MoIP

Interference-resisted

Wireless MAC Design

2007/11/30

Speaker: Yu-Hsiang Lei

Advisor: Hung-Yu Wei

2

Problem Overview

• For the 802.11 wireless system

– Contention based medium access

• No Qos mechanism avaiblable

– Multimedia connections require more bandwidth

• VoIP, video streaming

• Soft bandwidth guarantee

3

System Graph

MoIP nodes

(Interference-Resistant)

Challenge: provide QoS for MoIP nodes Other nodes

(normal)

4

Periodical CW Resetting

backoff

CW=CWmin

High QoS High QoS

T

backoff

CW=CWmin

backoff

CW=CWmin

High QoS

Throughput

Throughput

Time

MoIP node

Time

normal node

5

Periodical CW Resetting (cont.)

• To get a better performance, we can periodically allocate

resource for MoIP nodes

• Define a period T. After each period, we set the contention

window (CW) size of the interference-resistant nodes be

initial value (CWmin)

– Stations with smaller CW will have higher chance to access

the channel

6

To Implement Our Idea…

• We should first check if our idea would work

• Mathematical modeling

– Do the modeling for the system

• Methodology: Markov chain

• Deduce the collision and transmission rate

• Simulation

– Using NS2 and try to get the performance

• Implement the CW resetting module for the nodes

• Investigate the throughput and channel access probability for

the MoIP and normal nodes

• Using NOAH routing protocol to avoid relay

7

Markov Chain Model

• 802.11 back-off mechanism

• Let m be the maximum back-off stage

– CWmax=2m * CWmin

• Define two random variables

– b(t) : back-off stage of stations at instants t

• range from 0 ~ m

– s(t) : time slot of stations at instants t

• Assumption: period is the maximum back-off stage plus 1

• range from 1 to m+1

8

Mathematical modeling

0,1 1,1 2,1 … m-

1,1

m,1

0,2 1,2 2,2 … m-

1,2

m,2

0,3 1,3 2,3 … m-

1,3

m,3

…

0,m 1,m 2,m … m-

1,m

m,m

0,m

+1

1,m

+1

2,m

+1… m-

1,m+1

m,m+

1

1

1-p

1-p

1-p

p

MoIP node normal node

0,1 1,1 2,1 … m-

1,1

m,1

0,2 1,2 2,2 … m-

1,2

m,2

0,3 1,3 2,3 … m-

1,3

m,3

…

0,m 1,m 2,m … m-

1,m

m,

m

0,m

+1

1,m

+1

2,m

+1… m-

1,m+1

m,m+

1

1-p

1-p

1-p

p

9

Solve Markov Chain

To solve the steady state probability of this Markov Chain,we adopt the method from [2].

Consider an irreducible Markov Chain with one setof ergodic states and with transition matrix −→p . Letβj , j = 0, 1, · be a set of nonnegative numbers. If thevalue of βj satisfy

πj =∞∑

k=0

πkpkj , j = 0, 1, . . . , (1)

and∞∑

j=0

πj = 1. (2)

then βj , j = 0, 1, . . . , are the stationary probabilitiesof Markov chain.

10

Solve Markov Chain (cont.)

� We first solve the Markov chain of MoIP node� By the observation from the Markov chain, we can

make a guess as follows:

πi,j =(1− p)pi

m+ 1, 0 ≤ i ≤ j − 2, 2 ≤ j ≤ m+ 1

πi,i+1 =pi

m+ 1

� By checking the conditions (1) and (2), we can makesure that our guesses are true

11

Transmission & collision probabilities

0,m+1 1,m+1 2,m+1 … m-1,m+1 m,m+1

0,m 1,m 2,m … m-1,m

0,3 1,3 2,3

0,2 1,2

0,1

… … …

1-p

1-p

1-p

1-p

1-p 1-p 1-p

p

pp

pp p

↓↓↓↓mm-1…0

sgo

1

sg1

2

sg2 sgm-1 sgm

12

Transmission & collision probabilities

� The stationary probability of sgi , P (sgi), is the sumof ith column.

P (sg0) =m(1− pg)

m+ 1+

1

m+ 1

P (sg1) =(m− 1)(1− pg)pg

m+ 1+

pg

m+ 1

P (sg2) =(m− 2)(1− pg)p

2g

m+ 1+

p2g

m+ 1...

P (sgm−1) =

(1− pg)pm−1g

m+ 1+pm−1

m+ 1

P (sgm) =pmg

m+ 1

13

Transmission & collision probabilities

� The distribution of Bg conditioning on back-off stagei and time slot t

Pr{Bg = b |s = i} =1

2iCWmin

, for b = 0, 1, 2, · · · , 2iCWmin − 1.

� The average back-off counter in back-off stage i andtime slot t is

E[Bg|s = i] =2iCWmin − 1

2,

14

Transmission & collision probabilities

� The average back-off counter is computed as

E[Bg] =

m∑

i=0

E[Bg |s = sgi ] · P (sgi)

=

m−1∑

i=0

2iCWmin − 1

2· [(m − i)(1 − pg)p

ig

m + 1+

pig

m + 1] +

pmg

m + 1

2mCW − 1

2

=1

2(m + 1)

m−1∑

i=0

[(2iCW − 1)(m − i)(1 − pg) + 1]pig +(2pg)

mCW − pmg2(m + 1)

=1

2(m + 1)

m−1∑

i=0

[CW ·m(1 − pg)(2pg)i − CW (1 − pg)i · (2pg)

i −m(1 − pg)pig + (1 − pg)i · p

ig ]

+(2pg)

mCW − pmg2(m + 1)

=1 − pg2(m + 1)

{CW ·m1 − (2pg)

m

1 − 2pg− CW [

2pg [1 − (2pg)m−1]

(1 − 2pg)2+(m − 1)(2pg)

m

1 − 2pg] −m

1 − pmg1 − pg

+ [pg(1 − p

m−1g )

(1 − pg)2−(m − 1)pmg1 − pg

]} +(2pg)

mCW − pmg2(m + 1)

.

15

Transmission & collision probabilities

� τg, τn[3,4]

τg =1

E[Bg] + 1

τn =2(1− 2pn)

(1− 2pn)(CW + 1) + pnCW (1− (2pn)m),

� pg, pn

pg = 1− (1− τg)ng−1 × (1− τn)

nn−1,

pn = 1− (1− τn)nn−1 × (1− τg)

ng−1,

� Solve these four equations by numericalmethod.

16

Computation of throughput

• Transmission cycle

thg =Pg

TI + TC + TS

thn =Pn

TI + TC + TS

17

Computation of Pg and Pn

� Pg = sug ×L, Pn = sun ×L, where

sug = Pr{the transmitting node is a greedy node|number of transmitting node = 1}

=ng · τg(1− τg)ng−1(1− τn)nn

ng · τg(1− τg)ng−1(1− τn)nn + nn · τn(1− τn)nn−1(1− τg)ng

sun = Pr{the transmitting node is a normal node|number of transmitting node = 1}

=nn · τn(1− τn)

nn−1(1− τg)ng

ng · τg(1− τg)ng−1(1− τn)nn + nn · τn(1− τn)nn−1(1− τg)ng

� sug + sun = 1

18

Computation of Ts

DIFS

DATA

ACK

SIFS

� Consider the basic mode (without RTS/CTS)

TS = TDIFS+TPHY+TMAC+TDATA+TSIFS+π+TPHY+TACK+π

19

Computation of Tc

SIFS

DIFS

DATA

ACK

� Collision occurs if ACK is not received

TCsingle = TDIFS + TPHY + TMAC + TDATA + π.

� So the average collision time during a transmissioncycle can be expressed as

TC = E[NC ] · TCsingle

20

Computation of Tc

� Pc, collision probability

Pc = Pr{number of transmitting nodes ≥ 2|number of transmitting nodes ≥ 1}

=1− Pr{number of transmitting nodes = 0} − Pr{number of transmitting nodes = 1}

Pr{number of transmitting nodes ≥ 1}

=1− (1− τg)

ng (1− τn)nn − [ng · τg(1− τg)

ng−1(1− τn)nn + nn · τn(1− τn)

nn−1(1− τg)ng ]

1− (1− τg)ng (1− τn)nn

� We also know that

Pr{NC = i} = P ic · (1− Pc)

� So

E[NC ] =∞∑

i=0

i · Pr{NC = i}

=Pc

1− Pc

21

Computation of TI

� From the transmission cycle diagram, we know that

TI = (E[NC ] + 1) · σE[NS ]

� The distribution of NS is

Pr{NS = i} = [(1−τg)ng (1−τn)

nn ]i[1−(1−τg)ng(1−τn)

nn ]

� Therefore,

E[NS ] =∞∑

i=0

iPr{NS = i}

=(1− τg)

ng (1− τn)nn

1− (1− τg)ng (1− τn)nn

22

Channel access probability

Pksg =Pr{number of tx for greedy node i in a period = k}

=m−k∑

i=0

m−k−i∑

j=0

m!

k! · i! · j! · (m−k− i− j)!Pksg · (P

−1sg)i · (sun(1−Pc))

j ·Pm−k−i−jc

m∑

k=1

Pksg =Pr{number of tx for greedy node i in a period≥ 1}

= 1−P0sg

= 1−m∑

i=0

m−i∑

j=0

m!

i! · j! · (m− i− j)!(P−1sg )

i · (sun(1−Pc))j · Pm−i−jc

23

Parameters adopted both in simulation &

analysis

Table 1: values of parameterPHY header(including preamble): TPHY 192µ secMAC header: TMAC 224µ secchannel bit rate 1Mbpspropagation delay: π 1µ seclength of a time slot: σ 20µ secduration of SIFS: TSIFS 10µ secduration of DIFS: TDIFS 50µ secduration of ACK: TACK 304 µ secpayload 1000bytesCWmin 31CWmax 1023

24

Results - Modeling

• transmission probability of MoIP and normal node

25

Results - Modeling

• Collision probability of MoIP and normal node

26

Simulation environment

• NS-2

– 100 x 100 grid space

– CBR traffic with small interval for saturation

condition

27

Results – throughput

• Throughput for MoIP and normal nodes

– Node number of both MoIP and normal nodes are the same

28

Results – throughput

• Throughput for MoIP and normal nodes

– Node number of both MoIP and normal nodes are not the

same

Number of node(normal) = 2 Number of node(MoIP) = 2

29

Result - channel access probability

• Prob(number of tx in one period >= 1)

– Node number of both MoIP and normal nodes are the same

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 10 15 20

number of node

probability analytical-greedy

analytical-normal

simulation-greedy

simulation-normal

30

Result - channel access probability

• Prob(number of tx in one period >= 1)

– Node number of both MoIP and normal nodes are not the

same (number of MoIP node = 2)

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 10 15 20

number of node

probability analytical-greedy

analytical-normal

simulation-greedy

simulation-normal

31

Effect of CWmin - throughput

0

50

100

150

200

250

2 3 4 5 10 15 20

number of node

thro

ughput

(Kbps)

greedy(CW=16)

normal(CW=16)

greedy(CW=32)

normal(CW=32)

greedy(CW=8)

normal(CW=8)

32

Effect of CWmin - throughput

• The gap between MoIP node and normal node with

different initial contention window size (CWmin)

0

50

100

150

8 16 32 64 128

initial contention window size

(CWmin)

thro

ughput (K

bps)

greedy(node = 5)

normal(node = 5)

greedy(node = 10)

normal(node = 10)

33

Effect of CWmin – channel access probability

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 10 15

number of node

probability

simulation-greedy(16)

simulation-normal(16)

analytical-greedy(16)

analytical-normao(16)

simulation-greedy(32)

simulation-normal(32)

analytical-greedy(32)

analytical-normal(32)

34

Possible Future Work

• Simulation enhancement

– Asynchronous transmission

– VBR traffic

• Such as video(H.264) or voice transmission

• Fairness issue

CW=CWmin

backoff

High QoS High QoS

backoff backoffTr Tn

CW=CWmin CW=CWmin

T

High QoS

35

Possible Future Work

• Integrate with “Adaptive Video Frame Prioritization”

otherdata

APP-layer

MAC-layer

PHY-layer

36

Conclusion

• This method coheres with our expectation that MoIP node

has higher probability to access the channel than normal

node and higher throughput

• We propose a analytical model to approximately model

this mechanism

• The analytical results and simulation results can roughly

match

37

References

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Theory : the mathematics of computer performance modeling. Springer-

Verlag, 1995, pp. 348- 349

• [3] Yu-Liang Kuo, Chi-Hung Lu, Eric Hsiao-Kuang Wu, and Gen-Huey

Chen, “Performance Analysis of enhanced distributed coordination

function in IEEE 802.11e,” Proceedings of the IEEE Vehicular

Technology Conference Fall (VTC) Fall, vol. 3, Orlando U.S., pp.1412-

1416, October 2003

• [4] Y.-L. Kuo, C.-H. Lu, Eric H.-K. Wu, and G.-H. Chen, “An admission

control strategy for differentiated services in IEEE 802.11” Proceedings

of the IEEE Global Communications Conference (GLOBECOM), vol. 2,

San Francisco, December 2003, pp. 707-712

• [5] S. Mangold, C. Sunghyun, G. R. Hiertz, O. Klein, and B. Walke, “Analysis

of IEE 802.11e for QoS support in wireless LANs,” IEEE Wireless

Communications, vol. 10, pp. 40-50, 2003.

38

Thanks