frame delay distribution analysis of 802.11 using signal flow graphs

Ralf Jennen, ComNets, RWTH Aachen University

Frame Delay Distribution Frame Delay Distribution Analysis of 802.11 Using Signal Analysis of 802.11 Using Signal

Flow Graphs Flow Graphs Ralf Jennen

Communication Networks Research Group RWTH Aachen University, Faculty 6, Germany

FFV Workshop, 11.03.2011

1919thth FFV Workshop FFV Workshop

2Ralf Jennen, ComNets, RWTH Aachen University

OutlineOutline

• Scenarios• Distributed Coordination Function (DCF)

in IEEE 802.11• Modelling of IEEE 802.11a DCF

– Development of an analytical model– From a saturated to a non-saturated model

• VoIP capacity calculation• Conclusion & Outlook


MC1 = 64-QAM 3/4

TerminalBuffer

STA 01

AP

MC8 = BPSK 1/2…

STA N

STA 02…

α

• Best Case Scenario– All STAs with MC1

• Worst Case Scenario– All STAs with MC8

• Mixed Scenarios– Tagged MC1 / other STAs

MC8

– Tagged MC8/other STAs MC1

WLAN ScenariosWLAN Scenarios

AP = Access PointMC = Modulation and Coding STA = Station

Tagged StationTagged AP


Duration of a collision

Duration of other stations‘ collisions

Successful transmission

Ready to Send/Clear to Send (RTS/CTS)Ready to Send/Clear to Send (RTS/CTS)

Source/TaggedDestination/APOther Station

RTS

DIFSSIFS

CTSRTS Backoff

RTS

SIFS

Data

TCOLL

CTSTimeoutDIFS

Backoff

SIFS

ACK

TSUCC

DIFS

NAV (RTS)Station A/TaggedStation B/TaggedStation C

SLOT

Station D

TCOLL1

SIFS

CTS

DIFS

TCOLL2

TimeoutA

EIFS

RTSRTS

RTS

ACK = AcknowledgmentCTS = Clear to SendDCF = Distributed Coordination FunctionDIFS = DCF Interframce SpaceEIFS = Extended Interframe SpaceNAV = Network Allocation VectorRTS = Ready to SendSIFS = Short Interframe Space


Development of the Analytical ModelDevelopment of the Analytical Model

Frame delaydistributionVoIP QoS

Requirements

MMAP/G/1Queuing Model

VoIP delayQueuing delay and

service time

VoIP capacity

AP = Access pointG = General service time distribution i = per MCS and/or per STA or AP λ = Arrival rateMCS = Modulation and coding schemeMMAP = Marked Markov arrival process

SaturatedModel

RTS/CTSBasic access

p

τ

Signal Flow

GraphWLAN

ScenarioFrame delay

distribution for STAs

Non-saturatedModel

Link Adaptation

pi, τi, λ

QueuesWLAN

ScenarioSignal Flow

Graph

Frame delay distribution for

STAs

Up- andDownlink

Morkov Modulated Poisson Process

pi, τi

EmptyProbability

WLANScenario

VoIP traffic

Signal Flow

Graph

Frame delay distribution for STAs and AP

p = Collision probabilityQoS = Quality of ServiceSTA = Stationτ = Probability that station transmits in a given slot VoIP = Voice over IP


Saturated Conditions: Collision ProbabilitySaturated Conditions: Collision Probability

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

m,0 m,1 m,Wm…

……

…

…

…

p

p

p

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

B(i,j) = Backoff state (stage/counter) k = Maximum of retransmissionsm = Window is doubled m-timesWi = Contention window at stage ip = Collision probability

1/(W0+1) 1/(W0+1)

Related Work by:Bianchi, Duffy, Malone, Leith, Huang

1/(W0+1)

1-p

1-p

1-p

Columns: Backoff CounterRo

ws: B

acko

ff St

ages

Signal Flow Graph for Backoff Stage


Signal Flow Graph of one Backoff StageSignal Flow Graph of one Backoff Stage

Bi-1 Bipi 10 z

L11

I11

E1C11

S11

pidle

pcoll

psucc

piclzlz

z

piL21

I21

L22C21

S21

pidle

pcoll

psucc

clzlz

z I22

E2C22

S22

pidle

pcoll

psucc

clzlz

z

…

…

piLW1

IW1

LW2

pidle

pcoll

psucc

clzlz

z

EW

pidle

pcoll

psucc

clzlz

z

LWWCW1

SW1

IWW

CWW

SWW

… …Bi = Backoff state for stage iL = Listening I =Idle slotC = CollisionS = Successful transmisssion pi = Backoff counter probabilityW = Contention Windowz = Delay operatorlc = Duration of a collisionl = Duration of a transmissionGi(z) = Delay Generation Function

1 Backoff Slot

2 Backoff Slots

Collision

Success

Idle Slot

0 Backoff Slots

W Backoff Slots

Signal Flow Graph can be writtenas a Delay Generation Function:

)(zGi


Signal Flow Graph of one Backoff StageSignal Flow Graph of one Backoff Stage

Bi-1 Bipi 10 z

L11

I11

E1C11

S11

pidle

pcoll

psucc

piclzlz

z

piL21

I21

L22C21

S21

pidle

pcoll

psucc

clzlz

z I22

E2C22

S22

pidle

pcoll

psucc

clzlz

z

…

…

piLW1

IW1

LW2

pidle

pcoll

psucc

clzlz

z

EW

pidle

pcoll

psucc

clzlz

z

LWWCW1

SW1

IWW

CWW

SWW

… …Bi = Backoff state for stage iL = Listening I =Idle slotC = CollisionS = Successful transmisssion pi = Backoff counter probabilityW = Contention Windowz = Delay operatorlc = Duration of a collisionl = Duration of a transmissionGi(z) = Delay Generation Function

1 Backoff Slot

2 Backoff Slots

Collision

Success

Idle Slot

0 Backoff Slots

W Backoff Slots

For each modulation and coding scheme i an own C and S state with corresponding delays , must be added

ilz cilz

C1

I

C2

S1

S2

EWLW


Signal Flow Graph of the Uplink Frame Delay Signal Flow Graph of the Uplink Frame Delay for Saturated Trafficfor Saturated Traffic

T B0

)(0 zG

Bi = Backoff state for stage iE = Error stateF = Final stateGi(z) = Delay Generation Function for stage ik = Maximum of retransmissionsm = Backoff window is doubled m-timesp = Collision probabilityT = Transmit statez = Delay operator

…

F

COLLi GzpG )(1COLLGzpG )(1

SUCCGp)( 1

Bi-1 Bm… …

COLLi GzpG )(COLLm GzpG )(

COLLm GzpG )(Bk

COLLm GzpG )(COLLm GzpG )(

Ep

Bk-1

Consider previous transmission

Bi-1 Bipi 10 z

L11

I 11

E1C11

S11

pidle

pcoll

psucc

pi clzlz

z

piL21

I 21

L22C21

S21

pidle

pcoll

psucc

clzlz

z I 22

E2C22

S22

pidle

pcoll

psucc

clzlz

z

…

…

piLW1

IW1

LW2

pidle

pcoll

psucc

clzlz

z

EW

pidle

pcoll

psucc

clzlz

z

LWWCW1

SW1

IWW

CWW

SWW… …

)(zGi


From Saturated to Non-saturated Conditions: From Saturated to Non-saturated Conditions: Collision ProbabilityCollision Probability

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

m,0 m,1 m,Wm…

……

…

…

…

p

p

p

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

B(i,j) = Backoff state (stage/counter) k = Maximum of retransmissionsm = Window is doubled m-timesWi = Contention window at stage ip = Collision probability

1/(W0+1) 1/(W0+1)


1/(W0+1)

1-p

1-p

1-p

Columns: Backoff CounterRo

ws: B

acko

ff St

ages


Non-Saturated Conditions:Non-Saturated Conditions:Collision, Idle and Empty ProbabilityCollision, Idle and Empty Probability

0,0e 0,1e 0,W0e

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

…

m,0 m,1 m,Wm…

……

…

…

…

1-r3 1-r3

r3 r3

1-qm

(1-p)qm

p

p

p

(1-p)(1-qm)

(1-p)q1

(1-p)(1-q1)

(1-p)q0

(1-p)(1-q0)

…

(1-r1)pidle

(1-q0e)r1pidle(1-p)+(1-r2)(1-pidle)

r2(1-pidle) + q0er1pidle(1-p)

r1ppidle

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

1/(W0+1) 1/(W0+1)


qm

B(i,j) = Backoff state k = Maximum of retransmissionsm = Window is doubled m-timesWi = Contention Window at stage ipidle = Idle Probability 1-qi = Queue empty probabilityri = Arrival probabilities

Backoff withoutframe

Stage dependentempty probability


Non-Saturated Conditions:Non-Saturated Conditions:Previous Transmission Successful Previous Transmission Successful

0,0e 0,1e 0,W0e

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

…

m,0 m,1 m,Wm…

……

…

…

…

1-r 1-r

r r

1-qm

(1-p)qm

p

p

p

(1-p)(1-qm)

(1-p)q1

(1-p)(1-q1)

(1-p)q0

(1-p)(1-q0)

…

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

0,0f

1/(W0+1) 1/(W0+1) 1/(W0+1)q0f

1-q0f

(1-p)qmpqm

B(i,j) = Backoff state k = Maximum of retransmissionsm = Window is doubled m-timesWi = Contention window at stage ipidle = Idle probability 1-qi = Buffer empty probability r = Arrival probability


Special statewithout collisions

(1-r1)pidle



r1ppidle


Signal Flow Graph of the Frame Delay forSignal Flow Graph of the Frame Delay forNon-saturated Downlink TrafficNon-saturated Downlink Traffic

Bi = Backoff state for stage iE = Error stateF = Final stateGi(z) = Delay Generation Function for stage ik = Maximum of retransmissionsm = Backoff window is doubled m-timesp = Collision probabilityT = Transmit statez = Delay operator

T B0

)(0 zG…

F

COLLi GzpG )(1COLLGzpG )(1

SUCCGp)( 1

Bi-1 Bm… …

COLLi GzpG )(COLLm GzpG )(

COLLm GzpG )(Bk

COLLm GzpG )(COLLm GzpG )(

Ep

Bk-1T B0 B1 E

F



Bi = Backoff state for stage iE = Error stateF = Final stateG(i) = General service time distributionGi(z) = Delay generation function for stage iGQ(z) = Delay generation function for queuingi = Number of modulation and coding schemes k = Maximum of retransmissions

TW

S

)(zGQep1

ep

MMAP(i)/G(i)/1 with i different classes

B1

F

B0

)(zG0 )()( zGzpG coll1

)()( zGp SUCC1

… E

SA

SB

SC

Ap

Bp

Cp

m = Backoff window is doubled m-timesMMAP = Marked Markov arrival processp = Collision probabilitype = System empty probabilityS = Serving stateT = Transmit stateW = Waiting state

Related Work by:He, Takine, Göbbels


Duringcountdown

Three Possible Arrivals:Three Possible Arrivals:1. During Countdown1. During Countdown

0,0e 0,1e 0,W0e

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

…

m,0 m,1 m,Wm…

……

…

…

…

1-r3 1-r3

r3 r3

1-qm

(1-p)qm

p

p

p

(1-p)(1-qm)

(1-p)q1

(1-p)(1-q1)

(1-p)q0

(1-p)(1-q0)

…

(1-r1)pidle



r1ppidle

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

1/(W0+1) 1/(W0+1)

qm


Continue withbackoff stage 0




W

S

)(zGQep1

ep

T B1

F

B0


)()( zGp SUCC1

… E

SA

SB

SC

)(~))(( zGpzG SUCCA 1

)(~)( zGpzG COLLA

Ap

Bp

Cp


Coefficients of GA arefunctions of G0


In B(0,0)e andmedium idle

Three Possible Arrivals:Three Possible Arrivals:2. Medium Idle in B(0,0)2. Medium Idle in B(0,0)ee

0,0e 0,1e 0,W0e

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

…

m,0 m,1 m,Wm…

……

…

…

…

1-r3 1-r3

r3 r3

1-qm

(1-p)qm

p

p

p

(1-p)(1-qm)

(1-p)q1

(1-p)(1-q1)

(1-p)q0

(1-p)(1-q0)

…

(1-r1)pidle



r1ppidle

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

1/(W0+1) 1/(W0+1)

qm


Continue with orwithout frame




W

S

)(zGQep1

ep

T B1

F

B0


)()( zGp SUCC1

… E

SA

SB

SC


)(~)( zGp SUCC1

)(~)( zGpzG COLLA

)(~ zGp COLL

Ap

Bp

Cp


No additional delay


In B(0,0)e andmedium busy

Three Possible Arrivals:Three Possible Arrivals:3. Medium Busy in B(0,0)3. Medium Busy in B(0,0)ee

0,0e 0,1e 0,W0e

0,0 0,1 0,W0

1,0 1,1 1,W1

k,0 k,1 …

…

…

…

m,0 m,1 m,Wm…

……

…

…

…

1-r3 1-r3

r3 r3

1-qm

(1-p)qm

p

p

p

(1-p)(1-qm)

(1-p)q1

(1-p)(1-q1)

(1-p)q0

(1-p)(1-q0)

…

(1-r1)pidle



r1ppidle

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(W1+1) 1/(W1+1) 1/(W1+1)

1/(W0+1) 1/(W0+1) 1/(W0+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

1/(Wm+1) 1/(Wm+1) 1/(Wm+1)

k,Wm

1/(W0+1) 1/(W0+1)

qm


Continue withbackoff stage 0




W

S

)(zGQep1

ep

T B1

F

B0


)()( zGp SUCC1

… E

SA

SB

SC


)(~)( zGp SUCC1

)(~)( zGpzG COLLA

)(~ zGp COLL

Ap

Bp

Cp )())(( zGpzG SUCCC 1

)()( zpGzG COLLC


Coefficients of GC dependon GSUCC and GCOLL


45 50 55 600.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X: 53Y: 0.6736

Number of Stations

p

Access PointSTAs using MCS8Tagged STA using MCS1

VoIP Capacity ExampleVoIP Capacity Example

• Satisfied User Criteria– Mean opinion score– Satisfied if less then

2% of the packets do not arrive arrive successfully at the radio receiver within 50ms = 5555 SLOT

– • QoS Requirements

– Frame error rate– End to end delay– Jitter

• ITU G.711packet size=120 Byte packet rate=1/10 msactive=352 msinactive=650 ms

Related Work by:Tobagi, Hole,Chen, Garg, Kappes

610020 11 .).( )/( ksatisfiedp

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

5566

CWmin=31, m=5, k=7, N=52, N8=51, N1=1

delay [SLOT]

CD

F

Next steps:- Frame delay + waiting time- Find N that fulfils the satisfied user criteria


ConclusionConclusion & Outlook & OutlookConclusion• Development of the Analytical Model• Scenarios and DCF Overview• Signal Flow Graph Model of 802.11 DCF• Extension of the Signal Flow Graph

– Frame delay for non-saturated conditions– VoIP capacity calculation

Outlook• VoIP capacity for multiple scenarios• Interference model, additional packet loss• Validated results by event driven simulation


Thank you for your attention !

Ralf [email protected]

The research leading to these results has received funding from the European Union's Seventh Framework Programme ([FP7/2007-2013] ) under grant agreement number ICT-213311

frame delay distribution analysis of 802.11 using signal flow graphs

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