,ψ

k,6

);

• Compute(Resp

p,ψ

k,7

);

• Generate(Resp

p,ψ

opt

);

end

The extension of the proposed algorithm should

be straightforward, when this assumption does not

hold and its running time is O(n + m)

. So, Intu-

itively, we expect that our algorithm performs better

than the Buttazo and Stankovic one. We show the

results of our optimal proposed algorithm by means

of experimental result’s evaluation.

4 EXPERIMENTAL RESULTS

In order to evaluate our optimal OEDF algorithm, we

consider the following experiments.

4.1 Experiments

Running Example 1:

We apply our contribution to this ﬁrst running exam-

ple on the particular case of uni-processor systems

(k = 1) and we could observe that the recalculation

points of the utilization factor, when parameters of

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386

new tasks are modiﬁed, decreases and becomes less

than or equal to 1 and we can deduce that the system

is now feasible.

Running Example 2:

We apply our contribution to this second running

example and we could observe that the recalculation

points of the utilization factor, when parameters of

new tasks are modiﬁed, decreases and becomes less

than or equal to k on the case of multiprocessor

systems and we can deduce that the system is now

feasible.

4.2 Simulations

To quantify the beneﬁts of the proposed approach

(OEDF algorithm) over the predictive system shut-

down (PSS) approach, over the MIN algorithm, the

OPASTS algorithm and over the HPASTS algorithm.

We performed a number of simulations to compare

the response time and the utilization processor under

the four strategies. The PSS technique assumes the

complete knowledge of the idle periods while the

MIN algorithm assumes the complete knowledge

of the arrivals of sporadic tasks. For more details

about both four techniques, you can see (Mani

B. Srivastava, 1998). The OEDF scheduling result is

shown in ﬁgure 2.

Figure 2: Processor Utilization.

4.3 Discussion

In experiments, if the resulting U(t) > 1, we set U(t) to

be 1. We varied the average processor utilization from

the light workload (10 tasks) to heavy workload (100

tasks) generated randomly. We observe that our ap-

proach, by the solutions of the OEDF algorithm gives

us the minimum bound for response time and utiliza-

tion factor. This observation was proven by the re-

sults given by OEDF algorithm which are lower (bet-

ter) than these of the solutions given by the predic-

tive system shutdown approach, the MIN algorithm,

the OPASTS algorithm and the HPASTS algorithm.

Also, we observe that, when we have no knowledge

of the arrival of sporadic tasks, our proposed algo-

rithm is optimal and gives better results than others

for a big number of arrival sporadic tasks and in over-

load conditions, but in a small number of tasks or light

workload, OEDF algorithm is optimal but not strictly

since it gives results close to that of the solutions of

MIN, OPASTS and HPASTS algorithms, but it is ef-

ﬁcient and effective.

Moreover, if the number of solutions presented by the

intelligent agent to the user increases, then chances

of executing more new added tasks increase and the

performance of the real time scheduling is more efﬁ-

cient. This is due to the fact that the reconﬁguration

issues are increased, the user selects the best solution

which gives the minimum utilization factor of the sys-

tem and ameliorates the response time and hence the

chances of executing more new tasks are increased as

well.

The agent should deﬁne the different solutions for the

user. In this case, the user can choose the best solu-

tion that satisﬁes functional requirements. These re-

sults were suggested by the tool RT-Reconﬁguration

and give a feasible system which is proven also by

Cheddar.

5 CONCLUSIONS

This paper deals with reconﬁgurable homogeneous

multiprocessor systems to be implemented by hybrid

systems composed of a mixture of periodic and spo-

radic tasks that should meet real-time constraints. In

this paper, we propose an optimal scheduling algo-

rithm based on the EDF principles and on the dynamic

reconﬁguration for the minimization of the response

time of sporadic and periodic constrained deadline

real-time tasks on multiprocessor systems and proven

it correct. Finally, our important future work is the

generalization of our contributions for the Reconﬁg-

urable real-time embedded systems.

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Al-Saﬁ, Y. and Vyatkin, V. (2007). An ontology-based

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ICSOFT2013-8thInternationalJointConferenceonSoftwareTechnologies

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