Ralf Jennen, ComNets, RWTH Aachen University Frame Delay Distribution Analysis of Using Signal Flow Graphs Ralf Jennen Communication Networks Research Group RWTH Aachen University, Faculty 6, Germany FFV Workshop, th FFV Workshop

2Ralf Jennen, ComNets, RWTH Aachen UniversityOutline Scenarios Distributed Coordination Function (DCF) in IEEE Modelling of IEEE a DCF –Development of an analytical model –From a saturated to a non-saturated model VoIP capacity calculation Conclusion & Outlook

3Ralf Jennen, ComNets, RWTH Aachen University Best Case Scenario –All STAs with MC 1 Worst Case Scenario –All STAs with MC 8 Mixed Scenarios –Tagged MC 1 / other STAs MC 8 –Tagged MC 8 /other STAs MC 1 WLAN Scenarios AP= Access Point MC= Modulation and Coding STA = Station Tagged Station r1r1 MC 1 = 64-QAM 3/4 Terminal Buffer STA 01 AP r8r8 MC 8 = BPSK 1/2 … … STA N STA 02 … α Tagged AP

4Ralf Jennen, ComNets, RWTH Aachen University Duration of a collision Duration of other stations‘ collisionsSuccessful transmission Ready to Send/Clear to Send (RTS/CTS) Ready to Send/Clear to Send (RTS/CTS) Source/Tagged Destination/AP Other Station RTS DIFS SIFS CTS RTSBackoff RTS SIFS Data T COLL CTSTimeout DIFS Backoff SIFS ACK T SUCC DIFS NAV (RTS) Station A/Tagged Station B/Tagged Station C SLOT Station D T COLL1 SIFS CTS DIFS T COLL2 Timeout A EIFS RTS ACK= Acknowledgment CTS= Clear to Send DCF= Distributed Coordination Function DIFS= DCF Interframce Space EIFS= Extended Interframe Space NAV= Network Allocation Vector RTS= Ready to Send SIFS= Short Interframe Space

5Ralf Jennen, ComNets, RWTH Aachen University Development of the Analytical Model Frame delay distribution VoIP QoS Requirements MMAP/G/1 Queuing Model VoIP delay Queuing delay and service time VoIP capacity AP= Access point G= General service time distribution i= per MCS and/or per STA or AP λ = Arrival rate MCS= Modulation and coding scheme MMAP= Marked Markov arrival process Saturated Model RTS/CTS Basic access pτpτ Signal Flow Graph WLAN Scenario Frame delay distribution for STAs Non-saturated Model Link Adaptation p i, τ i, λ Queues WLAN Scenario Signal Flow Graph Frame delay distribution for STAs Up- and Downlink Morkov Modulated Poisson Process p i, τ i Empty Probability WLAN Scenario VoIP traffic Signal Flow Graph Frame delay distribution for STAs and AP p= Collision probability QoS= Quality of Service STA= Station τ = Probability that station transmits in a given slot VoIP= Voice over IP

6Ralf Jennen, ComNets, RWTH Aachen University Saturated Conditions: Collision Probability 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … m,0m,1m,Wmm,Wm … … … … … … p p p 1/(W 1 +1) 1/(W m +1) k,Wmk,Wm B(i,j)= Backoff state (stage/counter) k= Maximum of retransmissions m= Window is doubled m-times W i = Contention window at stage i p= Collision probability 1/(W 0 +1) Related Work by: Bianchi, Duffy, Malone, Leith, Huang 1/(W 0 +1) 1-p Columns: Backoff Counter Rows: Backoff Stages Signal Flow Graph for Backoff Stage

7Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of one Backoff Stage B i-1 BiBi pipi L 11 I 11 E1E1 C 11 S 11 p idle p coll p succ pipi pipi L 21 I 21 L 22 C 21 S 21 p idle p coll p succ I 22 E2E2 C 22 S 22 p idle p coll p succ … … pipi L W1 I W1 L W2 p idle p coll p succ EWEW p idle p coll p succ L WW C W1 S W1 I WW C WW S WW …… B i = Backoff state for stage i L= Listening I=Idle slot C= Collision S= Successful transmisssion p i = Backoff counter probability W= Contention Window z= Delay operator l c = Duration of a collision l= Duration of a transmission G i (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 written as a Delay Generation Function:

8Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of one Backoff Stage B i-1 BiBi pipi L 11 I 11 E1E1 C 11 S 11 p idle p coll p succ pipi pipi L 21 I 21 L 22 C 21 S 21 p idle p coll p succ I 22 E2E2 C 22 S 22 p idle p coll p succ … … pipi L W1 I W1 L W2 p idle p coll p succ EWEW p idle p coll p succ L WW C W1 S W1 I WW C WW S WW …… B i = Backoff state for stage i L= Listening I=Idle slot C= Collision S= Successful transmisssion p i = Backoff counter probability W= Contention Window z= Delay operator l c = Duration of a collision l= Duration of a transmission G i (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 C1C1 I C2C2 S1S1 S2S2 EWEW LWLW

9Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of the Uplink Frame Delay for Saturated Traffic TB0B0 B i = Backoff state for stage i E= Error state F= Final state G i (z)= Delay Generation Function for stage i k= Maximum of retransmissions m= Backoff window is doubled m-times p= Collision probability T= Transmit state z= Delay operator … F B i-1 BmBm …… BkBk E B k-1 Consider previous transmission

10Ralf Jennen, ComNets, RWTH Aachen University From Saturated to Non-saturated Conditions: Collision Probability 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … m,0m,1m,Wmm,Wm … … … … … … p p p 1/(W 1 +1) 1/(W m +1) k,Wmk,Wm B(i,j)= Backoff state (stage/counter) k= Maximum of retransmissions m= Window is doubled m-times W i = Contention window at stage i p= Collision probability 1/(W 0 +1) Related Work by: Bianchi, Duffy, Malone, Leith, Huang 1/(W 0 +1) 1-p Columns: Backoff Counter Rows: Backoff Stages

11Ralf Jennen, ComNets, RWTH Aachen University Non-Saturated Conditions: Collision, Idle and Empty Probability 0,0e0,1e0,W 0 e 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … … m,0m,1m,Wmm,Wm … … … … … … 1-r 3 r3r3 r3r3 1-q m (1-p)q m p p p (1-p)(1-q m ) (1-p)q 1 (1-p)(1-q 1 ) (1-p)q 0 (1-p)(1-q 0 ) … (1-r 1 )p idle (1-q 0e )r 1 p idle (1-p)+(1-r 2 )(1-p idle ) r 2 (1-p idle ) + q 0e r 1 p idle (1-p) r 1 pp idle 1/(W 0 +1) 1/(W 1 +1) 1/(W 0 +1) 1/(W m +1) k,Wmk,Wm 1/(W 0 +1) Related Work by: Bianchi, Duffy, Malone, Leith, Huang qmqm B(i,j)= Backoff state k= Maximum of retransmissions m= Window is doubled m-times W i = Contention Window at stage i p idle = Idle Probability 1-q i = Queue empty probability r i = Arrival probabilities Backoff without frame Stage dependent empty probability

12Ralf Jennen, ComNets, RWTH Aachen University Non-Saturated Conditions: Previous Transmission Successful 0,0e0,1e0,W 0 e 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … … m,0m,1m,Wmm,Wm … … … … … … 1-r rr 1-q m (1-p)q m p p p (1-p)(1-q m ) (1-p)q 1 (1-p)(1-q 1 ) (1-p)q 0 (1-p)(1-q 0 ) … 1/(W 0 +1) 1/(W 1 +1) 1/(W 0 +1) 1/(W m +1) k,Wmk,Wm 0,0f 1/(W 0 +1) q 0f 1-q 0f (1-p)q m pq m B(i,j)= Backoff state k= Maximum of retransmissions m= Window is doubled m-times W i = Contention window at stage i p idle = Idle probability 1-q i = Buffer empty probability r= Arrival probability Related Work by: Bianchi, Duffy, Malone, Leith, Huang Special state without collisions (1-r 1 )p idle (1-q 0e )r 1 p idle (1-p)+(1-r 2 )(1-p idle ) r 2 (1-p idle ) + q 0e r 1 p idle (1-p) r 1 pp idle

13Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of the Frame Delay for Non-saturated Downlink Traffic B i = Backoff state for stage i E= Error state F= Final state G i (z)= Delay Generation Function for stage i k= Maximum of retransmissions m= Backoff window is doubled m-times p= Collision probability T= Transmit state z= Delay operator TB0B0 … F B i-1 BmBm …… BkBk E B k-1 TB0B0 B1B1 E F

14Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of the Frame Delay for Non-saturated Downlink Traffic B i = Backoff state for stage i E= Error state F= Final state G(i)= General service time distribution G i (z)= Delay generation function for stage i G Q (z)= Delay generation function for queuing i= Number of modulation and coding schemes k= Maximum of retransmissions T W S MMAP(i)/G(i)/1 with i different classes B1B1 F B0B0 … E SASA SBSB SCSC m= Backoff window is doubled m-times MMAP= Marked Markov arrival process p= Collision probability p e = System empty probability S= Serving state T= Transmit state W= Waiting state Related Work by: He, Takine, Göbbels

15Ralf Jennen, ComNets, RWTH Aachen University During countdown Three Possible Arrivals: 1. During Countdown 0,0e0,1e0,W 0 e 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … … m,0m,1m,Wmm,Wm … … … … … … 1-r 3 r3r3 r3r3 1-q m (1-p)q m p p p (1-p)(1-q m ) (1-p)q 1 (1-p)(1-q 1 ) (1-p)q 0 (1-p)(1-q 0 ) … (1-r 1 )p idle (1-q 0e )r 1 p idle (1-p)+(1-r 2 )(1-p idle ) r 2 (1-p idle ) + q 0e r 1 p idle (1-p) r 1 pp idle 1/(W 0 +1) 1/(W 1 +1) 1/(W 0 +1) 1/(W m +1) k,Wmk,Wm 1/(W 0 +1) qmqm B(i,j)= Backoff state k= Maximum of retransmissions m= Window is doubled m-times W i = Contention window at stage i p idle = Idle probability 1-q i = Buffer empty probability r= Arrival probability Continue with backoff stage 0

16Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of the Frame Delay for Non-saturated Downlink Traffic B i = Backoff state for stage i E= Error state F= Final state G(i)= General service time distribution G i (z)= Delay generation function for stage i G Q (z)= Delay generation function for queuing i= Number of modulation and coding schemes k= Maximum of retransmissions W S TB1B1 F B0B0 … E SASA SBSB SCSC m= Backoff window is doubled m-times MMAP= Marked Markov arrival process p= Collision probability p e = System empty probability S= Serving state T= Transmit state W= Waiting state Coefficients of G A are functions of G 0

17Ralf Jennen, ComNets, RWTH Aachen University In B(0,0) e and medium idle Three Possible Arrivals: 2. Medium Idle in B(0,0) e 0,0e0,1e0,W 0 e 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … … m,0m,1m,Wmm,Wm … … … … … … 1-r 3 r3r3 r3r3 1-q m (1-p)q m p p p (1-p)(1-q m ) (1-p)q 1 (1-p)(1-q 1 ) (1-p)q 0 (1-p)(1-q 0 ) … (1-r 1 )p idle (1-q 0e )r 1 p idle (1-p)+(1-r 2 )(1-p idle ) r 2 (1-p idle ) + q 0e r 1 p idle (1-p) r 1 pp idle 1/(W 0 +1) 1/(W 1 +1) 1/(W 0 +1) 1/(W m +1) k,Wmk,Wm 1/(W 0 +1) qmqm B(i,j)= Backoff state k= Maximum of retransmissions m= Window is doubled m-times W i = Contention window at stage i p idle = Idle probability 1-q i = Buffer empty probability r= Arrival probability Continue with or without frame

18Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of the Frame Delay for Non-saturated Downlink Traffic B i = Backoff state for stage i E= Error state F= Final state G(i)= General service time distribution G i (z)= Delay generation function for stage i G Q (z)= Delay generation function for queuing i= Number of modulation and coding schemes k= Maximum of retransmissions W S TB1B1 F B0B0 … E SASA SBSB SCSC m= Backoff window is doubled m-times MMAP= Marked Markov arrival process p= Collision probability p e = System empty probability S= Serving state T= Transmit state W= Waiting state No additional delay

19Ralf Jennen, ComNets, RWTH Aachen University In B(0,0) e and medium busy Three Possible Arrivals: 3. Medium Busy in B(0,0) e 0,0e0,1e0,W 0 e 0,00,10,W 0 1,01,11,W 1 k,0k,1 … … … … m,0m,1m,Wmm,Wm … … … … … … 1-r 3 r3r3 r3r3 1-q m (1-p)q m p p p (1-p)(1-q m ) (1-p)q 1 (1-p)(1-q 1 ) (1-p)q 0 (1-p)(1-q 0 ) … (1-r 1 )p idle (1-q 0e )r 1 p idle (1-p)+(1-r 2 )(1-p idle ) r 2 (1-p idle ) + q 0e r 1 p idle (1-p) r 1 pp idle 1/(W 0 +1) 1/(W 1 +1) 1/(W 0 +1) 1/(W m +1) k,Wmk,Wm 1/(W 0 +1) qmqm B(i,j)= Backoff state k= Maximum of retransmissions m= Window is doubled m-times W i = Contention window at stage i p idle = Idle probability 1-q i = Buffer empty probability r= Arrival probability Continue with backoff stage 0

20Ralf Jennen, ComNets, RWTH Aachen University Signal Flow Graph of the Frame Delay for Non-saturated Downlink Traffic B i = Backoff state for stage i E= Error state F= Final state G(i)= General service time distribution G i (z)= Delay generation function for stage i G Q (z)= Delay generation function for queuing i= Number of modulation and coding schemes k= Maximum of retransmissions W S TB1B1 F B0B0 … E SASA SBSB SCSC m= Backoff window is doubled m-times MMAP= Marked Markov arrival process p= Collision probability p e = System empty probability S= Serving state T= Transmit state W= Waiting state Coefficients of G C depend on G SUCC and G COLL

21Ralf Jennen, ComNets, RWTH Aachen University VoIP 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.711 packet size=120 Byte packet rate=1/10 ms active=352 ms inactive=650 ms Related Work by: Tobagi, Hole, Chen, Garg, Kappes Next steps: - Frame delay + waiting time - Find N that fulfils the satisfied user criteria

22Ralf Jennen, ComNets, RWTH Aachen University Conclusion & Outlook Conclusion Development of the Analytical Model Scenarios and DCF Overview Signal Flow Graph Model of 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

23Ralf Jennen, ComNets, RWTH Aachen University Thank you for your attention ! Ralf Jennen The research leading to these results has received funding from the European Union's Seventh Framework Programme ([FP7/ ] ) under grant agreement number ICT