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Clustering
Based
Scheduling:
A
New
Approach
to
the
Design
of
Scheduling
Algorithms
for
WDM
Star
Networks
Sophia
G.
Petridou,
Panagiotis
G.
Sarigiannidis,
Graduate
Member;
IEEE
Georgios
I.
Papadimitriou,
Senior
Member;
IEEE,
Andreas
S.
Pomportsis
Aristotle
University
email:{
spetrido,sarpan,gp,apombo}
@csd.auth.gr
Abstract
Scheduling
algorithms
in
Wavelength
Division
Mul
approach
is
introduced
which
could
create
groups
of
nodes
tiplexing
(WDM)
single
hope
networks
aim
at
producing
an
with
similar
request
patterns.
Discovering
such
similar
patterns
effective
schedule
in
order
to
improve
the
networks'
performance.
and
prioritizing
them
properly
could
lead
to
higher
network
Up
to
now,
popular
approaches
schedule
network
traffic
based
on
nodes'
requests
which
are
considered
in
a
sequential
service
perfrmnc
withou
aggring
he
timeacompexity
of
the
order.
This
paper
presents
a
novel
packet
scheduling
scheme
scheduling
algorithm.
Clustering
has
already
been
used
in
for
WDM
star
networks
based
on
clustering
techniques.
Our
many
domains
and
especially
on
the
Web
aiming
at
improving
Clustering
Based
Scheduling
Algorithm
(CBSA)
organizes
the
Web
applications
[5],
[6].
nodes
of
a
network
into
groups
(i.e.
clusters)
according
to
the
The
remainder
of
this
paper
is
organized
as
follows.
number
of
their
requests
per
channel
and
then
it
defines
their
.

transmission
priority
beginning
from
the
nodes
belonging
to
Section
II
provides
the
network
structure
while
Section
III
the
cluster
with
greater
demands
and
ending
to
the
nodes
of
presents
related
packet
scheduling
algorithms
for
WDM
star
cluster
with
fewer
requests.
The
simulation
results
have
shown
networks.
Clustering
background
is
given
in
Section
IV.
that
the
proposed
approach
improves
network
performance
since
Section
V
presents
our
new
scheduling
algorithm
while
Sec
it
results
in
higher
network
throughput
keeping
mean
packet
tion
VI
discusses
the
simulation
results.
Finally,
conclusions
delay
at
low
levels
in
comparison
with
conventional
scheduling
and
future
work
insights
are
given
in
Section
VII.
algorithms.
I.
INTRODUCTION
II.
NETWORK
STRUCTURE
Popular
approaches
schedule
traffic
in
local
area
Wavelength
A
local
area
WDM
singlehop
network
with
broadcast
and
Division
Multiplexing
(WDM)
single
hope
networks
[1]
con
select
architecture
is
considered.
This
network
consists
of
n
sidering
nodes
in
a
sequential
service
order
[2],
[3].
How
nodes,
which
are
connected
in
a
passive
star
coupler
via
a
ever,
sequential
scheduling
leads
to
a
significant
performance
twoway
optical
fiber,
and
w
channels
(wavelengths),
where
degradation
in
terms
of
network
throughput
and
mean
packet
n
>
w.
Each
node
may
transmit
packets
on
different
channels
delay.
This
paper
presents
a
new
pretransmission
coordination
using
a
tunable
transmitter,
while
it
receives
packets
in
a
scheduling
algorithm
for
optical
WDM
star
networks
based
dedicated
channel
(home
channel)
using
a
fixed
receiver,
as
on
the
clustering
[4],
[5]
of
network
nodes.
The
proposed
depicted
in
Fig.
1.
In
this
TTFR
implementation,
it
is
clear
Clustering
Based
Scheduling
Algorithm
(CBSA)
rearranges
that
two
or
more
nodes
may
transmit
on
the
same
channel
the
service
order
of
the
network
nodes
by
organizing
them
into
at
the
same
time
causing
channel
collision.
Thus,
a
media
groups
(i.e.
clusters)
according
to
the
number
of
their
requests
access
protocol
(MAC)
is
needed
to
support
a
set
of
access
per
channel.
Then,
our
algorithm
defines
their
transmission
rules
aiming
at
preventing
collisions
and
specifying
the
way
priority
beginning
from
the
nodes
belonging
to
the
cluster
with
that
nodes
transmit
on
the
available
channels
[7],
[8].
greater
demands
and
ending
to
the
nodes
of
cluster
with
fewer
The
proposed
scheduling
algorithm
is
based
on
global
status
requests.
In
this
way,
we
decrease
both
the
unused
timeslots
information
which,
in
our
case,
is
the
n
x
w
demand
matrix
as
well
as
the
schedule
length
and
as
a
result
the
network
D,
where
d(i,
j)
element,
i
=
,,
n
and
j
1
,
,w
performance
is
significantly
upgraded.
indicates
the
number
of
data
packets
at
node
ui
that
are
This
work
is
inspired
by
the
fact
that
a
sequential
service
destined
to
channel
Aj.
Time
is
divided
in
timeslots
with
the
order
scheme
has
the
drawback
of
scheduling
nodes
without
packet
transmission
time
to
be
equal
to
one
timeslot
while
taking
into
account
their
specific
requests.
As
a
result,
nodes
the
transmission
process
is
organized
in
transmission
frames.
with
short
length
requests
(few
packets)
may
transmit
prior
to
Each
frame
has
two
phases
namely
the
reservation
and
the
those
with long
length
requests
leading
to
decreased
channel
data
phase.
During
the
reservation
phase
the
n
nodes
send
utilization
because
of
many
unused
timeslots.
Thus,
it
is
their
requests
to
the
common
data
channels
which
are
then
important
to
rearrange
the
nodes'
service
order
according
to
recorded
in
the
demand
matrix
D. At
the
same
time,
the
their
requests
on
each
channel.
Therefore,
a
nodes'
clustering
CBSA
operates
in
conjunction
with
a
distributed
scheduling
1
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I
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Symbol
DefiitioNode
1
n,w
Number
of
nodes
and
channels
TT
U
=
{ul,..
.
mun}
The
set
of
network's
nodes
A
=
{A1,,
A,}
The
set
of
network's
channels
FR
D
The
n
x
w
demand
matrix
k
The
upper
bound
of
nodes'
requests
Al_,
Aw
Node
2
t
Schedule's
length
in
timeslots
Al,
Aw
L
=
{1,...
l,t}
The
set
of
timeslots
S
The
w
x
t
scheduling
matrix
Node
n
Al,
w
n
x
n
passive
Fi
Cl
Clustering
process
starcoupler
noc
Number
of
clusters
C
Cluster,
j
=
1,
.
.
.,noc
f
(ui,
C3)
Function
membership
of
node
ui
to
cluster
Ci,
i
=
1,
...
.,
nXXX
Cluster
representative
n:
number
of
nodes
ci
w:
number
of
channels
MeansD
The
noc
x
w
clusters
representatives'
de
mand
matrix
Fig.
1.
Network
Topology
dist
Nodes
distance
over
channels
J
Criterion
function
TABLE
I
predict
the
demand
matrix
D
for
the
next
frame
according
to
BASIC
SYMBOLS
NOTATION
the
history
of
the
recent
requests.
Then
it
transmits
node's
requests
according
to
these
predictions.
At
the
same
time,
it
records
the
actual
requests
of
the
current
frame
to
the
predictors'
history
queues.
Thus,
this
scheme
saves
valuable
algorithm
and
produces
the
w
x
t
scheduling
matrix
S,
where
time
since
the
scheduling
algorithm
allows
the
packets'
trans
t
denotes
the
length
of
the
schedule
in
timeslots.
Each
s(i,
mission
in
parallel
with
the
prediction
of
the
next
transmission
element,~~~~
~ ~~
t'
=lso
In
waae
andh
the
...lo
of
the
rex
resentsthenod
element,
i
=1,...
w
and
j
=1,.
t,
represents
the
node
requests.
As
a
result,
POSA
leads
to
a
significant
decrease
of
that
transmits
on
channel
Ai
during
the
timeslot
Ij.
the
schedule
estimation
time.
III.
RELATED
SCHEDULING
ALGORITHMS
IV.
NETWORK
NODES
CLUSTERING
A
typical
pretransmission,
coordination
based
scheduling
Under
a
particular
Cl
clustering
process
noc
denotes
the
algorithm
for
optical
WDM
networks
is
the
Online
Interval
number
of
clusters
to
be
created.
Then,
U
denotes
the
set
based
Scheduling
(OIS)
[2].
OIS
incorporates
online
schedul
of
nodes
U
=
{U.
1,
m2
n}
that
is
to
be
clustered
while
ing
and
has
low
time
complexity
0(nw2
k),
where
k
is
the
Cl,...,
Cno,
denote
each
of
the
noc
clusters
consisting
of
upper
bound
of
nodes'
requests
on
each
channel.
According
1C,
.,
,
Cno,
members
(i.e.
nodes).
Under
this
notation,
the
to
this
algorithm
each
node
needs
to
maintain
a
list
of
time
clustering
process
Cl
is
defined
as
the
assignment
of
network
intervals
that
are
available
on
every
data
channel.
Further
nodes
to
groups
of
nodes
(i.e.
clusters):
more,
for
each
node
whose
request
is
being
processed,
nodes
Cl:
{1,.
.
.,
n}
{1,...
,
noc}
maintain
one
additional
list
of
intervals
that
have
not
yet
been
assigned
to
the
specific
node
for
transmission.
These
intervals
Nodes
assigned
to
the
same
cluster
are
"similar"
to
each
other
show
the
unallocated
time
on
a
specific
channel
or
node.
More
and
"
i
the
nodes
belonng
The
clusershin
.
. .
.
,,
~~~~~~~~terms
of
their
packets
requests
per
channel.
The
membership
specifically,
whenever
a
node
has
a
request
on
a
channel
the
q p
p
algorithm
examines
the
available
intervals
on
this
channel.
of
a
nod
,
where
i
y
the
to
as
Collwhr
Furthermore,
the
node's
list
of
interval
is
also
checked
to
determine
if
the
node
is
scheduled
to
transmit
on
any
other
f(ui
C_J
1
ifui
C
Ci
channel
during
the
time
interval
requested.
It
is
apparent
that
0
otherwise
the
algorithm
does
not
assign
more
than
one
node
at
the
same
Based
on
the
above,
it
is
apparent
that
the
notion
of
interval
for
the
same
channel
in
order
to
keep
the
schedule
similarity
is
fundamental
in
a
clustering
process,
and
so
far
collision
free.
Hence,
the
transmission
is
eventually
scheduled
it
is
quite
common
to
evaluate
the
dissimilarity
between
two
to
the
appropriate
intervals
and
the
lists
are
updated.
items
(in
our
case
nodes)
by
using
a
distance
measure
[4].
An
extension
of
OIS,
which
is
based
on
traffic
prediction,
To
proceed
with
our
network
nodes'
clustering
process,
we
is
the
Predictive
Online
Scheduling
Algorithm
(POSA)
[3].
employ
the
Squared
Euclidean
distance'
which
is
a
well
POSA
has
a
very
effective
traffic
prediction
mechanism
aiming
known
and
widely
used
distance
measure
in
the
vectorspace
at
drastically
reducing
the
computation
time
of
the
schedule.
This
mechanism
differentiates
POSA
from
QIS
while
both
of
1The
Squared
Euclidean
distance
uses
the
same
equation
as
the
Euclidean
distance,
but
does
not
take
the
square
root.
For
two
points
P
=(P17
Pn)
them
operates
the
same
scheduling
algorithm.
More
specifi
and
Q
(qi
,
,
qn)
in
inspace
their
Squared
Euclidean
distance
is
defined
cally,
POSA
maintains
a
set
of
n
x
w
predictors
which
try
to
as:
Ip2

ql2
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model
[4],
[6].
Given
that
each
node
ui
is
represented
by
..TRAFF
the
row
i
of
the
demand
matrix
D,
this
row
is
denoted
as
.
WDM
Star
>DEMANDMATRIXD(nxw)
I
a
multivariate
vector
consisting
of
w
values
as
follows:
.
Network
*.,
.w'*
. +'
CLUSTERING
D
(i,:
(d
(i,1),
,d(i,
w))
........
Therefore,
the
evaluation
of
the
dissimilarity
between
two
CIe
nodes
can
be
expressed
by
the
distance
of
their
demand
Clustdrs
vectors.
Thus,
we
will
use
the
expression
dist(ux,
uy),
where
ux,
Uy
C
U,
to
denote
the
Squared
Euclidean
distance
of
the
nodes'
demand
vectors
D(x,:)
and
D(y,:):
CLUSTERS'
SORTING
dist(ux,
uy)=
D(x,:)

D(y,:)
2
Then,
an
arbitrary
cluster
Cj,
where
j
1,
. .
.,
noc,
of
the
TRANSMISSION
lHl
nodes'
set
U
is
considered.
The
representation
of
the
cluster
[SDGMATRIX(
t)
j
Cj
when
clustering
process
Cl
is
applied
to
it,
collapses
the
nodes
belonging
to
Cj
into
a
single
point
(e.g.
the
mean
value
Fig.
2.
The
CBSA
overview
which
does
not
correspond
to
an
existing
node).
This
point
is
called
cluster's
representative
cj
(also
known
as
centroid)
since
formed,
the
algorithm
proceeds
to
the
second
step
called
the
each
node
ui
e
Cj
is
represented
by
cj.
Given
the
demand
scheduling
step.
The
goal
of
function
Schedule
is
to
form
the
vectors
of
ui
e
Cj,
the
demand
vector
of
cj
is
defined
as
scheduling
matrix
S
using
the
same
logic
as
POSA
algorithm.
follows:
1
n
Algorithm
1
The
CBSA
flow
control
MeansD(j,)=C
f(ui,)
*
D(i,
:),j
1,*..,
noc
Input:
A
set
U
of
n
nodes
whose
packets'
requests
on
each
of
the
w
channels
organized
in
an
n
x
w
demand
matrix
Since
both
D(i,:)
and
MeansD(j,:)
are
vectors,
their
dis
D,
the
upper
bound
on
nodes'
requests
k
and
the
number
similarity
is
measured
by
their
Squared
Euclidean
distance
of
clusters
noc.
dist(ui,
cj).
Considering
all
clusters,
the
clustering
process
is
Ouput:
The
scheduling
matrix
S.
guided
by
the
criterion
function
J
which
is
defined
to
be
the
1:
/*Clustering
Step*/
sum
of
distances
over
all
channels
between
each
node
and
the
2:
(Cl,
MeansD)
K
means(D,
noc)
representative
of
the
cluster
that
the
node
is
assigned
to:
3:
SortedMeans
Quicksort(MeansD)
noc
4:
ClusteredNodes
Arrange(SortedMeans)
J
=
E
S
dist(ui,
cj)
5:
/*Scheduling
Step*/
j=1
uiccj
6:
S
=
Schedule(ClusteredNodes)
Based
on
the
above
we
can
define
the
network
nodes
clustering
as
follows:
Given
a
network
with
n
nodes
whose
packets'
Theorem
1:
The
CBSA
has
time
complexity
O(nkw2).
requests
on
each
of
the
w
channels
are
organized
in
an
n
x
Proof:
During
the
clustering
step
we
employ
the
w
demand
matrix
D,
the
integers
noc
and
k,
and
the
criterion
Kmeans
algorithm
(line
2)
whose
time
complexity
is
function
J,
find
a
Cl
clustering
of
U
into
noc
clusters
such
0(n
noc
r),
where
n
is
the
number
of
nodes,
noc
the
number
that
the
J
is
minimized.
of
clusters
to
be
created
and
r
the
number
of
iterations
that
takes
the
algorithm
to
converge.
However,
both
noc
and
r
V.
THE
PROPOSED
CLUSTERING
BASED
SCHEDULING
are
relatively
small
compared
to
the
number
of
nodes
n
and
ALGORITHM
thus
their
contribution
to
the
algorithm's
complexity
can
be
The
CB
SA
is
a
twostep
process
depicted
in
Fig.
2.
Its
core
ignored
[4].
Thus,
the
Cl
clustering
is
computed
in
time
linear
idea
is
that
network
nodes
should
be
rearranged
according
to
on
the
number
of
nodes:
0(n).
The
Quicksort
function
(line
3)
their
packets'
requests
before
their
final
schedule.
During
the
sorts
clusters'
representatives
in
0(noc
log(noc))
time
while
first
step,
the
Cl
clustering
of
the
nodes'
set
U
is
produced
the
Arrange
function
(line
4)
takes
time
0(n)
to
arrange
based
on
the
n
x
w
demand
matrix
D.
For
this
clustering
the
n
nodes
according
to
the
SortedMeans.
The
total
time
the
Kmeans
algorithm
is
employed
which
is
a
widely
used
complexity
of
the
clustering
step
is
thus
O(n+noc
log(noc)
+
partitional
clustering
algorithm
[9].
The
Kmeans
minimizes
n)
which
becomes
0(n).
During
the
scheduling
step
the
the
objective
function
J
defined
in
Section
IV.
Next,
given
the
Schedule
function
(line
5)
needs
0(nkw2)
time
[3]
to
from
Cl
as
well
as
the
MeansD
table,
consisting
of
the
clusters
rep
the
scheduling
matrix
5,
where
k
is
the
upper
bound
of
nodes'
resentatives'
demand
vectors
MeansD(j,
:),
the
SortedMeans
requests
and
w
the
number
of
channels.
As
a
result,
the
total
is
computed
in
order
that
we
prioritize
the
clusters
with
greater
complexity
of
CBSA
is
0(m)
+
0(mkw2)
0
(mkw2).
U
requests.
The
calculated
SortedMeans
is
then
used
in
order
that
To
facilitate
the
comprehension
of
the
CBSA,
consider
the
network
nodes
are
rearranged.
Once
the
ClusteredNodes
is
a
network
consisting
of
nm
4
nodes
namely
U
=
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{u1,
u2,
u3,
u4}
and
w
=
3
channels
namely
A
=
{A1,
A2,
23}
22
while
the
upper
bound
of nodes'
requests
is
k
=
3.
Then,
a
4
21
CBA
x
3
demand
matrix
D
could
be
the
following:
0
(
0)
1
2)
)
t

<0
~19
D
~~~~~~~~~~~~~~~~~~~~~~~~18
132
17
Example
1.
In
the
above
demand
matrix
D
the
fact
that
z
16
D(3,
2)
=
3
means
that
the
node
identified
as
u3
requests
15
3
packets
on
channel
A2.
10
20
30
N
40
50
60
Applying
the
Kmeans
for
noc=
2
in
the
above
D
matrix
Nodes
results
in
Cl
=
(2,
2,
1,
1)
which
means
that
u1,
u2
C
C2
(a)
Network
throughput
as
a
function
of
the
number
of
while
u3,
u4
C
Cl.
Given
this
Cl
the
clusters
representatives'
nodes
demand
matrix
MeansD
is
formed
as
follows:
1500
MeansD=
(
15
3
2.5
)
100
Sorting
MeansD
results
in
giving
priority
to
Ci
and
thus
to
10
nodes
u3,u4.
Therefore,
the
schedule
service
order
defined
by
the
CBSA
will
be
U3,U4,U1,U2
instead
of
U1,U2,U3,U4
which
is
formed
by
the
POSA.
Tables
II
and
III
depict
the
500
scheduling
matrix
S
produced
respectively.
Based
on
these
tables,
CBSA
provides
16.7%
improvement
on
channels'
utilization
while
it
reduces
the
mean
packet
delay
from
4.6
il
14
15
16
17
18
19
20
21
22
to
3.7
timeslots.
Network
Throughput
(Gbps)
Timeslots
(b)
Mean
packet
delay
as
a
function
of
the
network
II
12
13
14
15
16
17
18 19
110
throughput
WI
U3
U4 U4
U2
U2
Fig.
3.
Results
for
w
=
8
and
noc=
7
W2
Ul
U3 U3
U3
U4 U4 U4
U2
W3
Ul
Ul
U3 U3
U4 U4 U4
TABLE
II
THE
SCHEDULING
MATRIX
S
PRODUCED
BY
CBSA
In
the
simulation
results
shown
in
this
section,
the
perfor
mance
of
POSA
and
CBSA
is
presented
in
terms
of
net
work
throughput
and
mean
packet
delay.
Network
throughput
represents
the
average
number
of
bits
transmitted
per
frame
W=====
i/I
~5
Timeslots
==
=
on
each
channel
while
mean
packet
delay
denotes
the
mean
Il
2
13
14
1
16
17
1
19
I
2
time
in
timeslots
that
packets
are
waiting
at
the
queues
till
W2
Ui
U2
U
U3
U
U
U
the
beginning
of
their
transmission.
We
experimented
with
W3
Ul
Ul
U3 U3
U/I4
U/I4
U
different
number
of
nodes
(n)
and
channels
(w).
TABLE
III
In
Fig.
3(a)
and
4(a)
the
algorithms'
input
is
set
to
n
THE
SCHEDULING
MATRIX
S
PRODUCED
BY
POSA
10,
20,
30,
40,
50,
60
nodes
while
the
number
of
channels
are
w
=
8
and
w
=
12
respectively.
Moreover,
we
fixed
the
upper
bound
of
nodes'
requests
in
k
=
(n*w)/51
[3]
for
scalability
reasons
and
set
the
number
of
clusters
to
noc
=
7.
From
VI.
SIMULATION
RESULTS
Fig.
3(a)
and
4(a),
which
depict
the
network's
throughput
as
To
evaluate
the
performance
of
the
CBSA
we
compared
it
a
function
of
the
number
of
nodes,
it
is
clear
that
CBSA
is
with
the
POSA.
The
experiments
we
carried
out
are
based
on
steadily
superior
to
POSA
both
for
w
=
8
and
w
=
12.
This
is
the
following
assumptions:
expected
since
CBSA
prioritizes
the
long
length
requests
and
1)
Traffic
pattern
is
uniform
i.e.
packets'
requests
are
thus
allocates
more
free
timeslots
for
the
rest
requests.
The
generated
with
equal
probability
for
every
node.
maximum
and
minimum
observed
differences
are
1.33
Gbps
2)
Nodes
may
request
0
to
k
packets
on
each
frame
with
(for
in
=20
nodes
and
w
=12
channels)
and
0.25
Gbps
(for
equal
probability,
in
=10
nodes
and
w
=12
channels)
correspondingly.
Fig.
3(b)
3)
The
line
is
defined
at
3
Gbps
per
channel
and
the
tuning
and
4(b),
which
represent
mean
packet
delay
as
a
function
of
time
is
considered
to
be
negligible,
the
network
throughput,
validate
the
CB
SA's
superiority
since
4)
The
outcome
results
from 10000
transmission
frames.
it
is
obvious
that
the
improvement
in
network's
throughput
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32
POS
VII.
CONCLUSIONS
AND
FUTURE
WORK
30
CBSAa
This
paper
introduces
and
evaluates
a
novel
packet
schedul
ing
algorithm
for
WDM
star
networks.
The
proposed
Clus
028
tering
Based
Scheduling
Algorithm
(CBSA)
rearranges
the
26
a
service
order
of
a
network's
nodes
by
organizing
them
into
m
24

//

groups
(i.e.
clusters)
according
to
the
number
of
their
packet
24.
requests
per
channel.
Then
it
defines
the
nodes'
transmission
z
//
priority
beginning
from
the
cluster
with
greater
demands
20
s//

and
ending
to
the
cluster
with
fewer
requests.
The
proposed
18X
_
algorithm
has
been
evaluated
under
uniform
traffic
for
different
10
20
30
Nodes
40 50
60
number
of
nodes
and
channels
and
it
has
resulted
in
upgrading
the
network
performance
while
keeping
low
the
mean
packet
(a)
Network
throughput
as
a
function
of
the
number
of
delay
in
comparison
with
the
POSA.
nodes
Future
work
aims
at
evaluating
the
proposed
scheme
under
2500
IPOSAI
poisson
and
bursty
traffic.
Moreover,
the
experimental
results
I,
CBSAt
offer
insight
for
sorting
not
only
the
clusters
but
also,
at
a
2000
second
step,
the
nodes
(members)
in
each
cluster
according
to
their
packet
transmission
requests.
Handling
appropriately
la
'5000
//
1
the
nodes
in
each
cluster
is
expected
to
further
improve
the
network's
performance.
m
1000
ID
//REFERENCES
500

[1]
B.
Mukherjee,
Optical
WDM
Networks.
Springer,
2006.
[2]
K.
Sivalingam,
J.
Wang,
J.
Wu,
and
M.
Mishra,
"An
intervalbased
2
scheduling
algorithm
for
optical
wdm
star
networks,"
J.
Photonic
Network
18
20
Netrp22
24
26
28
3(
0
32
Commun.,
vol.
4,
no.
1,
pp.
7387,
2002.
Netwrok
Throughput
(Gbps)
[3]
E.
Johnson,
M.
Mishra,
and
K.
Sivalingam,
"Scheduling
in
optical
wdm
(b)
Mean
packet
delay
as
a
function
of
the
network
networks
using
hidden
markov
chain
based
traffic
prediction,"
J.
Photonic
throughput
Network
Commun.,
vol.
3,
no.
3,
pp.
271286,
2001.
[4]
A.
Jain,
M.
Murty,
and
P.
Flynn,
"Data
clustering:
A
review,"
ACM
Fig.
4.
Results
for
w
=
12
and
noc
=
7
Computing
Surveys,
vol.
31,
no.
3,
pp.
264323,
1999.
[5]
J.
Srivastava,
R.
Cooley,
M.
Deshpande,
and
P.N.
Tan,
"Web
usage
mining:
Discovery
and
applications
of
usage
patterns
from
web
data,"
SIGKDD
Explorations,
vol.
1,
no.
2,
pp.
1223,
2000.
does
not
affect
the
mean
packet
delay.
More
specifically,
the
[6]
S.
Petridou,
V.
Koutsonikola,
A.
Vakali,
and
G.
Papadiniitriou,
"A
CBSA
keeps
lower
the
mean
packet
delay
in
comparison
with
divergenceoriented
approach
for
web
users
clustering,"
in
Proc.
of
P
An
p
d
t
oiobtains
International
Conference
on
Computational
Science
and
its
Apllications
POSA
independently
of
the
number
of
channels
while
obtalns
(ICCSA
'06),
Glaskow,
Scotland,
May
2006,
pp.
12291238.
higher
network
throughput.
For
example,
for
n
=
30
and
w
[7]
G.
Papadimitriou,
P.
Tsimoulas,
M.
Obaidat,
and
A.
Pomportsis,
Multi
12
CB
SA
offers
27.44
Gbps
network
throughput
causing
583
wavelength
Optical
LANs.
Wiley,
2003.
timeslots
as
mean
packet
delay
while
the
respective
values
for
[8]
P.
Sarigiannidis,
G.
Papadimitriou,
and
A.
Pomportsis,
"A
high
throughput
scheduling
technique,
with
idle
timeslot
elimination
mechanism,"
IEEE
POSA
are
26.51
Gbps
and
594
timeslots.
Journal
of
Lightwave
Technology,
vol.
24,
no.
12,
pp.
48114827,
2006.
[9]
T.
Hastie,
R.
Tibshirani,
and
J.
Friedman,
The
Elements
of
Statistical
Learning:
Data
Mining,
Inference,
and
Prediction.
Springer,
2001.
Authorized licensed use limited to: Aristotle University of Thessaloniki. Downloaded on October 7, 2008 at 5:59 from IEEE Xplore. Restrictions apply.