Enhancement of Generalized Earliest Deadline First Policy
Mourad Kaddes
1,2
, Laurent Amanton
1
, Alexandre Berred
3
, Bruno Sadeg
1
and Majed Abdouli
2
1
LITIS, Le Havre University, 25 rue Philipe Lebon, 76600 Lehavre, France
2
MIR@CL, P
ˆ
ole Technologique de Sfax, Sfax University, BP 242, 3021 Sfax, Tunisia
3
LMAH, Le Havre University, 25 rue Philipe Lebon 76600, Lehavre, France
Keywords:
Real-time Database System, Transaction Processing, Scheduling Policy, Success Ratio, Transaction Impor-
tance.
Abstract:
Scheduling transactions in real-time database systems (RTDBSs) is more complex than scheduling tasks in
real-time systems. In fact, the RTDBS must guarantee the database logical consistency, on one hand, and
it must schedule the transactions in order to meet their deadlines, on the other hand. The main policy used
to schedule transactions in RTDBSs is Earliest Deadline First (EDF). However, it is well-known that EDF is
not efficient for scheduling transactions in overload conditions. Consequently, different scheduling protocols:
AED, AEVD, APP, AEDF-Co, GEDF... were proposed to improve the system performances in firm RTDBSs,
i.e. late transactions are considered useless. Generalized Earliest Deadline First (GEDF) is a new scheduling
protocol in which transaction priority is assigned according to both deadlines and a parameter, called SPriority,
which expresses the importance of transactions. In this paper, an RTDBSs analysis is presented. The accuracy
of GEDF scheduling policy and the influence of database workload on the system performances is investigated.
This study enabled us to describe the complete behavior of the transaction success ratio. Moreover, based on
intensive simulations, we have derived the optimal values of the system parameters which improve the success
ratio without modifying GEDF protocol.
1 INTRODUCTION
A real-time database systems (RTDBSs) can be con-
sidered as a combination of a traditional database sys-
tem and a real-time system. RTDBSs have to satisfy
both temporal consistency and logical consistency of
the database, i.e. they must guarantee the transactions
ACID
1
properties on one hand, and they must sched-
ule the transactions in order to meet their individual
deadlines, on the other hand (Ramamritham et al.,
2004).
Different scheduling algorithms are proposed in
the literature according to the type of knowledge used
(see (Ramamritham et al., 2004; Han et al., 2012)).
The most performance studies use EDF scheduling
policy which is based on a priority assignment accord-
ing to the deadlines, i.e. the shortest is the transaction
deadline, the highest is its priority. However, with
EDF, successful transactions are prioritized in favor
of transactions which are close to their deadlines, i.e.
successful transactions are not necessarily the most
1
Atomicity, Consistency, Isolation, Durability
important transactions in the system. Moreover, it
is well-known that EDF is not efficient to schedule
transactions (or tasks) in overload conditions, leading
to the degradation of the system performances. This
is due to the assignment of high priorities to trans-
actions that finally might miss their deadlines. These
high-priority transactions also waste system resources
and delay other transactions (Yu et al., 1994). To
overcome these disadvantages, the study dealt with
in (Haritsa et al., 1991) introduced an extension of
EDF (called Adaptive Earliest Deadline: AED). AED
stabilizes the overload performance of EDF through
an adaptive admission control mechanism in an RT-
DBSs environment. In this method, the incoming
transactions are assigned to either hit or miss group.
Using a feedback mechanism, the capacity of the hit
group is adjusted dynamically to improve the perfor-
mances. Transactions in miss group receive process-
ing only if the hit group is empty. AED is later ex-
tended by Pang et al. (Pang et al., 1992) where they
proposed AEVD (adaptive earliest virtual deadline)
protocol which adresses the fairness issue in an over-
231
Kaddes M., Amanton L., Berred A., Sadeg B. and Abdouli M..
Enhancement of Generalized Earliest Deadline First Policy.
DOI: 10.5220/0004448802310238
In Proceedings of the 15th International Conference on Enterprise Information Systems (ICEIS-2013), pages 231-238
ISBN: 978-989-8565-59-4
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
loaded system. In AEVD, the virtual deadlines are
computed based on both arrival times and deadlines.
Since transactions with longer execution times will
arrive earlier relative to their deadlines, AEVD can
raise their priorities in a more rapid pace as their du-
rations in the system increase. Consequently, longer
transactions can exceed the priorities of shorter trans-
actions that have earlier deadlines but later arrival
times. To resolve some weaknesses of AEVD, Datta
et al. (Datta et al., 1996) have introduced priority
based scheduling policy, called AAP (Adaptive Ac-
cess Parameter) method where they use explicit ad-
mission control. In (Han et al., 2012), authors have
proposed a new scheduling algorithms called Adap-
tive Earliest Deadline First Co-Scheduling (AEDF-
Co). In AEDF-Co, a dynamic scheduling approach is
adopted to adaptively schedule the update and appli-
cation jobs based on their deadlines. The performance
goal of AEDF-Co is to determine a schedule for given
sets of periodic application and update transactions
such that the deadline constraints of all the applica-
tion transactions are satisfied and at the same time to
maximize the quality of data (QoD) of the real-time
data objects.
In this paper, we propose an improvement of the
GEDF scheduling policy presented by Semghouni et
al. (Semghouni et al., 2007). To this purpose, we ac-
curately study the GEDF scheduling policy and par-
ticularly study (i) the influence of the weight of the
SPriority (see formula 1), (ii) the rank assigned to
weight of transaction in the SPriority formula (see for-
mula 3) on RTDBSs performances according to the
workload, under the main concurrency and schedul-
ing protocol 2PL-HP (Two phase locking high pri-
ority). GEDF is based on a weight technique, i.e. a
weight is assigned to a transaction according to its
importance in the system. GEDF proposes to over-
come the shortcoming of EDF and is considered as
a generalization of EDF due to its flexibility and its
adaptability to the system workload conditions. To
show the improvement of GEDF scheduling policy
on RTDBSs performances, the system performances
according to the transactions success ratio with dif-
ferent values of the weight of the Spriority and the
transactions priority parameters are analyzed. Then
the optimal values of these parameters according to
the workload are deduced. To this purpose, we have
conducted intensive Monte Carlo simulations on the
RTDBSs simulator we have developed. The simula-
tor is based on components generally encountered in
RTDBSs (Kim and Son, 1996; Ramamritham et al.,
2004).
The remainder of this paper is organized as fol-
lows. In Section 2, we briefly present GEDF policy
and the simulator components. We present the met-
rics used in section 3. Section 4 presents the Monte
Carlo simulation experiments and shows how we can
improve the success ratio of GEDF by choosing the
optimal values of influent factors according to the sys-
tem status. Finally, in section 5, we conclude the pa-
per and discuss some aspects of our future work.
2 SYSTEM MODEL
AND SIMULATOR
2.1 System Model
Only firm real-time transactions are considered and
classified into update and user transactions. Update
transactions are periodic and only write temporal data
which capture the continuously state changing envi-
ronment. We assume that an update transaction is re-
sponsible for updating a single temporal data item in
the system. Each temporal data item is updated fol-
lowing a more-less approach where the period of an
update transaction is assigned to be more than half of
the validity interval of the temporal data (Xiong and
Ramamritham, 2004). User transactions can read or
write non-temporal data and only read temporal data.
User transactions arrive in the system according to a
Poisson process with an average rate λ. The number
of operations generated for each user transaction is
uniformly distributed in the user transaction size in-
terval (denoted User
SInerval
). Data accessed by the
operations of the transaction are randomly generated
and built according to the level of data conflicts (for
more detail see (Semghouni et al., 2008) ).
GEDF is a dynamic scheduling policy where
transactions are processed in an order determined
by their priorities, i.e. the next transaction to run is
the transaction with the highest priority in the active
queue. The priority is assigned according to both the
deadline which expresses the criticality of time and
the SPriority which expresses the importance of the
transaction. We consider that the zero value of the
Priority (Priority = 0), corresponds to the highest
priority in the system. Transaction T is assigned a
priority by the formula:
Priority(T ) = (1 − a) × Deadline(T ) + a × SPriority(T )
(1)
where :
• SPriority. System priority is a parameter related
to each transaction. It expresses the degree of im-
portance of the task(s) executed by a transaction
and defines its rank among all the transactions in
ICEIS2013-15thInternationalConferenceonEnterpriseInformationSystems
232
the system. Two weight functions are used ac-
cording to the transaction class to assign the SPri-
ority value and are described in what follows.
• 0 ≤ a ≤ 1, is the weight given to SPriority in the
priority formula.
1- Update Transactions Class. Let MaxPeriode be
the longest period among the periods of update trans-
actions. The SPriority of an update transaction T is
computed according to the following formula:
SPriority
update
= N ×
Periode
T
MaxPeriode
(2)
2- User Transactions Class. The user transaction
importance SPriority uses criteria based on both the
transaction ”write” set operations and the transaction
”read” set operations. A user transaction T is assigned
a SPriority value by the following formula:
SPriority
user
= MaxValue − γ×
Weight
T
− (1 − γ) × DBA
Value
(3)
where
1. Weight
T
denotes the weight of the current user
transaction and is given by
Weight
T
= (
n
∑
i=1
W read
T D
+
m
∑
j=1
W write
NT D
−
l
∑
k=1
W read
NT D
) (4)
where
(a) W read
T D
, W write
NT D
and W read
NT D
denote
respectively the weight assigned to a read op-
eration of a temporal data, the weight assigned
to a write operation of a non-temporal data and
the weight assigned to a read operation of a
non-temporal data (see the transaction charac-
teristics in Table 1).
(b) n, m, and l are the numbers of operations
(Read
T D
/ W rite
NT D
/ Read
NT D
) in each user
transaction.
2. γ ∈]0,1] is the rank assigned to the transaction
weight in the SPriority formula (see Table 1).
3. DBA
Value
is a uniform random variable between 0
and (MaxValue − N), i.e. Random(MaxValue −
N). We recall that N is the value that divides
the SPriority interval [0, MaxValue] according to
transactions class, i.e. SPriority
update
∈]0,N] and
SPriority
user
∈]N, MaxValue].
4. Maximum(γ × Weight
T
− (1 − γ) × DBA
Value
) ≤
MaxValue − N, because the user transactions
SPriority belongs to ]N,MaxValue].
2.2 Simulator
User transactions are submitted to the system follow-
ing a Poisson process (see Figure 1) with an average
rate λ into the active queue. The deadline controller
(DC) supervises the transactions’ deadlines, and in-
forms the transaction scheduler (TS) when a transac-
tion misses its deadline in order to abort it. Fresh-
ness manager (FM) exploits the absolute validity in-
terval (avi) to check the freshness of a data item be-
fore a user transaction accesses it and blocks all user
transactions which read stale temporal data. Transac-
tions data conflicts are resolved by the Concurrency
controller (CC) according to transactions priorities.
CC informs TS in the following cases: (a) when a
transaction is finished (committed) and its results are
validated in the database, (b) when a transaction is
blocked waiting for a conflict resolution, (c) when a
transaction is restarted, following the commit of other
transactions, (d) when a transaction is rejected be-
cause its restart is impossible, i.e. its best execution
time is higher than its deadline minus the current time
(BET
T
> DT − currenttime), (e) or when a transac-
tion is transferred from the blocked queue to the ac-
tive queue, i.e. its data conflicts are resolved.
Completed transactions
Active queue
Rejection queue
Tr Scheduler Concurrency controller
2PL−HP EDF
or
GEDF
Temporal Data
Rejected transactions
Freshness Manager
Deadline controller
Blocked queue
Non−Temporal Data
Periodic update transactions
Transactions
Transactions generator
(Poisson process)
Figure 1: Simulator architecture.
3 SYSTEM PERFORMANCE
METRICS
To measure the system performances, we consider
transaction success ratio as the main metric. The suc-
cess ratio is given by:
SRatio =
CommitT
SubmittedT
,
where CommitT indicates the number of transactions
committed by their deadlines, and SubmittedT indi-
cates all submitted transactions to the system in the
sampling period. We divide this metric into two parts
according to the class of transactions:
EnhancementofGeneralizedEarliestDeadlineFirstPolicy
233
• Success ratio of update transactions:
SRatio
U pdate
=
CommitT
U pdate
SubmittedT
U pdate
.
This ratio indicates the number of update trans-
actions committed by their deadline. It repre-
sents the consistency level of temporal data in the
database.
• Success ratio of user transactions:
SRatio
User
=
CommitT
User
SubmittedT
User
.
This ratio indicates the number of user transac-
tions committed by their deadlines.
4 RESULTS
In (Semghouni et al., 2007), the authors have shown
that GEDF scheduling policy gives better results than
EDF, notably when the system is overloaded. In
the present paper, we propose to improve the per-
formances of GEDF scheduling policy. To achieve
our goal, we analyse the influence of the SPriority
weight and the rank assigned to transaction weight on
the GEDF behavior and on the system performances.
For this, we varied the values of the parameter a in the
Formula 1 and we have assigned the value
4
5
= 0.8 to γ
parameter in order to minimize the effect of the DBA,
i.e. database administrator interaction, in the SPrior-
ity Formula 3 in the first step. In the second step, we
varied the value of the parameter γ in the SPriority and
we have fixed the value of a to 0.4 and then to 0.9 to
show the influence of the rank assigned to transaction
weight on the GEDF behavior and the system perfor-
mances. In the third step, we varied the value of a
and γ jointly to get the optimal system performances.
The assigned values used in simulations are a = 0, 0.1,
0.2, ..., 1.0, γ= 0.1, 0.2, 0.4, 0.5, 0.6, 0.8. This vari-
ation of parameters allows to deduce the appropriate
assigned values to the parameters a and γ according
to the system workload.
We carried out Monte Carlo simulations that al-
lows us to study the transactions’ success ratio behav-
ior and the system quality of service. According to
the system parameters given on Tables 1 and 2, we
repeat the experiment 1000 times in each simulation
in order to obtain a sample of 1000 values for the per-
formances.
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
mean(SRatio)
λ
SRatio
EDF
a=0.1
a= 0.2
a = 0.3
a = 0.4
a = 0.5
a = 0.6
a = 0.7
a= 0.8
a=0.9
a = 1.0
(a) Success ratio of transactions when using EDF Vs
GEDF
a=0.1,0.2,..,1.0
90
92
94
96
98
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
mean(SRatioUpdate)
λ
EDF
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(b) Success ratio of update transactions when using EDF Vs
GEDF
a=0.1,0.2,..,1.0
0
10
20
30
40
50
60
70
80
90
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
mean(SRatioUser)
λ
EDF
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(c) Success ratio of user transactions when using EDF Vs
GEDF
a=0.1,0.2,..,1.0
Figure 2: Influence of the SPriority weight parameter ac-
cording to system workload.
4.1 Influence of SPriority Weight on
System Performances According
to the System Workload
To show the importance of influence of SPriority
weight we have varied the values of the parameter
a form 0 to 1 using step 0.1 under different system
workloads. We note that the value of γ parameter is
set to
4
5
in order to minimize the influence of DBA.
Figure 2(b) shows that the best performances for
ICEIS2013-15thInternationalConferenceonEnterpriseInformationSystems
234
Table 1: Simulation parameters used for transaction characteristics.
Transaction characteristics
Notation Definition Values
ϕ Probability to execute a ”Read” or a
”Write” operation.
ϕ(Read) = 2/3, ϕ(W rite) = 1 −
ϕ(Read) = 1/3.
User
SInerval
User transaction size interval. [5, 45] combined operations.
U pdate
size
Number of operations in an update
transaction.
1 write operation.
SPriority Intervals of SPriority. SPriority
U pdate
∈ [0,16] and
SPriority
User
∈]16,80].
Table 2: Simulation parameters used for system characteristics.
System characteristics
Notation Definition Values
Quantum Execution capacity in one clock cycle. 20 Tasks/clock cycle
Task Atomic action. one Read or Write operation.
ReadTime Consumption of a read operation. 1 quantum unit.
WriteTime Consumption of a write operation. 2 quantum units.
Time Duration of one experiment. 1000 clock cycles.
DBSize Number of data in the DB. 300.
TD-size Number of temporal data in the DB. 15% × DBSize
update transactions are obtained with GEDF schedul-
ing policy: the success ratio is maximal, i.e. 100%
with different values of a, where a ∈ ]0, 1]. More-
over, we have obtained the same performances on the
update success ratio results for all system workload
conditions (Figure 2(b)). We can conclude that in-
creasing the user transactions number has no signifi-
cant effect on the update transactions performances.
With EDF, there is no difference between the two
classes of transactions, since only the deadline is
taken into account. Thus, user transactions can be
scheduled prior to update transactions if their dead-
lines are imminent, which affects (decreases) the suc-
cess ratio of update transactions and degrades the tem-
poral data consistency in the database. This affects
also considerably the success ratio of user transac-
tions, especially when the system workload is heavy.
In what follows, we study the user transactions
performances on three intervals: λ ∈ [0.1,0.6[ (light
workload to average workload), λ ∈ [0.6,0.8] (av-
erage workload) and λ ∈ ]0.8,2.3] (high workload).
Hence we explore the effects of SPriority weight a on
the success ratio : we compare the results obtained
under different values of a according to system work-
load. Figures 2(a), 2(b) and 2(c) illustrate graphically
this comparison.
When λ is in the interval [0.1,0.6[, i.e. the sys-
tem is not overloaded, EDF gives better performances
on user transactions SRatio
User
than GEDF, for differ-
ent values of a (see Figure 2(c)). Indeed, when using
GEDF scheduling policy, the lower priority transac-
tions must wait for the commit of the higher prior-
ity transactions to be executed even if their deadlines
are imminent. This has a negative effect when the
system workload is light, which reduces the chances
of lower priority transactions to commit, i.e. the user
transactions’ success ratio decreases. For an average
system workload, i.e. the value of λ is in the interval
[0.6,0.8[, we can see that GEDF provides better re-
sults than EDF according to the variations of the SPri-
ority weight parameter. The inflection points corre-
sponding to those situations can be seen in Figure 2(a)
and on firgure 2(c). When the system workload is
heavy, i.e. λ ∈ ]0.8, 2.3], the situation is completely
reversed in favor of GEDF that provides better per-
formances than EDF. We note that inflection points
are jointly related to a and the best performances are
given by different values of a according to the work-
load.
In the following, we discuss and compare the suc-
cess SRatio obtained under different values of SPri-
ority weight when using 2PL-HP protocol (see Fig-
ure 3). When we look at SRatio obtained under dif-
ferent values of SPriority weight parameter, we de-
duce that the form of the graphic depends on the
load of system (see Figure 3). When λ is in the
interval [0.1, 0.6[, EDF gives the best SRatio, i.e.
SRatio
EDF
> SRatio
GEDF
with different values of the
a parameter. Particularly, when λ is in the interval
[0.1, 0.4[, and when a increases, SRatio decreases.
EnhancementofGeneralizedEarliestDeadlineFirstPolicy
235
When λ is equal to 0.6, the best SRatio is provided
by GEDF for a = 0.4. The SRatio increases giving the
best SRatio when a = 0.4 and then decreases. When λ
is in interval [0.7, 1.1], SRatio provided by GEDF is
better than the SRatio provided by EDF for all values
of a. In the same way, SRatio increases given the best
SRatio when a = 0.5 and then decreases. When λ is
in the interval [1.2, 2.3), the peak of SRatio changes
from a = 0.6 to a = 0.9, simultaneously with the in-
creasing of λ. The difference between SRatio
EDF
and SRatio
GEDF
, achieves to 9% and 15% between
SRatio
EDF
user
and SRatio
GEDF
user
when λ = 1.4.
0.972
0.974
0.976
0.978
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean (SRatio)
a
Sratio
λ=0.4
(a) Success ratio of transactions when λ = 0.4 (light workload).
0.85
0.855
0.86
0.865
0.87
0.875
0.88
0.885
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean (SRatio)
a
Sratio
λ=0.8
(b) Success ratio of transactions when λ = 0.8 (average load).
0.67
0.68
0.69
0.7
0.71
0.72
0.73
0.74
0.75
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean (SRatio)
a
Sratio
λ=1.4
(c) Success ratio of transactions when λ = 1.4 (overload).
Figure 3: Influence of SPriority weight on transactions with
2PL-HP protocol when γ = 0.8.
4.2 Influence of the Rank assigned to
Transaction Weight (RTW) in the
SPriority on the System
Performances According to the
Workload
In order to study the influence of the rank assigned
to transaction weight, we analyze firstly the success
ratio of transactions obtained under different values
of RTW. Then we accurate our analysis by studying
the succes ratio of user transactions under different
values of RTW and SPriority weight.
In the previous section, we have studied the influ-
ence of SPriority weight according to the workload
when RTW value γ is equal to 0.8. We have seen
that when λ < 0.6, EDF gives the best SRatio whereas
when λ ≥ 0.6, GEDF gives the best SRatio. Particu-
larly when λ > 1.2, the best SRatio is given by GEDF
when a = 0.8. To analyze the impact of γ, we have
done the same analysis with γ = 0.2 (see Figure 4). In
the same way, when λ < 0.6, the best SRatio is given
by EDF and when λ ≥ 0.6, GEDF gives a better re-
sult than EDF. In fact, when λ is in [0.6, 0.8[, the best
SRatio is obtained when a = 0.2 (Figure 4(a)). When
the workload increases, the value of a increases too,
but does not exceed 0.5 (Figure 4(b)).
In the following section, we compare the
success ratio of user transactions under differ-
ent values of RTW and SPriority weight (γ =
0.1,0.2,0.4, 0.5,0.6, 0.8, a = 0.1, 0.2,...,1.0) accord-
ing to system workload. In all simulations, we have
seen that EDF is more efficient than GEDF when
λ < 0.6. Hence, we discuss and compare the suc-
cess SRatio
user
only in average and high workload and
how it is possible to exploit the flexibility of GEDF in
order to improve the systems performances. Figures
5(a) and 5(b) illustrate graphically this comparison.
The choice of RTW affects significantly the suc-
cess ratio of transactions when the weight of SPri-
ority is small, i.e. a ≤ 0.5. In fact, the range be-
tween the different values of SRatio
user
under various
RTW values reaches 8.5% (see Figure 5(a)).Whereas,
when the weight of SPriority is important, i.e., when
a > 0.7, the influence of RTW on the success ratio
of transaction decreases considerably. The range be-
tween the different SRatio
user
under various RTW val-
ues does not exceed 1.76%, (Figure 5(b)).
To get the optimal Sratio
user
under different work-
loads of systems, we have made a combination be-
tween all values of RTW and those of SPriority
weight. Table 4 in appendix gives the best and worst
values to assigne to the γ under various SPriority
weights according to the system workload.
ICEIS2013-15thInternationalConferenceonEnterpriseInformationSystems
236
0.885
0.89
0.895
0.9
0.905
0.91
0.915
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean (SRatio)
a
Sratio
λ=0.7
(a) Success ratio of transactions when λ = 0.7 (average workload).
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.6
0.61
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
mean (SRatio)
a
Sratio
λ=2.3
(b) Success ratio of transactions when λ = 2.3 (overload).
Figure 4: Influence of SPriority weight on transactions with
2PL-HP protocol when γ = 0.2.
Table 3 shows the optimal values of a and γ ac-
cording to the workload. To show the gain obtained
by using these optimal values, we have compared
SRatio
user
GEDF
when γ and a are assigned the follow-
ing optimal values (see Table 3); γ = 0.8, a = 0.9;
γ = 0.2, a = 0.1 and EDF (see Figure 6).
We note that when the system is moderately
loaded, the best SRatio
user
is given with a small value
of SPriority and with a small value of RTW. When the
workload increases, we have to increase the weight
of SPriority and RTW in order to obtain the best
SRatio
user
. This is illustrated in table 3.
Table 3: Influence of RTW and SPriority weight on
SRatio
user
.
λ ≤ 0.6 λ ∈ [0.7,1.1[ λ ∈ [1.1, 1.2[
EDF a= 0.3, γ = 0.2 a=0.4, γ = 0.2
λ ∈ [1.2,1.4[ λ ∈ [1.4,2.2[ λ ∈[2.2, 2.3[
a=0.5 ,γ = 0.5 a=0.6, γ = 0.5 a=0.7,γ = 0.5
5 CONCLUSIONS
GEDF is a multi-parameters scheduling policy based
on the well-known EDF policy. Its parameters have
10
15
20
25
30
35
40
45
50
55
60
65
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
mean(SRatio
user
)
λ
SRATIO
user
γ =0.8
γ =0.6
γ=0.5
γ =0.4
γ =0.2
γ =0.1
(a) influence of γ on SRatio
user
when a = 0.4.
15
20
25
30
35
40
45
50
55
60
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
mean(SRatio
user
)
λ
SRATIO
user
γ =0.8
γ =0.6
γ=0.5
γ =0.4
γ =0.2
γ =0.1
(b) influence of γ on SRatio
user
when a = 0.9.
Figure 5: Influence of γ in SRatio
user
.
0
10
20
30
40
50
60
70
80
90
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
mean(SRatio
user
)
λ
SRatio
Optimal a, γ values
EDF
γ = 0.8, a= 0.9
γ = 0.2, a= 0.1
Figure 6: Success ratio of user transactions with optimal
values of RTW and SPriority weight according to workload.
to be defined by taking into account the system char-
acteristics such as the workload. The analysis of the
system performances we have conducted in this pa-
per allows us to evaluate the optimal values for the
parameters in order to significantly increase the suc-
cess ratio of the transactions which is the main crite-
rion used in RTDBSs. In a future work, we plan to
study the influence of other parameters such as size
EnhancementofGeneralizedEarliestDeadlineFirstPolicy
237
of user transactions, proportion of temporal data in
the database and database size. We also plan to pro-
vide an adapted GEDF protocol analysis to different
extended transactions models such as nested transac-
tion.
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APPENDIX
Table 4: Influence of RTW and SPriority weight on
SRatio
user
.
a λ Best
γ
Worst
γ
maximal
range
0.1 λ ∈ [0.7, 2.3[ 0.1 0.8 8.15%
(λ = 1.0)
0.2 λ ∈ [0.7, 0.8[ 0.2 0.8 9.23%
(λ = 1.1)
λ ∈ [0.8, 2.3[ 0.1 0.8
0.3 λ ∈ [0.7, 0.8[ 0.4 0.8 8.35%
(λ = 1.2)
λ ∈ [0.8, 0.9[ 0.2 0.8
λ ∈ [0.9, 2.3[ 0.1 0.8
0.4 λ ∈ [0.7, 0.8[ 0.6 0.8 5.88%
(λ = 1.5)
λ ∈ [0.8, 1.0[ 0.5 0.8
λ ∈ [1.0, 1.1[ 0.4 0.8
λ ∈ [1.1, 1.5[ 0.2 0.8
λ ∈ [1.5, 2.3[ 0.1 0.8
0.5 λ ∈ [0.7, 0.8[ 0.8 0.2 4.55%
(λ = 2.0)
λ ∈ [0.8, 1.1[ 0.6 0.8
λ ∈ [1.1, 1.5[ 0.5 0.8
λ ∈ [1.5, 1.9[ 0.4 0.8
λ ∈ [1.9, 2.1[ 0.2 0.8
λ ∈ [2.1, 2.3[ 0.1 0.8
0.6 λ ∈ [0.7, 0.9[ 0.8 0.2 2.79%
(λ = 1.9)
λ ∈ [0.9, 1.2[ 0.6 0.8
λ ∈ [1.2, 1.9[ 0.5 0.8
λ ∈]1.9,2.3] 0.4 0.8
0.7 λ ∈ [0.7, 1.0 0.8 0.2 1.76%
(λ = 0.9)
λ ∈ [1.0, 1.5[ 0.6,0.5 0.2
λ ∈ [1.5, 2.3[ 0.5,0.4 0.8
0.8 λ ∈ [0.7, 1.5[ 0.8 0.2 1.22%
(λ = 1.2)
λ ∈ [1.5, 2.3] 0.6,
0.5
0.8,
0.2
0.9 λ ∈ [0.7, 1.7[ 0.8 0.2 1.72%
(λ = 1.1)
λ ∈ [1.7, 2.3[ - - (di f <
0.3)%
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