Modeling and Methodology for

Performance Evaluation in Next-

Generation Wireless

Communication Networks

Wuyi YUE

Department of Information Science and Systems Engineering

Konan University, Kobe, 658-8501 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

Multi-Channel 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High-speed Cellular Service腺腹Ubiquitous Service腺

Restaurant

In-building

Underground

High-speed Transport

OfficeNW (Ad Hoc)

City Information

ITS

1 Future mobile communications

Home NW

Next-Generation 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, next-generation 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 next-generation Internet

Next-Generation Wireless Ad

Hoc Networks

Next-Generation Wireless Ad

Hoc Networks

A general-purpose 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

> High-speed 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 general-purpose ad hoc network:

a heterogeneous network

different nodes in terms of transmission range as

well as communication technologies should be

allowed

A specific-purpose ad hoc network can be

formed with the support of a general-purpose ad

hoc network

For example: nodes of a general-purpose 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) Multi-Hop Communications

(iv) Hidden User Problem and Exposed User

Problem

Ad hoc networks require a peer-to-peer 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 any-where any-time 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 source-to-

destination paths, the performance evaluations such as

end-to-end 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

Trade-offs in using different performance measures

The maximum end-to-end throughput

The minimum end-to-end 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

Multi-Channel Networks

4 Algorithm for Channel Assignment

by Recursive Search

5 Conclusions

Buffer

Multi-channel

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): steady-state 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 non-linear 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

Multi-Channel 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 Multi-Channel 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

1e-012

1e-010

1e-008

1e-006

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

Timer-based

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]

Timer-based

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

Timer-based

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

1e-010

1e-008

1e-006

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

Timer-based

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

Multi-Channel 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

Multi-Channel 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 High-Speed 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

Co-channel Interference

Co-channel 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 semi-optimal solution

Characters of the proposal technique

Characters of the proposal technique

腅

It takes shorter time to find an optimal or

a semi-optimal channel assignment

腅

It satisfies co-channel 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

A-B, A-C: with interference

A-D: without interference

3.2 Co-channel 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 co-channel

interference

1 Future Mobile Communications

2 Analysis and Optimization of an

M

(

k

)

/M/k

QueueingSystem

3 Application to a Wire Resource Control in

Multi-Channel 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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1968.

[3] Hillier, F., “Economic modelsfonindustrial waiting line problems”,

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References (II)

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