Journal of the Society of Korea Industrial and Systems EngineeringVol, 28, No. 1, pp.129 133, March 2005.

무선 환경 하에서 방식의 다중채널Slotted ALOHA경쟁에 대한 지연시간분석

A delay analysis of multi-access protocol under wireless network

Sun Hur Jeong-Kee Kim Jin-Gyu Nam

Department of Industrial Engineering, Hanyang University

Slotted ALOHA(S-ALOHA) is widely used in local wireless network. We analyze the performance of contention-basedmodel in wireless LAN using S-ALOHA protocol. We analyze the performance of binary exponential backoff (BEB) algo-rithm under the slotted ALOHA protocol whenever a node’s message which tries to reserve a channel is involved in acollision for the th time, it chooses one of the next frames with equal probability and attempts the reservationagain. We derive the expected access delay and throughput which is defined as the expected number of messages that re-serve a channel in a frame. A simulation study is performed to verify our method.

MAC, Wireless Telecommunication Network, Binary Exponential Backoff, TDMA

서 론1.

Slotted ALOHA(S-ALOHA)MAC (reservation protocol)

[1]. S-ALOHA pureALOHA

. , S-ALOHA,

(con-tention protocol) . (collision) ,

,.

(re-transmission),

[10]. S-ALOHA

. S-ALOHA.

S-ALOHA,

[6]. , BinaryExponential Backoff (BEB) . BEBEthernet[4] LAN[5] randomaccess ,

(collision reso-lution)

[2]. BEB

[1], [7],[8]. Aldous[7] BEB 0

, Goodman et al.[8]

허 선 김정기 남진규⋅ ⋅

. Jeong & Jeon[1] LANS-ALOHA Exponential Backoff (EB)

full load throughput, EB .

Kwak et al.[2] EB saturation through-put ,

EB .LAN S-ALOHA

BEB.

,

.

,

.,

. BEB.

, ,.

, S-ALOHA BEB.

.,

,.

.IEEE 802.11 wireless LAN, ETSI HYPERLAN , IEEE

802.16 wireless MAN,

.. 2,

. 3. , 4

.

성능분석2.

시스템 설명2.1

S- ALOHABEB .

,,

.,

.,

S-ALOHA ,

..

,.

, BEB. <

1>

. ,4

.[2].

2.2.

그림 의 예< 1> BEB Algorithm

안정상태 메시지 수의 분포와 충돌발생 확률2.2

. (= )

무선 환경 하에서 방식의 다중채널 경쟁에 대한 지연시간분석Slotted ALOHA

. -- BEB

. ,

,.

,

,, (2.1)

.

1

, 1, 0,

n n n nn

n n

N J A NN

A N+

⎧ − + ≥⎪= ⎨

=⎪⎩ (2.1)

,

.Markov Chain . (2.1) 1-

(2.2) .

( )

( )

1

min ,

max 0,

Pr( )

Pr( ) ,

nij n

i V

j i k n nk i j

p N j N i

a J k N i

+

− += −

= = =

= = =∑ (2.2)

(2.2) , Poisson.

,. Szpankow-

ski[3] .

..

backoff.

( )( )

( ) ( )51110

16 16

11 2 12 .

1 11 2c cc c

cc cc

rγ γγ γ

γγ γγ

⎛ ⎞ −− −⎜ ⎟= +⎜ ⎟ − −−⎝ ⎠ (2.3)

(2.3)

,.

. , (2.3)

,

.

.

( ) ( )

( )

11

2 2 1

1

2

0

1 1 11 , Pr

11 1 1 .1 1

i y iym

c m y i

mm m

mj

j

yY m y M m

i V V

mV r rV V V j

γ

π

π

− −∞ −

= = =

−∞

∞=

=

−⎛ ⎞⎛ ⎞ ⎛ ⎞∑= − ⋅ ⋅ =∑ ∑ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

⎧ ⎫⎪ ⎪⎛ ⎞∑= − − + − ⋅⎨ ⎬⎜ ⎟− −⎝ ⎠⎪ ⎪ ∑⎩ ⎭ (2.4)

,

. ,

.

recursive

.

평균 메시지 대기시간2.3

BEBreducible

.

. ,.

,.

. ,

3/2 .

.

(2.4) .

허 선 김정기 남진규⋅ ⋅

( ) ( )15

0

2 3 4

5 6 7 8

16 9 10 11 12

13 14 15

( )

1 2.5 5.5 11.5 23.547.5 95.5 191.5 383.51 1 .

2 1 767.5 1535.5 2559.5 3583.5

4607.5 5631.5 6655.5

b

c c c c

c c c cc

c c c c c

c c c

E D E D B b P B b

γ γ γ γ

γ γ γ γγγ γ γ γ γ

γ γ γ

=∑= = =

⎛ ⎞+ + + +⎜ ⎟+ + + +− ⎜ ⎟= + ⎜ ⎟− + + + +⎜ ⎟⎜ ⎟+ + +⎝ ⎠

(2.4)

경쟁에서 성공한 메시지 개수의 분포2.4

S-ALOHA BEB.

,, Szpankowski[3]

(2.5), (2.6) .

( )

( ) ( ) ( )0 0

Pr

, , Pr .n

n y

X x

J y x Y n y N n∞

= =

=

∑= =∑ (2.5)

( ) ( )

( )

0 0

1

0

( , )Pr( )Pr

1 Pr .

n

n y

n

n

E X E X Y y N n Y y N n N n

rnr N nV

∞

= =

−∞

=

∑= = = = = =∑

⎛ ⎞∑= − =⎜ ⎟⎝ ⎠ (2.6)

수치 예제3.

S-ALOHA BEB

.< 1> .

표 수치예제 입력 데이터< 1>

Arrivals of new messages ~ ( )Poisson λ 1, 2, , 30λ = L

Numbers of request slots ( )V 15, 20, 25, 30V =

throughput(2.5) (2.6) . C++

Matlab10

. < 3> , offered load( V/λ )

. V=15, 20 and 25. 95%

. 0.3. V/λ 0.3

..

그림 평균대기 시간< 3> vs. Offered load ( )

V=30

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0

3

0.0

7

0.1

0.1

3

0.1

7

0.2

0.2

3

0.2

7

0.3

0.3

3

0.3

7

0.4

Offered load

Log

(Expect

ed D

elay)

Simulation

Analytic

그림 상태전이확률 다이어그램< 2>

0 1,1

T

B3.12,1cγ

cγ−1 )1(21

cγ− cγ−1

⋅⋅⋅cγ−1)1(

2110 cγ−

cγ cγ cγ1,2 2,2

cγ

)1(41

cγ−

21

cγ21

43 2,42,3

⋅⋅⋅32

21

)1(31

cγ− )1(21

cγ− cγ−1

cγ41 cγ3

1 cγ21

)1(81

cγ−

87

cγ87

15,1 ⋅⋅⋅1021

cγ1021

152,15

무선 환경 하에서 방식의 다중채널 경쟁에 대한 지연시간분석Slotted ALOHA

< 4>. V=15, 20 and 25

.

그림 도착률< 4> Throughput vs. ( )

V=30

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 11 12

Arrival Rate

Log(E

xpecte

d n

um

ber of

success m

essage)

Simulation

Analytic

< 4> 9. ,

V 0.3. throughput

V3.0≤λ .

결 론4.

S-ALOHA BEB. ,

.

recursive,

.

,.

throughput.

V3.0≤λ

. ,

LAN S-ALOHA BEB.

참고문헌

[1] D. G. Jeong, and W. S. Jeon, “Performance of an Ex-ponential Backoff for Slotted-ALOHA Protocol in LocalWireless Environment”, IEEE TRANS. Veh. Technol.,vol. 44, no. 3, pp. 470-479, Aug. 1995.

[2] B. J. Kwak, N. O. Song, and L. E. Miller, “Analysisof the stability and Performance of Exponential Backoff”,IEEE WCNC 2003, vol. 3, pp. 1754-1759, Mar. 2003.

[3] W. Szpankowski, “Analysis and stability considerationsin a reservation multiaccess system”, IEEE Trans. onComm., vol. com-31, no. 5, pp. 684-692, May 1983.

[4] R. M. Metcalfe, and D. G. Boggs, “Ethernet Distrib-uted packet switching for local computer network”,Comm. ACM, vol. 19, no. 7, pp. 395-404, July 1976.

[5] IEEE Std 802.11, “IEEE standard for wireless LANmedium access control and physical layer specifica-tions”, Nov. 1997.

[6] L. Kleinrock, “queueing system, vol. 2 computer ap-plications”, New York Wiley, 1976.

[7] D. J. Aldous, “Ultimate instability of exponential back-offprotocol for acknowledgement-based transmission controlof random access communication channels”, IEEETrans. Information Theory, vol. 33, no.2, pp. 219-213,Mar. 1987.

[8] J. Goodman, A. G. Greenberg, N. Madras, and P. March,“Stability of binary exponential backoff”, Journal ofACM, vol. 35, no. 2, pp. 579-602, July 1988.

[9] R. Rom, and M. Sidi, “Multiple Access protocols per-formance and analysis”, Springer-Verlag New York, 1990.