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Effective Capacity: A Wireless Link Model for Support of Quality of Service

D. Wu & R. Negi

IEEE Trans. On Wireless Communications vol. 2 no. 4, July, 2003

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OutlineOutline•• Motivation of this paperMotivation of this paper•• Brief review of Brief review of Effective BandwidthEffective Bandwidth•• New model used at upper layer to New model used at upper layer to

capture capture wireless channel qualitywireless channel quality•• SimulationSimulation•• ContributionContribution & & LimitationsLimitations

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QoS Provisioning in Wireless Networks Source

Receiver

Wireless network

How do we guarantee How do we guarantee QoSQoS to the user?to the user?

Streaming video

Quality of Service (QoS)•Data rate •Delay tolerable •Packet loss probability

RmaxD

lossPR

})({Prob maxDtDPloss ≥=noise, interference

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})({Prob maxDtDPloss ≥=

Key issue: time varying wireless channel

How do we estimate wireless channel capacity?How do we estimate wireless channel capacity?

Receiver moves

Power fluctuates

Data capacity changes

Packets get loss

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Need for a novel wireless channel model•“Radio layerRadio layer” channel models represent power fluctuationspower fluctuations

•Hard/impossible to extract QoSQoS metricsmetrics }P,D{R, lossmax

Markov model?Doppler spectrum?AR model?

Rayleigh fading?Gans spectrum?Step 1Step 1: Estimate

model parameters

Date rate (R)? Delay tolerable (D)? Packet loss probability (P)?

Step 2Step 2: Map estimated model to QoS metrics

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A “link-layer” channel model

Model as timeModel as time--varying servervarying server

What is channel “capacity”, when QoS is accounted for?

link-level channel model Easily computes delay

constrained capacity

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Motivation of This PaperMotivation of This Paper•• Model wireless channel in terms of Model wireless channel in terms of upperupper--

layer layer QoSQoS metricsmetrics such as such as data rate, delay, data rate, delay, and delayand delay--violation probabilityviolation probability to to facilitate facilitate support of support of QoSQoS in nextin next--generation wireless generation wireless networksnetworks– easy of translation into QoS guarantees– simplicity of implementation– accuracy

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Main IdeaMain Idea

Statistical Service Curve Statistical Service Curve

+Effective Bandwidth Theory Effective Bandwidth Theory

New Channel Capacity Model

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What is Effective What is Effective Bandwidth ?Bandwidth ?Data RateData Rate

TimeTime

Peak ratePeak rate

Average rateAverage rate

Traffic RateTraffic Rate

Effective Bandwidth was proposed by Gibbens& Hunt, Guerin, and Kelly in 1991

Minimum data rate needed for arrival traffic to meet its QoS requirements

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Definition of Effective BandwidthDefinition of Effective Bandwidth•• A(t) ( total arrival traffic during [0,t) ) has A(t) ( total arrival traffic during [0,t) ) has

stationary incrementsstationary increments

is called as effective bandwidth of arrival traffic

•• Range:Range:

)[0,tθ, ]logE[eθt1t)α(θ, θA(t) ∞∈=

t)α(θ,

∞→→→→

≤≤

θ as ratepeak t)α(θ,0θ as rate average t)α(θ,

ratepeak t)α(θ, rate average

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Effective Bandwidth & Effective Bandwidth & QoSQoS

ε D} P{delay ≤≥

θ

Data RateData RatePeak ratePeak rate

Average rateAverage rate

),(lim)( tt

θαθα∞→

=

Large

Small

Small

θ

θ)α(t,

Small

Large

Large

ε

θθ)α(t,

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ExamplesExamples•• Regulated TrafficRegulated Traffic

•• OnOn--Off TrafficOff Traffic

•• FBM TrafficFBM Traffic

ττ

ττ

ττ τ

)(Alimρ where

1)](e)(A

ρlog[1θ1)α(θ,

*

t

)(θA*

*

∞→=

−+=

))1(1log(1),( −+= θ

θτθα Pe

Pr

ON Off1-r/Pr/P

1-r/Pr/P

A*( )

A(t+ )-A(t)<A*( )

(0,1)HParamter Hurst ,tEZ 3.

0EZ 2. 0. Z1.rate icmean traffr βZrtA(t)

2H2t

t0

t

∈=

===+=

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21),( −+= Hr βθττθα

τττ

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Extended Definition of Effective Extended Definition of Effective BandwidthBandwidth

•• For a stochastic process {For a stochastic process {X(t),tX(t),t>0} with >0} with stationary and nonnegative incrementsstationary and nonnegative increments

is called as effective bandwidth of the stochastic process

)[0,t),,(- ],logE[etθ

1t),(α θX(t)X ∞∈∞∞∈= θθ

t),(αX θ

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Effective Bandwidth & Effective Bandwidth & QoSQoS

A(t)=A1(t)+A2(t)+…+An(t)A(t)=A1(t)+A2(t)+…+An(t)

A1(t)A1(t)

Ai(t)Ai(t)

An(t)An(t) FIFOFIFO

Q(t)Q(t)C(tC(t))

s)](C(t)A(s)[A(t)maxQ(t)ts0

C+−−=≤≤

x]P[Q(t)supx]P[Qt

≥=≥

∗∗

∞→≈≥⇔−≤≥

⇓∞→→+

θγθ

θαθα

x-ex}P{Q x}logP{Qx1lim

tas 0t),(-t),(

x

**A C

•• Assume aggregated traffic Assume aggregated traffic arrival process arrival process A(tA(t) and link ) and link capacity process capacity process C(tC(t) are ) are stationary, thenstationary, then

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Special CasesSpecial CasesrtC −=− ),( θα

A(t)=A1(t)+A2(t)+…+An(t)A(t)=A1(t)+A2(t)+…+An(t)

A1(t)A1(t)

Ai(t)Ai(t)

An(t)An(t) FIFOFIFO

Q(t)Q(t)C(tC(t))

s)](C(t)A(s)[A(t)maxQ(t)ts0

C+−−=≤≤

x]P[Q(t)supx]P[Qt

≥=≥

),(lim)( ]0)(Pr[)()(x]Pr[D(t)sup )(

t

1

tgtDrer

At

xrgr

θαθγ

γ

∞→

×−

=≥=

×≈≥−

utA =),(θα

),(lim)( ]0)(Pr[)()(x]Pr[D(t)sup )(

t

1

thtDueu

Ct

xuhu

θαθγ

γ

−−=≥=

×≈≥

∞→

×− −

C(t)=r*t è

A(t)=u*t è

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is called linkis called link--layer wireless channel modellayer wireless channel model)}(),({ 1 uhu −γ

Proposed Link-level channel model

•• According toAccording to:

• Interpretation– Probability of delay, experienced by CBR

traffic with rate u, more than D is bounded by

max1 )()( Duhueu ××− −

×γ

max1 )(

max )(})(Pr{sup Duhu

teuDtD ××− −

×≈≥ γ

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Simple Estimation AlgorithmSimple Estimation Algorithmmax

1 )(u max )(})(Pr{ DuheuDtD ××− −

×≈≥ γ

[ ])(

)()( 1 uhuutDE −×

=γ [ ] [ ] uEutDE s /Q(t))()( +=τ [ ]Q(t))(

)()(1

Euuuuh

s +×=−

τγ

•• Taking N samples over an interval with length TTaking N samples over an interval with length T– S(n) indicates whether a packet is in service at the n-th sample– Q(n) indicates queue length at the n-th sample– T(n) indicates the remaining service time of the packet at the n-th sample

Q)(h )(1 )(1Q )(1 1-

1s

11 +×==== ∑∑∑

=== s

N

n

N

n

N

n uunT

NnQ

NnS

N τγ

τγ

max1 )(

max })(Pr{ DuhueDtD ××− −

×≈≥ γ

average remaining time of a packet being served

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Summary of EC Link ModelSummary of EC Link Model

)}(),({ 1 uhu −γ

)}(),({ 1 uhu −γ

)(tC),(lim)( th Ct

θαθ −=∞→

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Simulation ResultsSimulation Results

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Accuracy

Rayleigh fading channelSNRavg = 15 dBrawgn =100 kb/sfm =30 Hz

Traffic rate = 85 kb/s

Traffic rate = 80 kb/s

Traffic rate = 75 kb/s rawgn=B*log(1+SNRavg)

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Rayleigh fading channel SNRavg = 0 dBrawgn =100 kb/sfm =30 Hz

Accuracy

Traffic rate = 85 kb/s

Traffic rate = 80 kb/s

Traffic rate = 75 kb/s

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Rayleigh fading channel

SNRavg = 15 dBrawgn =100 kb/sfm = 5 Hz

Accuracy

Traffic rate = 80 kb/s

Traffic rate = 85 kb/s

Traffic rate = 75 kb/s

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Contribution of This PaperContribution of This Paper

max1 )(

max )(})(Pr{sup Duuh

teuDtD ×− −

×≈≥ γ

linklink--layer wireless channel modellayer wireless channel model )}(),({ 1 uhu −γ

for QoS Guarantees

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Limitation of This PaperLimitation of This Paper•• Not solid theoretical foundationNot solid theoretical foundation

•• Are the algorithms based on sampling accurate and simple? Are the algorithms based on sampling accurate and simple?

•• Are the algorithm easy to use?Are the algorithm easy to use?•• Only for CBR trafficOnly for CBR traffic•• Does not explicitly take modulation and channel coding into accoDoes not explicitly take modulation and channel coding into accountunt

Q)(h )(1 )(1Q )(1 1-

1s

11 +×==== ∑∑∑

=== s

N

n

N

n

N

n uunT

NnQ

NnS

N τγ

τγ

∗∗

∞→≈≥⇔−≤≥

⇓∞→→+

θγθ

θαθα

x-ex}P{Q x}logP{Qx1lim

tas 0t),(-t),(

x

**A C

max1 )(

max})(Pr{ DuhueDtD ××− −

×≈≥ γ

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Future WorkFuture Work•• More deeply use effective bandwidth More deeply use effective bandwidth

theorytheory•• Take its advantage but avoid it Take its advantage but avoid it

disadvantagedisadvantage•• Build a more power channel capacity model Build a more power channel capacity model

for for QoSQoS provisioningprovisioning•• Implementation in 3G or 4GImplementation in 3G or 4G