Modeling and Methodology for
Performance Evaluation in Next
Generation Wireless
Communication Networks
Wuyi YUE
Department of Information Science and Systems Engineering
Konan University, Kobe, 6588501 Japan
July 22, 2004
Outline
1 Future Mobile Communications
2 Analysis and Optimization of an
M
(
k
)
/M/k
QueueingSystem
3 Application to a Resource Control in
MultiChannel Networks
4 Algorithm for Channel Assignment
by Recursive Search
5 Conclusions
Location free service
(Anywhere, Anytime, Anyone)
Location dependent service
(Regional, Timely, Personalized)
Communication within accessible
distance and time
Communication beyond location (and time)
腹Highspeed Cellular Service腺腹Ubiquitous Service腺
Restaurant
Inbuilding
Underground
Highspeed Transport
OfficeNW (Ad Hoc)
City Information
ITS
1 Future mobile communications
Home NW
NextGeneration Wireless Ad
Hoc Networks
Computers will be a part
All equipment in various places
such as homes, offices, streets
Consider: these computers
will be connected to the Internet
(IP on Everything)
Drastic innovations are required
of the Internet's architecture in
order to cope with such an
environment
In this context, nextgeneration ad hoc
networks may create a new paradigm in the
history of mobile communication technology
Novel concepts will also be required in mobile
Communication
Ad hoc networks may hold the key as a basis
of nextgeneration Internet
NextGeneration Wireless Ad
Hoc Networks
NextGeneration Wireless Ad
Hoc Networks
A generalpurpose ad hoc network
An open network
It can be used by
anybody, anytime, anywhere
Overview of Researches Activities
(1)Innovative radio transmission and
advanced system control technologies
toward
> Highspeed and High capacity
cellular systems
> Ubiquitous and Personalized
communication systems
(2) New concept wireless communication
technologies
Modeling and Performance Evaluation of
Wireless Communication Networks
A generalpurpose ad hoc network:
a heterogeneous network
different nodes in terms of transmission range as
well as communication technologies should be
allowed
A specificpurpose ad hoc network can be
formed with the support of a generalpurpose ad
hoc network
For example: nodes of a generalpurpose ad hoc
network can be used as routers for a specific purpose
ad hoc network in order to increase connectivity and
reliability
Modeling and Performance Evaluation of
Wireless Communication Networks
Main characteristics of wireless ad hoc
networks relevant to the performance
analysis we consider
(i) Dynamic Network
(ii) Bandwidth Constraints and Variable Link
Capacity
(iii) MultiHop Communications
(iv) Hidden User Problem and Exposed User
Problem
Ad hoc networks require a peertopeer architecture
Dynamic topology of the network depends on the
location of different mobile users, which changes
randomly and rapidly over all possible times
Dynamic Network
We all want anywhere anytime communication
Ubiquitous communication has been made possible
in the recent years with the advent of mobile ad hoc
networks
Network topological changes can occur since the
breakdown of a mobile user in a hostile environment
Failure of a connected link since signal interference
and changes in signal propagation conditions
Dynamic Network
Ad hoc routing protocol must be able to dynamically
update the status of its links
Reconfigure itself in order to maintain strong connectivity
to support communications among the users
given a channel access protocol and a set of sourceto
destination paths, the performance evaluations such as
endtoend throughput and delay are widely used
Dynamic Network
Since the network topology is dynamically changing
However
In wireless networks
Performance analysis:
Dynamic Network
Design of routing protocols
Tradeoffs in using different performance measures
The maximum endtoend throughput
The minimum endtoend delay
Total power, bandwidth, and the shortest path
/minimum hop
To make
Outline
1 Future Mobile Communications
2 Analysis and Optimization of
M
(
k
)
/M/k
QueueingSystem
3 Application to a Wire Resource Control in
MultiChannel Networks
4 Algorithm for Channel Assignment
by Recursive Search
5 Conclusions
Buffer
Multichannel
Switch
2Modeling and Performance Evaluation
of Wireless Communication Networks
Researches in queueing theory
Descriptive studies, including structures of
queues and their applications
Optimal design & control of queueing
systems
Howover
Most research assumed that the arrival rate
is independent of the number of servers
2.1Optimization of
M
(
k
)
/M/k
QueueingSystem
This research considers the optimal design
problem in an
M
(
k
)/
M
/
k
queueing system
with the arrival rate of customers
dependin
g
upon the number of servers.
All servers are identical, with service rate
µ
1
2
k
…
Arrival rate
λ
(
k
)
n
customers waiting in
queue with holding cost
k
servers with service cost
Departs
M
(
k
)/
M
/
k
QueueingSystem
2.2 System Model
k
:number of servers (decision variable)
λ
(
k
) : arrival rate, being a function of
k
µ
: mean service rate for each server
ρ
(
k
)=
λ
(
k
)/(
kµ
)<1:traffic intensity
h
(
n
,
k
): holding cost rate when n customers
waiting in queue
H
(
k
): expected holding cost rate
S
(
k
): service cost rate for operating
k
servers
C
(k): steadystate expected total cost rate
Steady Stateof the System
•Steady probability of
n
customers in the system:
,)()(
!
1
1 ,)()(
!
1
)(
0
0
≥
≤≤
=
knkkk
k
knkkk
n
k
nk
nn
n
πρ
πρ
π
where
1
1
0
0
)(1
1
!
)(
!
)(
)(
−
−
=
∑
−
⋅+=
k
i
kkii
kk
kk
i
kk
k
ρ
ρρ
π
•Average number of customers in the queue:
∑
⋅
−
=−⋅=
∞
=
+
+
0
0
2
1
)(
)](1[!
)(
)()()(
n
kk
n
k
kk
kk
knkkLq
π
ρ
ρ
π
Cost Structure of the System
When the case of a linear holding cost rate
+
−⋅=)(),(knhknh
∑
⋅=−⋅⋅=Σ=
∞
=
+
∞
=
0
0
)()()(),()()(
n
nn
n
kLqhknhkknhkkH
ππ
)()()()()(kLqhkSkHkSkC
⋅
+
=
+
=
Expected holding cost rate:
Total cost rate of system in the steady state:
2.3 Properties of
Lq
(
k
)
LEMMA 1If
ρ
(k) is decreasing in k, then the
average number of customers in the queue Lq(k)
is rapidlydecreasing in k
Corollary 1 If
ρ
(k) is decreasing in k, then the
holding cost rate H(k) is rapidly decreasing in k
•Monotony of
Lq
(
k
) and
H
(
k
)
.1 ,0)(
)1()(
)1()1(
)1(
)1(
22
2
≥<∆≤
+
−+
−<
−
−kkLq
kgkg
gkg
λµ
λ
LEMMA
2If
ρ
(k) is decreasing in k, then we
have upper and lower bounds of ∆Lq(k)as
given by
•Bounds of ∆
Lq
(
k
)
2.4Optimal Number of Servers
The objective is to minimize the total cost rate
in the steady state:
},2,1)({min
⋅
⋅
⋅
=
kkC
)()()()1()(kHkSkCkCkC
∆
+
∆
=
−
+
≡
∆
Denote
k*
: Optimal number of servers
THEOREM
1
1) If ∆C(k)>0, ∀k,then k*
=1
2) If ∆C(k)<0, ∀k,then k*
=+∞
3) If there is k0≥1 such that ∆C(k)<0for all
k<k0
and ∆C(k+1) ≥0for all k≥k0
, then k*=k0
THEOREM
2 If
ρ
(k) is decreasing in kand
then k*
is finite
+
∞=
+∞→
)(limkS
k
When the linear service cost rate:
S
(
k
)=
s
0
+
s
⋅
k
,
s
>0
.
Let
}
)1()1(
)1()(
,:{min
s
h
gkg
kgkg
NkkK>
−+
+
∈=
LEMMA
3 If
ρ
(k)is decreasing in kthen K is finite
THEOREM
3
If
ρ
(k) is decreasing in k, then k*
is
less than K and k*
equals 1 when
.
)1(
)1(
22
2
λµ
λ
−
>s
2.5 Numerical Results
Consider the cases of linear holding cost
rate and linear service cost rate:
S (k)=s0
+s⋅k, s>0, H(k)=h⋅Lq(k)
We have
.
)1()(
)(
)()()()(
+
∆
−=∆+=∆+∆=∆
kgkg
kLqh
skLqhskHkSkC
So
r
h
s
kgkg
kg
kC≡<
+
∆
⇔>∆
)1()(
)(
0)(
EXAMPLE
1
Assumelinear arrival rate:
λ
(k)=
λ⋅
k, and then
ρ
(k)=
λ
/
µ
denoted by
ρ
0
Table 1 Optimal number of servers
with linear arrival rate
126359111
ρ
0
=0.99
1052111
ρ
0
=0.7
111111
ρ
0
=0.1
r=0.05r=0.1r=0.2r=0.5r=1.0r=10k*
Example 1
Example 2
E
XAMPLE
2
Assume that the traffic
intensity
ρ
(k)=
λ
(k)/(k
µ
) has different forms as
given in Table 2 and the results:
Table 2 Optimal number of servers
with nonlinear arrival rate
2
3
5
r=0.05
1111
ρ
(k)=1/ek
3221
ρ
(k)=sin
π
/3k
4321
ρ
(k)=0.9/k
r=0.2r=0.5r=1.0r=10k*
Outline
1 Future Mobile Communications
2 Analysis and Optimization of
M
(
k
)
/M/k
QueueingSystem
3 Application to a Wire Resource Control in
MultiChannel Networks
4 Algorithm for Channel Assignment
by Recursive Search
5 Conclusions
OXC
OXC
OADM
OADM
Router
Router
Base
Base
Networks
Networks
Wide
Wide
Networks
Networks
LAN
LAN
腅
腅
Access
Access
Networks
Networks
3 Application to a Wire Resource
Control in MultiChannel Networks
3.2
3.2
M(k)/M/k/k
M(k)/M/k/k
Network Model
Network Model
Scheduler
...
Servers :W
Geometric arrivals
Slot size: T
Arrival Prob.:
Poisson arrivals
Rate:
o
λ
Exponentially distributed
service time
Rate:
λ
µ
T
T
T
1
−
−
λ
e
Time
Number of bursts
W
0
T2T3T
Poisson Arrival
Departure
Cycle
Geo Arrival
Number of bursts in the System
Tp
q
P
W
o
W
loss
λ
+
=
)
1
(
T
e
λ
−
−
T
o
λ
+
1
T
e
λ
−
−
Performance Analysis
Loss Probability:
T
)1(
W
o
p
−
+
λ
=
hr
T
(b)
)
1
(
T
e
λ
−
−
1
W
q )
−
(
Burst
BurstThroughput:
)1(
W
o
p
T
−
+
=
λ
M
λ
{
}
hr
T
(d)
)
1
(
T
e
λ
−
−
1
W
q )
−
(
Data
DataThroughput:
10
10
0.1
1.0101001000
10
10
10
10
1
2
3
4
5
6
Burst assembly processing time (T) [ms]
Burst throughput [Number of bursts/s]
32
=
W
5
=
L
T
λ
= 1.0
µ
1
= 1.0
o
λ
...
λ
= 1.0
ρ
= 0.5, 0.75, 1.0
W =32
T =0.01~1000
λ
= 1.0
µ
1
= 1.0
SimAna
ρ
=0.5
ρ
ρ
=0.75
=1.0
Burst throughput [Number of bursts/s]
3.3 Numerical Results
32
=
W
5
=
L
T
λ
= 1.0
µ
1
= 1.0
o
λ
W=32
T: 0.01~1000
...
λ
= 1.0
ρ
= 0.5, 0.75, 1.0
100
150
200
250
300
350
400
Data throughput [Gbps]
0.1
1.0101001000
Burst assembly processing time (T) [ms]
SimAna
ρ
=0.5
ρ
ρ
=0.75
=1.0
Data throughput vsBurst assembly processing time
W=32
5
=
L
λ
µ
1
= 1.0
o
λ
W=32
: 0.0004~0.005
...
λ
=3.0, 5.0, 10.0
Τ
= 1.0 ms
T=1.0
λ
o
1e012
1e010
1e008
1e006
0.0001
0.01
1
0.001
0.002
0.003
0.004
0.005
Burst loss probability
Arrival rate of bursts from other nodes ( )
λ
o
Timerbased
Erlang
Ana
Sim
λ
=10.0
λ
=5.0
λ
=3.0
Burst loss probability vs Arrival rate of bursts from other nodes
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.0010.0020.0030.0040.005
Arrival rate of bursts from other nodes ( )
λ
o
Burst throughput [Number of bursts/s]
Timerbased
Erlang
Ana
Sim
λ
=10.0
λ
=5.0
λ
=3.0
W=32
5
=
L
λ
µ
1
= 1.0
o
λ
W=32
: 0.0004~0.005
...
λ
=3.0, 5.0, 10.0
Τ
= 1.0 ms
T=1.0
λ
o
Burst throughputvsArrival rate of bursts from other nodes
0
5
10
15
20
25
30
35
0.0010.0020.0030.0040.005
Arrival rate of bursts from other nodes ( )
Data throughput [Gbps]
λ
o
λ
=10.0
λ
=5.0
λ
=3.0
Timerbased
Erlang
Ana
Sim
W=32
5
=
L
λ
µ
1
= 1.0
o
λ
W=32
: 0.0004~0.005
...
λ
=3.0, 5.0, 10.0
Τ
= 1.0 ms
T=1.0
λ
o
Data throughputvsArrival rate of bursts from other nodes
W
5
=
L
λ
= 10.0
µ
1
= 1.0
o
λ
W:2~84
: 0.001~0.004
...
λ
=10.0
Τ
= 1.0 ms
T=1.0
λ
o
o
1e010
1e008
1e006
0.0001
0.01
1.0
0
10
20
30
40
50
60
70
80
=0.001
λ
o
=0.002
λ
o
=0.003
λ
o
=0.004
λ
Timerbased
Erlang
Ana
Sim
Number of wavelengths (W)
Burst loss probability
Burst loss probability vsNumber of wavelengths
Outline
1 Future Mobile Communications
2 Analysis and Optimization of
M
(
k
)
/M/k
QueueingSystem
3 Application to a Wire Resource Control in
MultiChannel Networks
4 Algorithm for Channel Assignment
by Recursive Search
5 Conclusions
Outline
1. Analysis and Optimization of
M
(
k
)
/M/k
QueueingSystem
2. Application to a Wire Resource Control in
MultiChannel Networks
3. Algorithm for Channel Assignment
by Recursive Search
4. Conclusion
cellular mobile wireless system
cellular mobile wireless system
To satisfy a rapid growth in the required
Channels are reused and channel are reassigned
Available frequency spectrum
is employed more efficiently
3. A HighSpeed Optimal Channel
Assignment using Recursive
Search in Cellular Wireless Networks
Channel Assignment
Channel Assignment
Channel Assignment Technique
Dynamic Channel Assignment
(DCA)
Fixed Channel Assignment
(FCA)
艑
艑
艑
艑
Cochannel Interference
Cochannel Interference
Channels ch 腠ch assigned
腩A cell interferes with its surroundings cells in the single belt
interfered with the channels having the same numbers
Channels in
Channel Assignment without Interference
Channel Assignment without Interference
•Number of combinations for FCA is too many
•optimal solution is calculated for a long time
In the literature
Search Methods:
•
Neural network
•GA腩Genetic Algorithm
They take a long time to obtain an optimal or
a semioptimal solution
Characters of the proposal technique
Characters of the proposal technique
腅
It takes shorter time to find an optimal or
a semioptimal channel assignment
腅
It satisfies cochannel interference
腅
It used fewestchannels
•new method using recursive search algorithm
based on a 7 cells repetition
•To apply the technique to several different channel
assignment environments
The same channel cannot be
simultaneously used are
labeled by gray color
AB, AC: with interference
AD: without interference
3.2 Cochannel Interference
Network Environment: 49 cells
Network Environment: 49 cells
Seven cells to be one cluster named “seven cell cluster”
Seven cells to be one cluster named “seven cell cluster”
腅The method assigning a
channel by the same pattern
for every cluster repeatedly
is the most efficient
3.3 Algorithm for Channel Assignment
腅If channels 1, 2, …, 7 are
assigned to the network
system, then the same
channels will be assigned
in the same cell of each
seven cell cluster
Flowchart of
Fixed Channel
Assignment
Flowchart of
Fixed Channel
Assignment
Channel: Assignment
channel numbers
RC i : number of channels
required by cell i
M : The threshold which
performs recursive
search
Channel Assignment by Recursive Search
Channel Assignment by Recursive Search
腅
Number of assigned cells for a channel number is smaller than M,
recursive search is applied as in Step (G) and reassignment of
channels is performed by recursive search algorithm
Channel number of assigned
Required channel number
With seven cell
cluster condition
With recursive
search algorithm
L: # of cells that the number RCi
of channels required is not
equal to 0
xi: # of each of such cells
(i= 1, 2, ..., L)
P: set of these numbers
P={x1, x2, ..., xL}
Qx: subset of P satisfying condition
that their distances to the cell x
are larger than two cells
3.4 Channel Assignment by Recursive Search
3.4 Channel Assignment by Recursive Search
Procedure of the proposed recursive search algorithm
Procedure of the proposed recursive search algorithm
F(x, P): Recursive function to perform the recursive search for
subset Qx
),(PxF
Do cells in Set
P be visited
Yes
剥牮⁴漠瑨異灥ﱥ癥ﰀ
No
call F(y, Qx)
for all y \in Qx
Sever the maximum
number
with the
maximum number of
assigned of cells
Yes
No
Example by using recursive search algorithm
Example by using recursive search algorithm
3.5 Simulation Results
Result of channel assignment
Result of channel assignment
腅Required channel numbers
Comparison with optimal solution
Comparison with optimal solution
腅We define the optimal channel assignment to be that both
number of channels used in the system and the total
adjacent channel interference are the smallest
腩膖Average result among 20 times
伀瀀瑩洀愀ﰀﰀ瑩潮 眀漠眀ﬀ㌀豈
匀ﰀ瑩潮⁷椀瑨⁴
瀀爀潰ｳ慬攀琀潤
㌲︲散﹤㈳︳︀
Our solution is very close to the optimal solution
by using a very short calculation time
•It ended in dozens of seconds
•The total number of channels used in the whole system is 23
Result of channel assignment considered the cochannel
interference
1 Future Mobile Communications
2 Analysis and Optimization of an
M
(
k
)
/M/k
QueueingSystem
3 Application to a Wire Resource Control in
MultiChannel Networks
4 Algorithm for Channel Assignment
by Recursive Search
5Conclusions
Further studies should include research
into dynamic control of such queueing
systems where the arrival rate depends
on the number of servers
Further Research
References (I)
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References (II)
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