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This workshop discusses the analysis of frame delay distribution in 802.11 using signal flow graphs. It covers scenarios, DCF in IEEE 802.11, analytical modeling, VoIP capacity calculation, and more.
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19th FFV Workshop Frame Delay Distribution Analysis of 802.11 Using Signal Flow Graphs Ralf Jennen Communication Networks Research Group RWTH Aachen University, Faculty 6, Germany FFV Workshop, 11.03.2011
Outline • 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
WLAN Scenarios • 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 Tagged Station MC8 = BPSK 1/2 Tagged AP … MC1 = 64-QAM 3/4 … α r1 … AP r8 STA 02 Terminal Buffer STA 01 STA N AP = Access PointMC = Modulation and Coding STA = Station
Readyto Send/Clear to Send (RTS/CTS) SIFS SIFS SIFS CTSTimeout DIFS DIFS DIFS Source/Tagged RTS Backoff RTS Data Destination/AP CTS ACK Other Station RTS Backoff Duration of a collision Successful transmission TSUCC TCOLL ACK = AcknowledgmentCTS = Clear to SendDCF = Distributed Coordination FunctionDIFS = DCF Interframce SpaceEIFS = Extended Interframe SpaceNAV = Network Allocation VectorRTS = Ready to SendSIFS = Short Interframe Space SLOT SIFS DIFS TimeoutA Station A/Tagged RTS NAV (RTS) EIFS Station B/Tagged Station C RTS Station D CTS RTS Duration of other stations‘ collisions TCOLL2 TCOLL1
Development of the Analytical Model SaturatedModel RTS/CTSBasic access Signal Flow Graph p τ Frame delay distribution for STAs WLANScenario Non-saturatedModel Link Adaptation Signal Flow Graph Frame delay distribution for STAs pi, τi, λ Queues WLANScenario pi, τi EmptyProbability WLANScenario VoIP traffic Up- andDownlink Morkov Modulated Poisson Process Signal Flow Graph Frame delay distribution for STAs and AP VoIP delay Queuing delay and service time Frame delaydistribution VoIP QoSRequirements VoIP capacity MMAP/G/1Queuing Model 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 p= Collision probabilityQoS = Quality of ServiceSTA = Stationτ = Probability that station transmits in a given slot VoIP = Voice over IP
Saturated Conditions: Collision Probability Columns: Backoff Counter Signal Flow Graph for Backoff Stage 1/(W0+1) 1/(W0+1) 1/(W0+1) 0,0 0,1 0,W0 Related Work by: Bianchi, Duffy, Malone, Leith, Huang … 1-p p … 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … 1-p p Rows: Backoff Stages … … 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … 1-p p B(i,j) = Backoff state (stage/counter) k = Maximum of retransmissionsm = Window is doubled m-timesWi= Contention window at stage ip= Collision probability … … 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm …
Signal Flow Graph of one Backoff Stage 0 Backoff Slots pi Bi-1 Bi Idle Slot pidle IW1 pidle 1 Backoff Slot I11 Collision pcoll pcoll LW1 LW2 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 pi L11 C11 E1 psucc psucc Success S11 2 Backoff Slots pidle pidle I21 I22 pcoll pcoll pi L21 C21 L22 C22 E2 psucc psucc S21 S22 W Backoff Slots … … … pidle IWW pi pcoll Signal Flow Graph can be written as a Delay Generation Function: … EW CW1 LWW CWW psucc SW1 SWW
Signal Flow Graph of one Backoff Stage 0 Backoff Slots pi Bi-1 Bi Idle Slot pidle IW1 pidle 1 Backoff Slot I11 Collision pcoll pcoll LW1 LW2 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 pi L11 C11 E1 psucc psucc Success S11 2 Backoff Slots pidle pidle I21 I22 pcoll pcoll pi L21 C21 L22 C22 E2 psucc psucc S21 S22 W Backoff Slots I … … … pidle IWW C1 For each modulation and coding scheme i an own C and S state with corresponding delays , must be added pi pcoll … C2 EW CW1 LWW CWW LW EW psucc S1 SW1 SWW S2
Signal Flow Graph oftheUplink Frame Delay forSaturated Traffic T B0 Bk Bm E … … … Bk-1 Bi-1 Consider previous transmission F 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
From Saturated to Non-saturated Conditions: Collision Probability Columns: Backoff Counter 1/(W0+1) 1/(W0+1) 1/(W0+1) 0,0 0,1 0,W0 Related Work by: Bianchi, Duffy, Malone, Leith, Huang … 1-p p … 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … 1-p p Rows: Backoff Stages … … 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … 1-p p B(i,j) = Backoff state (stage/counter) k = Maximum of retransmissionsm = Window is doubled m-timesWi= Contention window at stage ip= Collision probability … … 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm …
Non-Saturated Conditions:Collision, Idle and Empty Probability 1/(W0+1) 1/(W0+1) 1/(W0+1) Backoff withoutframe (1-q0e)r1pidle(1-p)+(1-r2)(1-pidle) 0,0e 0,1e 0,W0e 1-r3 1-r3 (1-r1)pidle … r3 r3 r2(1-pidle) + q0er1pidle(1-p) … 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) (1-p)(1-q0) 0,0 0,1 0,W0 Related Work by: Bianchi, Duffy, Malone, Leith, Huang … (1-p)q0 r1ppidle p … (1-p)(1-q1) 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … (1-p)q1 Stage dependentempty probability p … … (1-p)(1-qm) 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … (1-p)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 p … … 1-qm 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm qm …
Non-Saturated Conditions:Previous Transmission Successful 1/(W0+1) 1/(W0+1) 1/(W0+1) (1-q0e)r1pidle(1-p)+(1-r2)(1-pidle) 0,0e 0,1e 0,W0e 1-r 1-r (1-r1)pidle … r r r2(1-pidle) + q0er1pidle(1-p) … Special statewithout collisions 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) (1-p)(1-q0) 0,0f q0f 0,0 0,1 0,W0 1-q0f Related Work by: Bianchi, Duffy, Malone, Leith, Huang … (1-p)q0 r1ppidle p … (1-p)(1-q1) 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … (1-p)q1 p … … (1-p)(1-qm) 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … (1-p)qm 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 p … … 1-qm 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm (1-p)qm … pqm
Signal Flow Graph of the Frame Delay forNon-saturated Downlink Traffic T B0 B1 E T B0 F Bk E Bm … … … Bk-1 Bi-1 F 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
Signal Flow Graph of the Frame Delay forNon-saturated Downlink Traffic MMAP(i)/G(i)/1 with i different classes W T B0 B1 E … F Related Work by: He, Takine, Göbbels S SA SB SC 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 m = Backoff window is doubled m-timesMMAP = Marked Markov arrival processp= Collision probabilitype = System empty probabilityS = Serving stateT = Transmit stateW = Waiting state
Three Possible Arrivals:1. During Countdown 1/(W0+1) 1/(W0+1) 1/(W0+1) Duringcountdown (1-q0e)r1pidle(1-p)+(1-r2)(1-pidle) 0,0e 0,1e 0,W0e 1-r3 1-r3 (1-r1)pidle … r3 r3 r2(1-pidle) + q0er1pidle(1-p) … 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) (1-p)(1-q0) Continue withbackoff stage 0 0,0 0,1 0,W0 … (1-p)q0 r1ppidle p … (1-p)(1-q1) 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … (1-p)q1 p … … (1-p)(1-qm) 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … (1-p)qm 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 p … … 1-qm 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm qm …
Signal Flow Graph of the Frame Delay forNon-saturated Downlink Traffic W T B0 B1 E … F S SA Coefficients of GA arefunctions of G0 SB SC 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 m = Backoff window is doubled m-timesMMAP = Marked Markov arrival processp= Collision probabilitype = System empty probabilityS = Serving stateT = Transmit stateW = Waiting state
Three Possible Arrivals:2. Medium Idle in B(0,0)e 1/(W0+1) 1/(W0+1) 1/(W0+1) In B(0,0)e andmedium idle (1-q0e)r1pidle(1-p)+(1-r2)(1-pidle) 0,0e 0,1e 0,W0e 1-r3 1-r3 (1-r1)pidle … r3 r3 r2(1-pidle) + q0er1pidle(1-p) … 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) (1-p)(1-q0) Continue with orwithout frame 0,0 0,1 0,W0 … (1-p)q0 r1ppidle p … (1-p)(1-q1) 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … (1-p)q1 p … … (1-p)(1-qm) 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … (1-p)qm 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 p … … 1-qm 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm qm …
Signal Flow Graph of the Frame Delay forNon-saturated Downlink Traffic W T B0 B1 E … F S SA No additional delay SB SC 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 m = Backoff window is doubled m-timesMMAP = Marked Markov arrival processp= Collision probabilitype = System empty probabilityS = Serving stateT = Transmit stateW = Waiting state
Three Possible Arrivals:3. Medium Busy in B(0,0)e 1/(W0+1) 1/(W0+1) 1/(W0+1) In B(0,0)e andmedium busy (1-q0e)r1pidle(1-p)+(1-r2)(1-pidle) 0,0e 0,1e 0,W0e 1-r3 1-r3 (1-r1)pidle … r3 r3 r2(1-pidle) + q0er1pidle(1-p) … 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) 1/(W0+1) (1-p)(1-q0) Continue withbackoff stage 0 0,0 0,1 0,W0 … (1-p)q0 r1ppidle p … (1-p)(1-q1) 1/(W1+1) 1/(W1+1) 1/(W1+1) 1,0 1,1 1,W1 … (1-p)q1 p … … (1-p)(1-qm) 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) m,0 m,1 m,Wm … (1-p)qm 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 p … … 1-qm 1/(Wm+1) 1/(Wm+1) 1/(Wm+1) k,0 k,1 k,Wm qm …
Signal Flow Graph of the Frame Delay forNon-saturated Downlink Traffic W T B0 B1 E … F S SA SB Coefficients of GC dependon GSUCC and GCOLL SC 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 m = Backoff window is doubled m-timesMMAP = Marked Markov arrival processp= Collision probabilitype = System empty probabilityS = Serving stateT = Transmit stateW = Waiting state
VoIP Capacity Example • Satisfied User Criteria • Meanopinion score • Satisfiediflessthen 2% ofthepackets do not arrivearrivesuccessfullyattheradioreceiverwithin 50ms = 5555 SLOT • QoSRequirements • 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 • Next steps: • Frame delay + waiting time • Find N that fulfils the satisfied user criteria
Conclusion & Outlook Conclusion • 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 Jennen jen@comnets.rwth-aachen.de 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