EDeg-fs

A Heuristic for Scheduling and Dynamic Power Management in Embedded Energy

Harvesting Systems with DVFS Facilities

Hussein El Ghor

and Maryline Chetto

Lebanese University, IUT of Saida, Saida, Lebanon

IRCCyN Laboratory, University of Nantes, 1 Rue de la Noe, F-44321 Nantes, France

Keywords:

Real-time, Energy Harvesting, Power Management, Dynamic Voltage and Frequency Selection (DVFS), Task

Scheduling.

Abstract:

This work investigates the problem of dynamic power management and scheduling for a uniprocessor system

with dynamic voltage and frequency scaling (DVFS) facilities. This one is qualiﬁed as real-time since jobs

have to be executed before deadlines. In addition, it is an energy harvesting system since its supply energy

is drawn from the environment. We assume that the preemptable jobs receive dynamic priorities according to

the Earliest Deadline First (EDF) rule. We propose to extend the dynamic power management scheme called

EDeg that must be adapted to a processor with DVFS capabilities. We show how to adjust dynamically the

frequency in order to gain quality of service measured in terms of deadline miss rate.

1 INTRODUCTION

Environmental energy harvesting is deemed promis-

ing for the supply of embedded and wireless sen-

sor systems. Many sensing environments provide en-

ergy that can be harvested and converted into elec-

tricity so as to power these systems on an inﬁnite

time. Consequently, energy harvesting can make

them self-sufﬁcient often for decades (Roundy et al.,

2004), having a behavior which is called energy neu-

tral. For example, wireless distributed sensor net-

works (WDSN) (Lewis, 2004) are mainly used in

critical conditions like natural catastrophe and arti-

ﬁcial disruptions. The main role of WDSN is to

help in monitoring physical and environmental con-

ditions like temperature and pressure. However,

WDSN have some drawbacks that are limited bat-

tery life and less processing efﬁciency (Nallusamy

and Duraiswamy, 2011). Therefore, energy harvest-

ing seems to be an appropriate approach to increase

the life time of WDSNs in environmental applica-

tions. Several technologies to extract energy from the

environment have been demonstrated including so-

lar, motion-based, biochemical, and vibrational ener-

gies. Many other ones are being developed (Kotz and

Carlen, 2000). And many prototypes for energy har-

vesting have been described in the scientiﬁc literature.

The ﬁrst ones are certainly Heliomote (Raghunathan

et al., 2005) and Prometheus (Jiang et al., 2005).

The work presented in that paper provides the fol-

lowing contributions to research: We present an on-

line algorithm that permits to answer the three follow-

ing questions dynamically: how and when to decide

whether to put the processor in idle or active mode?

How to select the active task? How to compute the

frequency of the processor for executing the selected

task? Our scheduler is model-free with respect to the

energy source i.e. it can be implemented without prior

information about the source which may be uncon-

trollable and time-varying. The power management

policy is based on trading the slack time and the slack

energy for energy efﬁciency. And the DVFS technol-

ogy enables us to achieve the lowest energy dissipa-

tion. The Quality of Service in terms of deadline suc-

cess ratio is improved.

The rest of this paper is organized as follows. The

energy harvesting system model and some assump-

tions are described in Section 2. Section 3 gives nec-

essary backgroundmaterials. Section 4 introduces the

proposed scheduling and power management frame-

work. Section 5 presents the related research works.

We summarize and describe our current work in Sec-

tion 6.

140

El Ghor H. and Chetto M..

EDeg-fs - A Heuristic for Scheduling and Dynamic Power Management in Embedded Energy Harvesting Systems with DVFS Facilities.

DOI: 10.5220/0005247401400145

In Proceedings of the 5th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS-2015), pages

140-145

ISBN: 978-989-758-084-0

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

2 SYSTEM MODEL AND

TERMINOLOGY

The real-time energy harvesting system considered in

this work consists of three major units: energy har-

vesting unit (EHU), energy storage unit (ESU) and

energy dissipation unit (EDU). The energy harvest-

ing unit harvests the energyfrom external sources like

sun, wind, etc. The harvested energy is stored in the

energy storage unit for future use at any time since

it does not leak any energy over time. This helps

continuous execution of tasks even at times of deﬁ-

ciency. Apart from the applications running in the

energy dissipation unit, there is an additional soft-

ware running in the uniprocessor system, namely the

scheduler. Earliest deadline First (EDF) is the ﬁrst dy-

namic priority scheduler used in our algorithm. The

other used scheduler is the DVFS which slows down

task execution under deadline constraints depending

on the energy harvested and energy in the storage unit.

T1 T2 T3 Tn

Ready Queue

Uniprocessor Computing System

EDF Scheduling

Dynamic Voltage and

Frequency Scaling

Energy Harvesting

Unit

Energy Storage Unit

Pr(t)

Scheduled Tasks

{T1,T2,…,Tn}

Figure 1: A Real-Time Energy Harvesting System model.

2.1 Energy Harvesting Unit (EHU)

We assume that ambient energy is harvested and con-

verted into electrical power. We cannot control the

energy source but we can predict the expected avail-

ability with a lower bound on the harvested source

power output, namely P

(t). Clearly, we make no as-

sumption about the nature and dynamics of the en-

ergy source, making our approach more easily imple-

mented in real systems where data about the energy

source may not be available beforehand.

The energy harvested in an interval of time [t

]

is denoted by E

) and can be calculated using the

following formula:

) =

(t)dt (1)

2.2 Energy Storage Unit (ESU)

We use in our work an ideal energy storage unit (su-

percapacitor or battery) that can be recharged up to

a nominal capacity C. Since we use an ideal energy

storage unit, then the amount of energy wasted in the

process of charging and discharging is neglected. The

energy level has to remain between two boundaries

min

and C

max

with C = C

max

−C

min

. The lower limit

of the energy storage unit (C

min

) is not zero since there

must always be a reserved energy in the energy stor-

age unit for worst case scenarios.

2.3 Energy Dissipation Unit (EDU)

We consider a real-time system equipped with a

DVFS-enabled processor. The variable speed proces-

sor is assumed to be working with N discrete frequen-

cies ranging from f

min

= f

≤ f

≤ ··· ≤ f

= f

max

The total energy consumption of a running job in the

processor depends on the processor’s frequency. The

power consumption and voltage level relative to clock

frequency f

are denoted by P

and V

respectively.

We consider the slowdown factor S

as the fre-

quency f

which is normalized with respect to the

maximum frequency f

max

. S

ranges from S

min

to 1:

max

(2)

We consider that each task is characterized by dif-

ferent power dissipation values according to the se-

lected processor frequency. Any job that results from

task execution has maximum energy consumption if

executed entirely at maximum frequency; And higher

is the processor frequency higher is the energy con-

sumption of the job.

Consequently, besides its timing parameters, ev-

ery task τ

is characterized by N values that respec-

tively correspond to their worst case energy consump-

tion for each of the N different processor frequencies.

The application software is composed of indepen-

dent preemptable periodic tasks: Γ = {τ

|1 ≤ i ≤

n}. A 3-tuple (C

) characterizes task τ

, where

, D

and T

indicate the worst case execution time

(WCET) at maximum frequency, the relative deadline

and the period respectively. τ

generates an inﬁnite set

of jobs that release at times kT

, k = 0,1,2,· ··. When

we stretch any job of task τ

by a slowdown factor

, then its actual execution time (C

(a)) at frequency

will be C

. When the processor is running at

it maximum frequency, then C

(a) = C

. We assume

that 0 ≤ C

≤ D

≤ T

for each 1 ≤ i ≤ n.

EDeg-fs-AHeuristicforSchedulingandDynamicPowerManagementinEmbeddedEnergyHarvestingSystemswith

DVFSFacilities

141

3 BACKGROUND MATERIAL

3.1 EDF Scheduling

The problem of scheduling deadline constrained tasks

on one processor with no energy consideration has

been an active area of research for more than thirty

years (Liu, 2000). One of the most popular ap-

proaches is the dynamic priority driven scheduling

algorithm, known as Earliest Deadline First (EDF).

EDF schedules at each instant of time t, the ready

job (i.e. the job that may be processed and is not yet

completed issued from the task set) whose deadline

is closest to t. EDF has been proved to be optimal

in that sense that if a task set is schedulable by any

algorithm, then it can be feasibly scheduled by EDF.

Moreover, EDF fully exploits the processor, reaching

up to 100% of the available processing time. In gen-

eral, implementation of EDF consists in ordering jobs

according to their absolute deadline either as soon as

possible (EDS) or as late as possible (EDL) (Chetto

and Chetto, 1989), (Silly-Chetto, 1999).

In a system with limitations and ﬂuctuations in

energy availability, simply executing jobs according

to the EDF rule, either as soon as possible (EDS) or

as late as possible (EDL) may lead to violate some

deadlines because of energy starvations. This is why,

in energy constrained systems, dynamic power man-

agement plays a crucial role due to its impact on the

resulting performance. The dynamic power manage-

ment rule will permit to decide when to put the pro-

cessor in the active mode and for how long time.

The objective of such a policy is to prevent from en-

ergy starvation while still preserving the system from

deadline violation.

3.2 EDeg Scheduling

In a recent work, we provided a dynamic power man-

agement policy called EDeg (Earliest Deadline with

energy guarantee) . EDeg orders the ready jobs ac-

cording to the EDF rule but performs a test before

dispatching the highest priority job so as to prevent

from energy starvation. More precisely, if the deci-

sion test receives a “yes” answer, the processor is au-

torized to be in the active mode since two conditions

can be satisﬁed. Firstly, the energy level in the battery

is sufﬁcient enough to execute the active job. Sec-

ondly, executing the active job will not provoke any

energy starvation including for a future occurring job.

We introduced the concept of slack energy of a job

deﬁned as the maximum energy that could be con-

sumed by a lower priority job for avoiding its energy

starvation. And the so-called system slack energy rep-

resents the maximum energy that could be consumed

at the current time while guaranteeing absence of en-

ergy starvation in the system.

The decision test may lead to a “no” answer thus sig-

nifying that the processor has to sleep so that the en-

ergy storage unit recharges sufﬁciently. Deciding for

how long time recharging should be performedis very

ﬂexible. Nevertheless, the best solution is to recharge

the battery at its entire capacity whenever possible,

as long as all the deadlines can still be met despite

execution postponement. As a consequence, such ap-

proach requires to compute at run-time the so-called

slack time of the system whenever necessary in order

to avoid any deadline missing.

3.2.1 Computation of Slack Time

The slack time of a hard deadline set of jobs (which

generally are issued from a periodic task set) at cur-

rent time t is the length of the longest interval starting

at t during which the processor may be idle continu-

ously while still satisfying all the timing constraints.

The determination of slack time at run-time for jobs

issued from a periodic task set can be performed efﬁ-

ciently through a method initially described in (Silly-

Chetto, 1999). Some parts of the computation are

performed once for all and permit to limit the online

overhead.

3.2.2 Computation of Slack Energy

Let P

(k) be the source power that varies with time

k and C(t) be the energy storage capacity at time t.

Let A

be the total energy demand of jobs ready to

be processed between t and d

with a higher priority

than job J

. Consequently, A

∑

≤d

. The slack

energy of any job J

, Slack.Energy(J

,t), is given by

C(t) +

Ps(k)dk− A

The slack energy at current time t,

Slack.Energy(t), is deﬁned as the maximum

amount of energy that can be consumed from t

by the currently highest priority job. Consequently,

Slack.Energy(t) is given by the minimal slack energy

from the all the jobs with a priority higher than one

of the active job.

4 THE EDeg-fs ALGORITHM

We are now ready to describe a new scheduling and

power management scheme called EDeg-fs (EDeg

with frequency scaling facilities). We will show how

to optimize the energy consumption of jobs with the

dynamic voltage and frequency scaling facilities of

PECCS2015-5thInternationalConferenceonPervasiveandEmbeddedComputingandCommunicationSystems

142

the processor. In addition to the functionalities of

EDeg, EDeg-fs selects the execution speed of a run-

ning job from the stored energy as well as the avail-

able harvested energy and deadline of that job.

4.1 Description of EDeg-fs

The idea behind the EDeg-fs algorithm is to still or-

der the jobs according to the EDF rule. The EDeg-

fs schedule differs from the EDF schedule in that the

jobs are not executed as soon as possible with the clas-

sical work-conserving manner. In addition, EDeg-fs

differs from EDeg in that it decides when to execute

jobs at full processor speed and when to decrease the

processing: speed.

Before authorizing a job to execute, it must be

guaranteed that the energy level in the storage be suf-

ﬁcient to provide energy for all future occurring jobs,

be given their energy requirements and the replenish-

ment rate of the storage unit. In other words, sufﬁcient

energy must permit to execute this job completely.

This is realized by computing the slack energy of the

active job as described in the EDeg algorithm. If the

slack energy is negative, this signiﬁes that energy fea-

sibility can be guaranteed only by decreasing the en-

ergy consumption of some jobs through adaptation of

the processor frequency.

Let assume that jobs are ordered according to re-

lease time.If the job J

starts execution at current

time t, its ﬁnishing time could be at least ft

= t +

Slack.Time(t)) while guaranteeing the timing feasi-

bility of the system. That means that in the worst case,

the maximal energy that could be consumed between

t and ft

is C(t) + E

(t, ft

). Consequently, we look

for the slowdown factor, namely S

that leads to an

energy consumption for job J

that is less than C(t) +

(t, ft

). Necessarily, the selected slowdown value

should satisfy S ≥ S

. In the other hand, we compute

the processor speed so that C

(a) = Slack.Time(t).

The slowdown factor must satisfy S ≤ S

with S

Slack.Time(t)

. Finally, the selected slowdown factor is

the lowest value that satisﬁes both S ≥ S

and S ≤ S

Such a computation of the slowdown factor permits

to guarantee both the timing and energy requirements

of the system. If no such a value exists then, the job

should be discarded.

The major components of the EDeg-fs algorithm

are C(t), Slack.Energy(t) and Slack.Time(t) where

t is the current time, C(t) the amount of energy

that is currently stored at time t i.e. the remaining

amount of energy in the energy storage at time t.

Slack.Energy(t) and Slack.Time(t) are respectively

the slack energy of the system and the slack time of

the system at time t. The function execute() puts the

processor in the active mode for executing the ready

job with the earliest deadline.

The EDeg-fs algorithm works as follows: First,

EDeg-fs checks if there are jobs in the ready queue. If

not, the processor is made idle until the next release

time. Otherwise, EDeg-fs selects the highest priority

job ready for execution.

Before authorizing the execution of that job,

EDeg-fs computes ﬁrst the slack energy and second

the energy level in the storage. If the system slack en-

ergy is positive and there is sufﬁcient energy for exe-

cution, then the job will be executed with the high-

est speed. Otherwise, the processor speed is com-

puted from the slack time of the system which leads

to stretch the execution of the job without violating

deadlines. As decreasing the instantaneous process-

ing speed leads to decrease the total energy consumed

by the running job, the level of energy in the storage

will be decreasing more slowly than with the highest

processor speed.

The main contributions of EDeg-fs can be sum-

marized as follows: The energy optimization process

is based on both energy limitations and timing con-

straints. It fully explores the possibility of trading

both the slack time and slack energy for energy sav-

ing especially when considering multiple jobs in the

queue at the same time. It allows DVFS techniques

to achieve lowest energy dissipation while respecting

deadlines. And it avoids wasting the over low energy.

Energy is wasted only when there are no pending jobs

and the storage unit is full.

4.2 Illustrative Example

Let us consider the three following periodic tasks.

= (1, 3,5), τ

= (2,7,10) and τ

= (3, 12, 20). We

assume that the energy storage capacity is C = 200

energy units at t = 0. For simplicity, we assume that

the rechargeable power P

is constant along the hyper-

period (least multiple of the periods) equal to 10. The

processor has eight discrete slowdown factors: 1, 0.8,

0.7, 0.5, 0.4, 0.3 ,0.2 and 0.1. The total energy con-

sumption of every periodic task τ

is shown in table

Let us execute the jobs generated by the task set

Γ according to EDeg-fs within the ﬁrst hyperperiod

from 0 to 20. The EDeg-fs schedule for Γ is illustrated

by ﬁgure 2.

We notice that Γ is schedulable since all tasks are

executed without violating deadlines and without get-

ting out of energy. At timet = 0, all tasks are ready. τ

is the highest priority task and is executed until t = 1

where C(1) = 180 energy units. At time t = 1, τ

executed until t = 3 where C(3) = 120 energy units.

EDeg-fs-AHeuristicforSchedulingandDynamicPowerManagementinEmbeddedEnergyHarvestingSystemswith

DVFSFacilities

143

Table 1: Energy dissipation of tasks τ

Energy Dissipation S = 1 S = 0.8 S = 0.7 S = 0.5 S = 0.4 S = 0.3 S = 0.2 S = 0.1

Task τ

30 25 20 15 11 8 6 3

Task τ

80 65 55 40 32 24 16 10

Task τ

180 140 125 90 70 55 35 20

103 7 8

11 15

18 200

0.2

0.6

1.0

Figure 2: Schedule produced by EDeg-fs.

At t = 3, τ

is the highest priority task ready to be pro-

cessed but it cannot run at maximum speed because of

insufﬁcient energy in the battery. So, we have to slow-

down the processor in such a way that the deadline is

not violated. We have Slack.Time(3) = 4. Thus, the

actual execution time for τ

could be 4 and the slow-

down factor is 3/4. Consequently, the energy dissipa-

tion for τ

is E

= 140. (see table 1). In the other side,

as C(3) + E

(3,7) = 160, we notice that it is possible

to execute τ

as regards it new energy consumption

equal to 140 energy units.

Now, τ

is executed from t = 3 to t = 7 with a

slowdown factor 0.75 where C(7) = 20 energy units.

At time t = 7, τ

is executed until t = 8 where the

battery is fully discharged. The processor is then idle

from time t = 8 until t = 10 whereC(10) = 20 energy

units. At time t = 10, τ

is executed until t = 11 where

the battery is fully discharged. τ

is now ready to be

processed, but it cannot run at maximum speed since

the battery is fully discharged. Slack time is equal

to 2, the actual execution time for τ

is equal to 4

and the slowdown factor is 0.5. According to table 1,

= 40 energy units. Now, τ

is executed fromt = 11

to t = 15 with a slowdown factor equal to 0.5 where

C(15) = 0 energy units. This procedure continues till

the end of the hyperperiod where C(20) = 39 energy

units.

Let us now consider the EDeg schedule where

all the jobs are processed at the constant highest fre-

quency (see ﬁgure 3). The total energy consumed un-

der EDeg-fs is about 22 percent less than under EDeg

104 5 8

11 15

18 200

0.2

0.6

1.0

Slack time =4

Energy Storage is

insufficient to complete

execution

Figure 3: Schedule produced by EDeg.

while still guaranteeing the timing requirements of all

the jobs. We may consider that EDeg-fs has signiﬁ-

cant improvement over EDeg for that illustrative ex-

ample.

5 RELATED WORK

Energy harvesting systems design has been exten-

sively studied in the past years. In practice, the total

energy which can be consumed by a task is not nec-

essarily proportional to its execution time and slack

time is not used for energy savings. Clearly, as an

embedded system uses a unique energy storage con-

sidered as the critical resource of the system, a suc-

cessful power-awarescheme must consider these non-

computation activities and coordinate their power us-

age as a whole system. Under these assumptions,

we presented a scheduling algorithm, EDeg (Earliest

Deadline with energy guarantee) (Ghor et al., 2011),

that takes into consideration the limits of both time

and energy. EDeg relies on two basic concepts: slack

time and slack energy. The main idea behind EDeg

is to run tasks according to the earliest deadline ﬁrst

rule. However, before authorizing a task to execute,

we must ensure that the energy storage is sufﬁcient

to execute all future occurring tasks. When this con-

dition is not veriﬁed, the processor has to stay idle

so that the storage unit recharges as much as possible

and as long as all the deadlines can still be met despite

execution postponement.

Later in (Chetto et al, 2011), we proved by per-

formance evaluations the efﬁciency of this sched-

uler. However, EDeg is a clairvoyant algorithm since

it needs the characteristics of the future tasks and

the energy source proﬁle to build an optimal sched-

ule. To achieve better system performance and en-

ergy efﬁciency, classical priority driven scheduling

has been extendedto variable-voltageprocessors. The

idea is to save power by slowing down the processor

just enough to meet the deadlines. In (Allavena and

Mosse, 2001), A. Allavena et al. describe an off-line

scheduler that uses voltage and frequency selection

(DVFS) for a frame based system. While they per-

mit to reduce power consumption by slowing down

task execution under deadline constraints, their ap-

proach relies on the unrealistic assumption that both

PECCS2015-5thInternationalConferenceonPervasiveandEmbeddedComputingandCommunicationSystems

144

the instantaneous consumption power and production

power are constant.

S. Liu et al. (Liu et al., 2008) propose an en-

ergy aware dynamic voltage and frequency selection

algorithm, called EA-DVFS, for periodic tasks. The

purpose of EA-DVFS is to efﬁciently use the slack

to reduce the deadline miss rate. Processors must

select between running with maximum power or re-

duced power based on the available energy. If the

system has sufﬁcient energy, the task is executed at its

full speed; otherwise, it is stretched and executed at a

lower speed. In case of low workload, EA-DVFS al-

gorithm reduces deadline miss rate by 50% compared

to LSA and decreases the minimum storage size by

25% when the deadline miss rate is zero. The advan-

tage of EA-DVFS is that it reduces the deadline miss

rate and storage capacity in case of low overload.

Later in (Liu et al., 2012), Liu et al. presented a

harvesting-awareDVFS (HA-DVFS) algorithm to im-

prove the system performance by fully exploiting the

task slack under timing and energy constraints. HA-

DVFS utilizes adaptive scheduling techniques com-

bined with dynamic voltage and frequency selection

to reduce the deadline miss rate when compared to

LSA and EH-DVFS.

6 CONCLUDING REMARKS

In this paper we have described an integrated frame-

work for deadline constrained job scheduling, dy-

namic power management and voltage/frequency se-

lection in real-time energy harvesting systems. The

scheduler is a dynamic priority driven one that uses

the Earliest Deadline First rule. The dynamic power

management policy consists in checking the energy

feasibility through computation of the so-called slack

energy. This is to verify that deadlines will be met

while guaranteeing no energy starvation; And the

voltage/frequency selection policy slowdowns task

execution whenever the system has slack time.

We are now conducting an experimental study in

order to compare the EDeg-fs and EDeg algorithms.

We want to evaluate (in comparison to EDeg) how

much EDeg-fs permits to increase the resulting Qual-

ity of Service i.e. the deadline success ratio. More-

over, it could be interesting to show the improvement

of EDeg-fs over EDeg regarding the minimum energy

storage capacity requirement to achieve zero deadline

miss ratio.

REFERENCES

S. Roundy, D. Steingart, L. Frechette, P. K. Wright, and

J.M. Rabaey. Power sources for wireless sensor net-

works. In Proc. Euro.Workshop Wireless Sensor Net-

works, pp. 117, 2004.

R. Kotz and M. Carlen. Principles and applications of elec-

trochemical capacitors. In Electrochimica Acta 45,

pages 2483-2498. Elsevier Science Ltd., 2000.

V. Raghunathan, A. Kansal, J. Hsu, J. Friedman, and M.

B. Srivastava. Design considerations for solar energy

harvesting wireless embedded systems. In Proc. Int.

Symp. Inf. Process. Sensor Netw., pp. 457462, 2005.

X. Jiang, J. Polastre, and D. E. Culler. Perpetual envi-

ronmentally powered sensor networks. In Proc. Int.

Symp. Inf. Process. Sensor Netw., pp. 463468, 2005.

F. L. Lewis. Smart Environments: technologies, protocols,

and Applications. John Wiley, New York, 2004.

R. Nallusamy and K. Duraiswamy. Solar Powered Wireless

Sensor Networks for Environmental Applications with

Energy Efﬁcient Routing Concepts: A Review. Infor-

mation Technology Journal, 10: 1-10, 2011.

A. Kansal, J. Hsu. Harvesting aware power management

for sensor networks. In IEEE Proceedings of design

automation conference, 2006.

J-W-S. Liu. Real-time systems. Prentice-Hall, 2000.

H. Chetto, M. Chetto. Some results of the earliest deadline

scheduling algorithm. IEEE Transactions on Software

Engineering 1989;15(10):12619, 1989.

M. Silly-Chetto. The EDL server for scheduling periodic

and soft aperiodic tasks with resource constraints.

Real-Time Systems; 17(1):125, 1999.

H. El Ghor, M. Chetto and R. Hajj Chehade. A Real-Time

Scheduling Framework for Embedded Systems with

Environmental energy Harvesting. In Computers &

Electrical Engineering, 2011.

M. Chetto, H. EL Ghor and R. Hage Chehade. Real-Time

Scheduling for Energy Harvesting Sensors. The 6th

International Conference for Internet Technology and

Secured Transactions, Abu Dhabi, UAE, December

11-14, pp. 396 - 402, 2011.

A. Allavena, and D. Mosse. Scheduling of Frame-

Based Embedded Systems with Rechargeable Batter-

ies. Proc. of Workshop on Power Management for

Real-time and Embedded Systems, May 2001.

S. Liu, Q. Qiu, Q. Wu. Energy aware dynamic voltage and

frequency selection for real-time systems with energy

harvesting. In: Proceedings of the conference on de-

sign, automation and test in Europe, p. 236241, 2008.

S. Liu, J. Lu, Q. Wu and Q. Qiu. Harvesting-Aware Power

Management for Real-Time Systems With Renewable

Energy. IEEE Transactions on Very Large Scale Inte-

gration (VLSI) Systems, Vol. 20, No. 8, August 2012.

EDeg-fs-AHeuristicforSchedulingandDynamicPowerManagementinEmbeddedEnergyHarvestingSystemswith

DVFSFacilities

145