Frame Delay Distribution Analysis of 802.11 Using Signal Flow Graphs
description
Transcript of Frame Delay Distribution Analysis of 802.11 Using Signal Flow Graphs
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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
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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
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3Ralf Jennen, ComNets, RWTH Aachen University
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
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4Ralf Jennen, ComNets, RWTH Aachen University
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
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5Ralf Jennen, ComNets, RWTH Aachen University
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
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6Ralf Jennen, ComNets, RWTH Aachen University
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
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7Ralf Jennen, ComNets, RWTH Aachen University
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
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8Ralf Jennen, ComNets, RWTH Aachen University
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
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9Ralf Jennen, ComNets, RWTH Aachen University
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
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10Ralf Jennen, ComNets, RWTH Aachen University
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)
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
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11Ralf Jennen, ComNets, RWTH Aachen University
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)
Related Work by:Bianchi, Duffy, Malone, Leith, Huang
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
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12Ralf Jennen, ComNets, RWTH Aachen University
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
Related Work by:Bianchi, Duffy, Malone, Leith, Huang
Special statewithout collisions
(1-r1)pidle
(1-q0e)r1pidle(1-p)+(1-r2)(1-pidle)
r2(1-pidle) + q0er1pidle(1-p)
r1ppidle
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13Ralf Jennen, ComNets, RWTH Aachen University
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
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14Ralf Jennen, ComNets, RWTH Aachen University
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 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
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15Ralf Jennen, ComNets, RWTH Aachen University
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
(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 = Buffer empty probability r = Arrival probability
Continue withbackoff stage 0
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16Ralf Jennen, ComNets, RWTH Aachen University
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 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
W
S
)(zGQep1
ep
T B1
F
B0
)(zG0 )()( zGzpG coll1
)()( zGp SUCC1
… E
SA
SB
SC
)(~))(( zGpzG SUCCA 1
)(~)( zGpzG COLLA
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
Coefficients of GA arefunctions of G0
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17Ralf Jennen, ComNets, RWTH Aachen University
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
(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 = Buffer empty probability r = Arrival probability
Continue with orwithout frame
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18Ralf Jennen, ComNets, RWTH Aachen University
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 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
W
S
)(zGQep1
ep
T B1
F
B0
)(zG0 )()( zGzpG coll1
)()( zGp SUCC1
… E
SA
SB
SC
)(~))(( zGpzG SUCCA 1
)(~)( zGp SUCC1
)(~)( zGpzG COLLA
)(~ zGp COLL
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
No additional delay
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19Ralf Jennen, ComNets, RWTH Aachen University
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
(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 = Buffer empty probability r = Arrival probability
Continue withbackoff stage 0
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20Ralf Jennen, ComNets, RWTH Aachen University
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 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
W
S
)(zGQep1
ep
T B1
F
B0
)(zG0 )()( zGzpG coll1
)()( zGp SUCC1
… E
SA
SB
SC
)(~))(( zGpzG SUCCA 1
)(~)( zGp SUCC1
)(~)( zGpzG COLLA
)(~ zGp COLL
Ap
Bp
Cp )())(( zGpzG SUCCC 1
)()( zpGzG COLLC
m = Backoff window is doubled m-timesMMAP = Marked Markov arrival processp = Collision probabilitype = System empty probabilityS = Serving stateT = Transmit stateW = Waiting state
Coefficients of GC dependon GSUCC and GCOLL
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21Ralf Jennen, ComNets, RWTH Aachen University
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
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22Ralf Jennen, ComNets, RWTH Aachen University
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
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23Ralf Jennen, ComNets, RWTH Aachen University
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