Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
6,
No.
3,
June
2016,
pp.
1023
–
1030
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
1023
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Dynamic
contr
ol
and
Resour
ce
management
f
or
Mission
Critical
Multi-tier
A
pplications
in
Cloud
Data
Center
C.
N.
Sahoo
*
and
V
eena
Goswami
**
*
School
of
Computer
Engineering,
KIIT
Uni
v
ersity
,
Bhubanesw
ar
-751024,
India
**
School
of
Computer
Application,
KIIT
Uni
v
ersity
,
Bhubanesw
ar
-751024,
India
Article
Inf
o
Article
history:
Recei
v
ed
Feb
5,
2016
Re
vised
May
7,
2016
Accepted
May
19,
2016
K
eyw
ord:
Cloud
computing
V
irtual
machines
Multi-tier
application
Queueing
Dynamic
control
Resource
management
ABSTRA
CT
The
multi-tier
architecture
style
has
become
an
industry
standard
in
modern
data
centers
with
each
tier
pro
viding
certain
functionality
.
T
o
a
v
oid
congestion
and
to
adhere
the
SLA
under
fluctuating
w
orkload
and
unpredictable
f
ailures
of
Mission
Critical
Multi-tier
applica-
tions
hosted
in
the
cloud,
we
need
a
Dynamic
admission
control
polic
y
,
suc
h
that
the
requests
must
be
processed
from
the
first
tier
to
the
last
without
an
y
delay
.
This
paper
presents
the
least
strict
admission
control
polic
y
,
which
will
induce
the
maximal
throughput,
for
a
tw
o-
tier
system
with
parallel
serv
ers.
W
e
propose
an
optimization
model
to
minimize
the
total
number
of
virtual
machines
for
computing
resources
in
each
tier
by
dynami
cally
v
arying
the
mean
service
rate
of
the
VMs.
Some
performance
indicators
and
computational
results
sho
wing
the
ef
fect
of
model
parameters
are
presented.
This
model
is
also
applicable
to
priority
as
well
as
real-time
based
applications
in
Cloud
based
en
vironment.
Copyright
c
2016
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
C.
N.
Sahoo
School
of
Computer
Engineering,
KIIT
Uni
v
ersity
Bhubanesw
ar
-751024,
India
Phone:
+91-9880149447
Email:
nishikant.choudhury@gmail.com
1.
INTR
ODUCTION
Cloud
comput
ing
greatly
lo
wers
the
threshold
for
deplo
ying
and
maintaining
web
applications
since
it
pro-
vides
infrastructure
as
a
service
(IaaS)
and
platform
as
a
service
(P
aaS)
for
web
applications
[1].
Consequently
,
a
number
of
web
applications,
particularly
the
web
applications
of
medium
and
small
enterprises,
ha
v
e
been
b
uilt
into
a
cloud
en
vironment.
Meanwhile,
leading
IT
companies
ha
v
e
established
pu
bl
ic
commercial
clouds.
F
or
e
xample,
Google
App
Engine
enables
enterprises
to
b
uild
and
host
web
applications
on
the
same
systems
that
po
wer
Google
applications.
App
Engine
of
fers
f
ast
de
v
elopment
and
deplo
yment;
simple
adm
inistration,
with
no
need
to
w
orry
about
hardw
are,
patches
or
backups;
and
ef
fortless
scalability
[2].
IBM
also
pro
vides
cloud
options
[3].
Amazon
Elastic
Compute
Cloud
(Amazon
EC2)
is
a
web
service
that
pro
vides
resizable
compute
capacity
in
the
cloud.
It
is
designed
to
mak
e
web-scale
computing
easier
for
de
v
elopers
[4].
W
e
e
v
en
can
establish
a
pri
v
ate
cloud
with
Ub
untu
Enterprise
Cloud
to
of
fer
immediac
y
and
elasticity
i
n
the
infrastructure
of
web
applications
[5].
In
summary
,
both
of
the
numbers
of
cloud
applications
and
pro
viders
ha
v
e
k
ept
gradually
increasing
for
a
couple
of
years
[6,
7].
As
a
resul
t,
comput-
ing
resource
scheduling
and
performance
managing
ha
v
e
been
one
of
the
most
important
aspects
of
cloud
computing
[8,
9].
This
paper
focuses
on
queueing-based
analytical
model
for
performance
of
web
based
applications
with
multi-tiered
architecture.
It
is
quite
dif
ficult
to
predict
the
traf
fic
in
web
based
applications.
In
case
of
Real-time
or
Mission-Critical
applications,
requests
must
be
processed
from
the
1st
tier
to
the
last
wit
hout
an
y
delay
.
If
the
release
and
processing
times
of
requests
are
kno
wn,
the
problem
for
determining
the
processing
order
of
requests
is
typically
a
scheduling
probl
em.
Ho
we
v
er
,
if
requests
arri
v
e
randomly
,
in
order
to
pre
v
ent
an
y
del
ay
of
requests
currently
in
the
system
and
ensure
that
the
ne
w
request
will
go
through
all
the
tiers
successfully
,
an
admission
control
should
be
used
to
decide
whether
or
not
to
accept
the
ne
w
request.
This
paper
deals
with
the
admission
control
policies
for
no-w
ait
tandem
queueing
systems.
W
e
present
the
least
strict
admission
control
polic
y
,
which
will
induce
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.
1024
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
the
maximal
throughput,
for
a
tw
o-tier
system
with
parallel
serv
ers
(VMs).
This
polic
y
can
be
easily
e
xtended
for
multi-tier
systems.
In
order
to
maxi
mize
the
total
profit,
t
he
system
dynamically
decides
whether
to
accept
a
ne
w
request
based
on
his
bandwidth
requirement
and
duration
time
and
the
system
data
(the
numbers
of
requests
in
system
and
their
remaining
service
times).
Based
on
the
kno
wn
service
times
at
all
tiers
of
the
ne
w
request
and
the
system
information
upon
arri
v
al,
the
system
decides
whether
to
accept
this
ne
w
request
such
that
all
accepted
requests
will
go
through
the
rest
of
tiers
successfully
.
In
this
paper
,
we
present
a
feasible
admission
control
polic
y
,
called
the
ne
w
ne
v
er
block
the
old
[10]
(NNBO)
polic
y
.
The
main
idea
of
this
p
ol
ic
y
is
that
the
presence
of
a
ne
wly
admitted
request
will
not
block
other
e
xisting
requests.
It
can
be
easily
sho
wn
that
the
NNBO
polic
y
is
the
least
strict
polic
y
.
F
or
a
controlled
system,
an
important
performance
measurement
is
the
resulting
loss
probability
of
an
y
request
or
,
equi
v
alently
,
the
loss
rate
of
the
system.
It
is
a
greedy
system
in
the
sense
that
requests
try
their
best
to
enter
all
tiers.
Therefore,
intuiti
v
ely
,
the
total
loss
rate
from
all
tiers
in
a
free
system
may
be
smaller
than
the
loss
rate
in
a
controlled
system.
Ho
we
v
er
,
it
is
e
vident
that,
under
the
e
xponential
service
times,
the
loss
rates
of
NNBO
system
and
the
free
system
are
equal
when
there
is
only
one
serv
er
at
the
1st
tier
.
The
rest
of
the
paper
is
or
g
anized
as
follo
ws.
Section
2
briefly
re
vie
ws
the
related
w
orks.
Section
3
presents
the
system
description.
Model
description
and
its
analysis
is
carried
out
in
Section
4.
V
arious
performance
measures
are
e
v
aluated
in
Section
5.
Section
6
contains
computational
numerical
illus
trations
with
a
v
ariety
of
Results
and
Discussion
in
the
form
of
graphs
to
sho
w
the
ef
fecti
v
eness
of
the
model
parameters.
Section
7
concludes
our
paper
.
2.
RELA
TED
W
ORK
Jung
et
al.
[11]
proposed
a
generating
adoption
for
multi-tier
applications
in
virtualized
consolidated
serv
er
en
vironments.
It
pro
vides
dynamic
management
method
and
optimizes
of
fline
resources
to
generate
suitable
config-
urations
by
e
v
aluating
a
model
consisting
of
multi-tier
M
=
M
=n
queues.
Ur
g
aonkar
et
al.
[12]
proposed
a
model
for
multi-tier
internet
applications
to
pro
vide
the
resources
to
each
tier
of
the
application,
and
combine
predicti
v
e
and
reacti
v
e
methods.
The
closed
system
model
of
muti-tier
b
usiness
applications
based
on
mean
v
alue
analysis
(MV
A)
algorithm
to
predict
performance
of
multi-tier
applications
has
been
discussed
i
n
Chen
et
al
.
[13].
A
nonlinear
inte
ger
optimization
model
for
determining
the
number
of
machines
at
each
tier
in
a
multi-tier
serv
er
netw
ork
has
been
stud-
ied
in
Zhang
et
al.
[14].
A
single
queue
model
for
all
tiers
to
pre
v
ent
o
v
erload
and
maintain
absolute
client
response
time
has
been
reported
in
Kamra
et
al.
[15].
W
ang
et
al.
[16]
presented
a
ne
w
self-adapti
v
e
capacity
management
frame
w
ork
for
multi-tier
virtualized
en
vironments.
It
e
x
ecutes
periodically
and
reassigns
resources
by
e
v
aluating
a
model
consisting
of
multi-tier
M
=
M
=
1
queues
and
solv
es
an
optimization
problem
[17].
A
model
for
dynamic
resource
pro
visioning
in
multi-tier
internet
applications
captures
v
arious
characteristics
of
an
arbitrary
number
of
heterogeneous
tiers
has
been
reported
in
Ur
g
aonkar
et
al.
[18].
Ardagna
et
al.
[19]
de
v
eloped
a
heuristic
solution
for
maximization
of
profits
using
a
cost
model
for
multi-tier
data
controller
center
.
Chang
et
al.
[10]
proposed
a
model
for
Admission
control
policies
for
tw
o-stage
tandem
queues
with
no
w
aiting
spaces
to
pro
vide
the
resources
to
each
tier
of
the
just-in-time
based
production
lines
and
compare
the
resulting
loss
rate
of
the
controlled
system
with
the
loss
rate
of
a
system
without
an
y
admission
control
called
the
free
system.
This
model
is
also
applicable
to
systems
where
the
system
manager
must
maintain
the
no-w
ait
pri
vile
ge
for
the
higher
priority
customers
in
order
to
dif
ferentiate
the
qualities
of
the
services.
In
our
w
ork
we
propose
an
optimization
model
to
minimize
the
total
number
of
virtual
machines
for
computing
resources
in
each
tier
by
dynamically
v
arying
the
mean
service
rate
of
the
virtual
machines
(VMs).
3.
SYSTEM
DESIGN
This
section
presents
the
architecture
of
the
hosting
platform
required
in
our
w
ork.
3.1.
Ar
chitectur
e
o
v
er
view
Model
V
ie
w
Controller
(MVC)
frame
w
ork
comprises
of
multiple
tiers
such
as
web-tier
,
middle-tier
and
persistence
tier
.
W
eb-tier
typically
consists
of
web-serv
ers
whereas
middle-tier
consists
of
app-serv
ers,
file-serv
ers
to
host
middle
w
are
technologies
and
persistence-tier
consists
of
Databases
or
back
end
systems
such
as
le
g
ac
y
systems.
The
MVC
design
pattern
is
a
w
ay
of
taking
an
application
and
breaking
it
into
three
distinct
parts:
the
model,
the
vie
w
,
and
the
controller
.
The
adv
antage
of
using
the
MVC
pattern
is
that
there
is
no
b
usiness
or
Model-specific
processing
within
the
presentation,
or
vie
w
,
component
itself.
The
opposite
is
also
t
rue;
that
is,
there
is
no
presentation
logic
in
the
model
and
b
usiness
layers.
This
impro
v
es
component
reuse
there
and
also
impro
v
e
the
abilit
y
to
change
a
tier
implementations
with
minimal
ef
fect
on
the
other
tiers
[20,
21].
Figure
1
sho
ws
the
request
processing
flo
w
IJECE
V
ol.
6,
No.
3,
June
2016:
1023
–
1030
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
1025
Figure
1.
A
typical
3-tier
application
in
cloud
of
a
typical
three
tier
MVC
based
web
application
deplo
yed
in
cloud,
in
which
each
rectangle
represents
a
tier
.
A
request
mo
v
es
through
the
tiers
,
may
visit
a
tier
multiple
times
and
get
processed
at
the
visited
tier
.
Finally
,
the
processing
completes
and
returns
to
request
senders
from
the
front
tier
.
Since
dif
ferent
tiers
are
designed
to
pro
vide
dif
ferent
functionalities,
tiers
could
be
clustered
by
a
group
of
s
erv
er
s
with
similar
resource
characteristics.
F
or
e
xample,
a
middle-tier
b
usiness
logic
serv
er
w
ould
be
better
to
ha
v
e
f
ast
processing
capability
,
while
a
back
end-tier
database
serv
er
is
usually
required
to
pro
vide
high
I/O
operation
rate
and
W
eb-T
ier
doesn’
t
ha
v
e
an
y
processing
logic
rather
it
w
orks
as
a
request
forw
arding
agent.
Therefore,
ph
ys
ical
serv
ers
are
clustered
int
o
dif
ferent
groups
(VMs),
serving
dif
ferent
tiers
of
applications.
The
architecture
of
a
shared
data
center
is
sho
wn
in
Figure
2,
which
consists
Figure
2.
V
irtualized
Data
Center
architecture
consisting
of
VMs
in
IaaS
of
heterogeneous
ph
ysical
nodes
(IaaS),
shared
by
multiple
independent
applications,
hosting
web
application
from
dif
ferent
companies
or
or
g
anizations.
Modern
transactional
web
applicati
ons
are
designed
using
multiple
tiers,
which
are
often
distrib
uted
across
dif
ferent
serv
ers.
Acti
v
e
VM
Load
Balancer
maintains
information
about
each
VM
along
with
the
number
of
requests
currently
allocated
to
VMs
in
a
intended
tier
.
When
a
request
to
allocate
a
ne
w
VM
arri
v
es,
it
identifies
an
e
xisting
free
VM.
3.2.
V
irtualized
Multi-tier
A
pplication
Queueing
Model
A
virtualized
multi-tier
application
in
cloud
computing
en
vironment
is
deplo
yed
on
multiple
virtual
machines,
and
each
tier
pro
vides
cert
ain
functionality
to
its
preceding
tier
.
Let
us
consider
an
online
application
that
consists
of
n
tiers,
T
1
;
T
2
;
:
:
:
;
T
n
.
W
e
assume
that
there
are
c
parallel
identical
VMs
in
each
tier
b
ut
the
y
are
pro
visioned
when
needed.
The
load
balancer
distrib
utes
the
load
to
dif
ferent
parallel
VMs
queueing
models
of
that
tier
to
e
x
ecute.
Each
tier
is
assumed
to
emplo
y
a
perfect
load-balancing
element
for
a
virtualized
applicat
ion
that
is
responsible
for
processing
requests
at
that
tier
,
and
each
request
is
forw
arded
to
it
s
succeeding
tier
for
further
processing.
Figure
3
represents
T
andem
queueing
system
with
zero-b
uf
fer
and
there
are
multiple
nodes
with
multiple
Serv
ers
(VMs)
at
each
node.
4.
MODEL
DESCRIPTION
AND
AN
AL
YSIS
W
e
discuss
the
dynamic
admission
control
to
a
tw
o-tier
no-w
ait
tandem
queueing
system
with
N
1
VMs
at
tier
1
and
N
VMs
at
tier
2.
W
e
consider
the
epoch
when
a
ne
w
request
X
,
whose
service
time
at
stage
j
is
denoted
Multi-tier
Applications
in
Cloud
Data
Center
Evaluation Warning : The document was created with Spire.PDF for Python.
1026
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
Figure
3.
Zero-Buf
fer
T
andem
queues
by
X
j
;
j
=
1,
2,
arri
v
es.
Suppose
that
there
are
n
1
and
n
2
requests
a
lready
at
stage
1
and
stage
2,
respecti
v
ely
.
As
per
NNBO
admission
control
polic
y:
X
is
admitted
if
and
only
if:
(i)
When
X
arri
v
es,
there
is
at
least
one
free
VM
at
tier
1.
(ii)
Based
on
the
system
data
observ
ed
upon
X
0
s
arri
v
al,
there
should
be
at
least
one
free
VM
at
tier
2
when
X
enters
tier
2.
(iii)
During
the
X
0
s
sojourn
at
tier
2,
an
y
of
those
n
1
requests
left
behind
by
X
at
tier
1
can
still
enter
tier
2.
Here
we
consider
a
no-w
ait
tandem
queueing
system
in
which
there
is
only
one
serv
er
(
n
1
=
1)
at
stage
1.
Assume
that
requests
arri
v
e
according
to
a
Poisson
process
with
rate
and
the
service
times
of
each
request
at
stages
1
and
2
are
e
xponentially
distrib
uted
with
rate
1
and
2
,
respecti
v
ely
.
In
this
section,
we
define
the
states
as
(
n
1
;
n
2
)
,
where
n
1
and
n
2
are
the
numbers
of
requests
at
stages
1
and
2,
respecti
v
ely
.
The
stationary
state
balance
equations
are
gi
v
en
as
P
0
;
0
=
2
P
0
;
1
;
(1)
(
+
n
2
2
)
P
0
;n
2
=
1
P
1
;n
2
1
+
(
n
2
+
1)
2
P
0
;n
2
+1
;
1
n
2
N
1
;
(2)
(
1
+
n
2
2
)
P
1
;n
2
=
P
0
;n
2
+
(
n
2
+
1)
2
P
1
;n
2
+1
;
0
n
2
N
1
;
(3)
(
+
N
2
)
P
0
;N
=
1
(
P
1
;N
1
+
P
1
;N
)
;
(4)
(
1
+
N
2
)
P
1
;N
=
P
0
;N
:
(5)
From
(5),
we
get
P
1
;N
=
1
+
N
2
P
0
;N
:
(6)
Using
(6)
in
(4)
and
simplifying,
we
ha
v
e
P
1
;N
1
=
N
2
(
+
1
+
N
2
)
(
1
+
N
2
)
1
P
0
;N
:
(7)
Substituting
n
2
=
N
1
in
(3),
yield
P
0
;N
1
=
(
1
+
(
N
1)
2
)(
+
1
+
N
2
)
N
2
(
1
+
N
2
)
1
N
2
1
+
N
2
P
0
;N
:
(8)
Solving
(2)
and
(3),
recursi
v
ely
,
we
obtain
P
1
;n
2
1
=
+
n
2
2
1
P
0
;n
2
n
2
+
1
1
P
0
;n
2
+1
;
n
2
=
N
1
;
:
:
:
;
2
;
1
;
(9)
P
0
;n
2
=
1
+
n
2
2
P
1
;n
2
(
n
2
+
1)
2
P
1
;n
2
+1
;
n
2
=
N
1
;
:
:
:
;
1
;
0
:
(10)
W
e
can
obtain
P
0
;N
by
applying
Normalizing
condition
N
P
n
2
=0
(
P
0
;n
2
+
P
1
;n
2
)
=
1
.
4.1.
Recursi
v
e
algorithm
In
this
section,
we
establish
a
computational
algorithm
to
compute
recursi
v
ely
stationarity
state
probabilities
according
to
the
follo
wing
algorithm:
IJECE
V
ol.
6,
No.
3,
June
2016:
1023
–
1030
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
1027
Step
1
:
Assume
P
0
;N
=
1
.
Step
2
:
Calculate
P
1
;N
from
(6).
Step
3
:
Calculate
P
1
;N
1
and
P
0
;N
1
,
using
(7)
and
(8).
Step
4
:
Balance
equations
for
states
(1
;
N
2)
;
(1
;
N
3)
;
:
:
:
;
(1
;
0)
yield
P
1
;n
2
,
n
2
=
N
2
;
N
3
;
:
:
:
;
0
as
function
of
P
0
;n
2
.
Step
5
:
Balance
equations
for
states
(0
;
N
2)
;
(0
;
N
3)
;
:
:
:
;
(0
;
0)
yield
P
0
;n
2
;
n
2
=
N
2
;
N
3
;
:
:
:
;
0
as
function
of
P
1
;n
2
.
Step
6
:
Repeat
Steps
4
and
5
for
n
2
=
N
2
;
:
:
:
;
0
.
Step
7
:
Normalization:
N
P
n
2
=0
(
P
0
;n
2
+
P
1
;n
2
)
=
1
yields
P
0
;N
.
Step
8
:
Compute
P
n
1
;n
2
=
P
n
1
;n
2
P
0
;N
for
n
1
=
0
;
1;
n
2
=
0
;
1
;
:
:
:
;
N
.
5.
PERFORMANCE
MEASURES
Performance
measures
are
the
means
to
e
xamine
the
ef
ficienc
y
of
the
queueing
system
under
consideration.
As
the
steady-state
probabilities
at
v
arious
epochs
are
kno
wn,
the
main
performance
measures
of
the
queueing
system
can
be
obtained
as
follo
ws:
The
probability
that
an
arri
v
al
finds
Node-1
(tier
-1)
full
is
gi
v
en
by
L
1
=
N
P
n
2
=0
P
1
;n
2
.
A
v
erage
number
of
lost
customers
per
unit
time
at
T
ier
-1
is
L
T
1
=
N
P
n
2
=0
P
1
;n
2
.
A
v
erage
number
of
lost
customers
per
unit
time
at
T
ier
-2
is
L
T
2
=
1
P
1
;N
.
Loss
rate
of
the
NNBO
System
is
gi
v
en
by
L
Loss
=
N
P
n
2
=0
P
1
;n
2
+
1
1
+
N
2
P
0
;N
.
5.1.
Cost
analysis
W
e
de
v
elop
a
total
e
xpected
cost
function
per
unit
time
for
the
t
andem
queuing
system
where
the
number
of
nodes
are
represented
by
n
and
number
of
VMs
in
each
node
is
represented
by
c
.
Our
objecti
v
e
is
to
determine
the
optimum
number
of
VMs
c
,
say
c
,
and
the
optimum
number
of
nodes
n
,
say
n
,
as
decision
v
ariables
so
that
the
e
xpected
cost
function
is
minimized.
Let,
C
h
=
holding
cost
per
unit
time
for
each
client
request
present
in
the
system.
C
1
=
fix
ed
cost
per
unit
time
during
the
b
usy
period
for
node
1
C
2
=
fix
ed
cost
per
unit
time
during
the
b
usy
period
for
node
2.
C
3
=
fix
ed
cost
for
e
v
ery
lost
client.
Let
F
(
c;
n
)
be
the
e
xpected
cost
per
unit
time.
Using
the
definitions
of
each
cost
element
and
its
corresponding
system
characteristics,
we
ha
v
e
F
(
c;
n
)
=
C
h
(
N
+
1)
+
C
1
L
T
1
+
C
2
L
T
2
+
C
3
L
Loss
(11)
The
objecti
v
e
is
to
determine
the
optimum
number
of
VMs
c
and
optimum
system
size
(nodes)
n
to
minimize
the
cost
function
F
(
c;
n
)
.
Here,
we
are
specifically
considering
2-Nodes,
hence
n
=
2
.
Hence,
the
cost
function
reduces
to
F
(
c
)
.
W
e
ha
v
e
implemented
the
numerical
searching
approach
for
the
cost
function
using
the
genetic
algorithm.
The
genetic
algorithm
is
a
probabilistic
search
algorithm
that
iterati
v
ely
transforms
a
set
(cal
led
a
population)
of
mathematical
objects,
each
with
an
associated
fitness
v
alue,
into
a
ne
w
population
of
of
fspring
object
s
using
the
natural
selection
and
mutation.
Haupt
et
al.
[22].
Genetic
algorithms
are
adapti
v
e
search
algorithms
based
on
the
e
v
olutionary
ideas
of
natural
selection
and
genetics.
It
represents
potential
solutions
by
bit
strings
of
a
fix
ed
length.
By
analogy
to
genetics,
the
strings
can
be
rendered
as
chromosomes
with
indi
vidual
bits
refe
rring
the
presence
(bit
=
1)
or
abs
ence
(bit
=
0)
of
a
gene.
A
genetic
algorithm
allo
ws
a
population
composed
of
man
y
indi
viduals
to
e
v
olv
e
under
specified
selection
rules
that
minimize
the
fitness
function,
that
is,
the
cost
function
in
this
paper
.
A
population
of
alternati
v
e
possible
solutions
(chromosomes)
is
created
and
allo
wed
to
e
v
olv
e
through
a
number
of
generations.
Old
generations
be
get
ne
w
generations
in
a
f
ashion
that
mimics
gene
tic
change
in
nature.
The
solution
procedure
is
as
follo
ws:
INPUT
:
;
1
;
2
;
C
h
;
C
1
;
C
2
;
C
3
;
c;
n
and
genes,
probability
of
crosso
v
er
,
and
probability
of
mutation.
Multi-tier
Applications
in
Cloud
Data
Center
Evaluation Warning : The document was created with Spire.PDF for Python.
1028
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
OUTPUT
:
approximate
solution
c
;
n
;
F
.
Step
1
:
Population
Initialization.
An
implement
ation
of
genetic
algorithm
initiates
with
a
encoding
of
each
input
into
a
chromosomes.
Each
gene
v
alue
either
0
or
1
is
randomly
generated.
Step
2
:
Fitness
Computation.
T
o
determine
the
optimal
e
xpected
profit
per
unit
time
for
optimal
virtual
machines
and
system
capacity
,
the
fitness
of
a
chromosome
is
computed
using
the
e
xpected
cost
function
F
(
c;
n
)
in
equation
(11).
Step
3
:
Selection
and
Crosso
v
er
.
The
selection
is
a
process
which
mimics
the
natural
survi
v
al
of
the
fittest
creatures.
Each
chromosome
has
a
fitness
v
alue
obtained
through
the
fitness
function.
The
chromosomes
which
perform
better
fitness
v
alues
are
gi
v
en
more
chances
and
it
discards
poor
quality
genes
based
on
their
fitness
v
alue.
Crosso
v
er
is
done
by
selecting
tw
o
parents
during
reproduction
and
combining
their
genes
to
produce
of
fspring.
The
parent
chromosomes
are
then
mated
to
generate
a
ne
w
set
of
of
fspring
chromosomes.
This
mated
procedure
is
also
called
crosso
v
er
.
Step
4
:
Mutation.
Mutation
is
the
random
changing
of
one
or
more
bits
in
a
chromosome.
It
is
useful
to
crea
te
ne
w
genes
that
are
not
in
the
initial
set
of
population,
or
ones
that
ha
v
e
e
v
olv
ed
out
of
the
population,
b
ut
no
w
w
ould
be
beneficial.
Step
5
:
Repeat
Step
2
-
Step
4
until
the
stopping
criterion
is
met.
W
e
use
50
generations
as
our
stopping
criterion.
6.
RESUL
TS
AND
DISCUSSION
In
this
section
some
numerical
results
are
discussed.
Numerical
results
for
v
arious
system
performance
measures
are
presented
in
T
able
1.
W
e
observ
e
that
for
fix
ed
1
as
2
increases:
(i)
The
optimum
cost
increases.
This
is
because
the
number
of
the
VMs
in
the
system
also
increases.
But
for
fix
ed
2
as
1
increases:
(i)
The
optimum
cost
and
ot
her
performance
measures
such
as
P
l
oss
decreases.
This
is
because
t
he
number
of
the
VMs
in
the
system
remains
the
same.
W
ith
the
same
number
of
VMs
and
fix
ed
2
,
as
1
increases
both
L
T
1
&
L
T
2
decreases.
Figures
T
able
1:
Optimal
system
performance
measures
1
2
c
F
(
c;
n
)
L
T
1
L
T
2
P
Loss
0.5
1
5
196.00
1.6
0.00001
0.8
2
10
347.45
1.63516
0.04394
0.81757
4
12
408.57
1.85527
0.00081
0.92763
5
14
466.67
1.66667
0.00024
0.83333
0.75
1
5
194.55
1.45455
0.00001
0.72727
2
10
347.32
1.51703
0.08592
0.75851
4
12
408.03
1.79648
0.00243
0.89823
5
14
465.73
1.57143
0.00069
0.78571
1
1
5
193.33
1.33333
0.00000
0.66667
2
10
347.61
1.42327
0.13490
0.71163
4
12
407.58
1.74471
0.00518
0.87235
5
14
465.04
1.5
0.00142
0.74999
1.25
1
5
192.31
1.23077
0.00001
0.61541
2
10
348.18
1.34683
0.18860
0.67341
4
12
407.22
1.69883
0.00912
0.84941
5
14
464.51
1.44444
0.00244
0.72222
4
and
5
sho
w
the
ef
fect
of
2
on
the
e
xpected
number
of
lost
customers
per
unit
time
at
T
ier
-1
and
T
ier
-2,
respecti
v
ely
.
It
is
seen
that
as
2
increases,
L
T
1
and
L
T
2
increases
monotonically
t
o
certain
e
xtend
then
monotonically
decreases.
From
Figure
4,
as
1
increases,
lost
customers
per
unit
time
at
tier
-1
L
T
1
decreases.
Whereas
from
Figure
5,
lost
customers
per
unit
time
at
tier
-2
L
T
2
increases
as
1
increases.
This
is
because
of
the
admission
control
polic
y
.
Figure
6
depicts
the
impact
of
VMs
on
the
Cost.
It
can
be
observ
ed
that
cost
increases
as
the
c
and
2
increases.
F
or
the
fix
ed
number
of
VMs
and
2
,
the
cost
in
v
olv
ed
remains
almost
same,
that
is,
the
small
v
ariation
in
cost
is
due
to
the
v
ariation
in
1
.
The
ef
fect
of
VMs
on
the
P
Loss
is
represented
in
Figure
7.
It
is
seen
that
as
2
increases,
P
Loss
IJECE
V
ol.
6,
No.
3,
June
2016:
1023
–
1030
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
1029
1
1.5
2
2.5
3
3.5
4
4.5
5
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
L
T
1
µ
2
µ
1
µ
1
= 0.5
µ
1
= 0.75
µ
1
= 1.0
µ
1
= 1.25
Figure
4.
Impact
of
2
on
L
T
1
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Lost Requests at Tier 2 − L
T2
µ
2
µ
1
µ
1
= 0.5
µ
1
= 0.75
µ
1
= 1.0
µ
1
= 1.25
Figure
5.
Ef
fect
of
2
on
L
T
2
5
10
12
14
0
50
100
150
200
250
300
350
400
450
500
c
Cost
µ
2
µ
2
= 1.0
µ
2
= 2.0
µ
2
= 5
µ
2
= 4.0
Figure
6.
Impact
of
VMs
on
Cost
5
10
12
14
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
c
P
Loss
µ
2
µ
2
= 4.0
µ
2
= 5.0
µ
2
= 2.0
µ
2
= 1.0
Figure
7.
Impact
of
P
Loss
on
VMs
1
2
3
4
5
5
10
15
100
200
300
400
500
µ
2
c − No of VMs
Cost
Figure
8.
Cost
v
ersus
c
v
ersus
2
1
2
3
4
5
0.5
1
1.5
0.65
0.7
0.75
0.8
0.85
0.9
0.95
µ
2
µ
1
P
Loss
Figure
9.
Cost
v
ersus
c
v
ersus
2
increases
(with
a
small
v
a
riation
at
2
=
4)
and
hence
resulting
more
loss.
This
is
because
of
more
loss
at
node-1,
t
hat
is,
L
T
1
.
The
impact
of
dif
ferent
parameters
on
Cost
and
P
Loss
is
sho
wn
on
Figure
8
and
Figure
9,
respecti
v
ely
.
It
can
be
seen
from
Figure
8,
the
Cost
increases
monotonically
as
the
2
and
number
of
VMs
increases.
But
in
case
of
Figure
9,
with
the
increase
of
2
and
1
,
the
P
Loss
increases
monotonically
till
2
=
4
and
then
decreases.
This
sho
ws
that
due
to
dynamic
admission
polic
y
more
loss
is
happening
at
node-1,
that
is,
L
T
1
.
7.
CONCLUSION
Highly
performance
sensiti
v
e
mission
cr
itical
as
well
as
real-time
applications
are
rarely
hosted
in
public
Clouds.
W
ith
a
dynamic
admission
control
polic
y
,
we
can
easily
address
these
type
of
application
specific
issues
where
e
xtra
cost
is
incurred
to
ensure
high-a
v
ailability
as
well
f
ault
tolerance.
In
this
paper
,
we
propose
an
optimal
polic
y
for
pro
visioning
of
VMs
in
cloud
data
center
to
minimize
the
congestion
in
the
netw
ork
by
v
arying
the
service
rate
of
the
virtual
machines.
An
analytical
model
is
de
v
eloped
to
fit
cloud
en
vironment
with
heterogeneous
serv
ers
(as
required
Multi-tier
Applications
in
Cloud
Data
Center
Evaluation Warning : The document was created with Spire.PDF for Python.
1030
ISSN:
2088-8708,
DOI:
10.11591/ijece.v6i3.10087
for
dif
ferent
tiers)
to
minimize
the
total
number
of
VMs
and
finally
cutting
do
wn
the
cost
in
v
olv
ed.
The
objecti
v
e
is
to
impro
v
e
the
ef
ficienc
y
and
fle
xibility
in
cloud
en
vironment
for
resource
pro
visioning.
A
v
ariety
of
numerical
results
in
the
form
of
tables
and
graphs
are
discussed
to
display
the
ef
fect
of
the
system
parameters
on
the
performance
measures.
Cost
analysis
has
been
done
to
impro
v
e
the
grade
of
service
by
selection
of
appropriate
system
parameters
using
genetic
algorithm.
T
o
achie
v
e
significant
performance
le
v
el,
we
adopted
Service
Le
v
el
Agreement
based
ne
gotiation
of
prioritized
applications
to
determine
the
costs
and
penal
ties.
It
is
a
trade-of
f
that
potential
applications
need
to
consider
in
deciding
the
performance
e
v
aluation
of
serv
er
f
arms
as
an
important
aspect
of
cloud
computing
which
is
of
crucial
interest
for
both
cloud
pro
viders
and
cloud
customers.
As
future
w
ork,
research
will
be
carried
out
on
useful
algorithms
for
measuring
deplo
yment
costs
of
virtual
resources
in
multi-cloud
en
vironments.
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