Wavelet and Time -Domain Modeling of Multi -Layer VBR...

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Wavelet and TimeWavelet and Time--Domain Domain Modeling of MultiModeling of Multi--Layer Layer

VBR Video TrafficVBR Video Traffic

Min Dai, Dmitri LoguinovTexas A&M University

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Agenda

• Background– Importance of traffic modeling

– Goals of traffic modeling

– Preliminary knowledge of video traffic

• Challenges & Current Status

• Our Work– Modeling single-layer video traffic

– Modeling multi-layer video traffic

• Conclusion

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Importance of Traffic Modeling

• Properly allocate network resources

• Evaluate protocols and effectively design networks

• Use as traffic descriptor to achieve certain Quality of Service (QoS) requirements

• Analyze and characterize a queue or a network

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Goals of Traffic Modeling

• Capture the characteristics of video frame size sequences

– The marginal probability density function (PDF) of frame sizes

– The autocorrelation function (ACF) of video traffic

• Accurately predict network performance

– Buffer overflow probabilities

– Temporal burstiness

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Preliminary

I0 B1 B2 P3 B4 B5 P6 I7

Intra-GOP CorrelationInter-GOP Correlation

Group of Pictures (GOP)

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Agenda



– Preliminary knowledge




• Conclusion

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Challenges

• The PDF is different among I, P, and B-frame sizes

• VBR video traffic exhibits both long range dependency (LRD) and short range dependency (SRD).

• Single-layer and base layer video traffic:

– Coexistence of inter- and intra-GOP correlation

• Multi-layer video traffic:

– Strong cross-layer correlation

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Current Status

• It is hard to capture both LRD and SRD properties of the autocorrelation function of video traffic

• Little work has considered the intra-GOP correlation

• Most existing models only apply to single-layer VBR video traffic

• Current multi-layer traffic models do not capture the cross-layer correlation

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Agenda







• Conclusion

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Our Work

Intra-GOP

CorrelationI-frame

Size ModelingP and B-frame Size Modeling

Inter-GOP Correlation

Wavelet Domain Time Domain

Enhancement Layer Frame Size Modeling

Cross-layer Correlation

Single-layer & Base layer

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Wavelet Decomposition

• Wavelet function generates the detailed coefficients {Dj} and scaling function generates the approximation coefficients {Aj}, where j is the decomposition level.

A typical wavelet decomposition.

DA

D

A

DA

wavelet functionscaling

function

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Wavelet Decomposition (cont.)

The ACF structures of {D3} and {A3} (left). The PDF of I-frame sizes and that of {A3} (right).

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bytesp

rob

abil

ity

I-frame size

approx. coefficients

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lag

auto

corr

elat

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ACF approx.

ACF detailed

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Modeling I-Frame Sizes

• Estimate the coarsest approximation coefficients {AJ} :– Prior work — independent random Gaussian

or Beta variable

– Our model — dependent random variables with marginal Gamma distribution

• Estimate detailed coefficients {Dj} at each level:– Prior work — i.i.d. Gaussian random variables

– Our model — i.i.d. mixture Laplacian random variables

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Estimate Detailed Coefficients

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10000

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coefficients (bytes)

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Mixture-Laplacian

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GGD

GaussianActual

Mixture – Laplacian

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Performance Comparison

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lag

auto

corr

elat

ion

actual

our model

nested AR

The ACF structure of the actual and that of the synthetic traffic in a long range (left) and short range (right).

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lagau

toco

rrel

atio

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actual

our model

GBAR

Gamma_A

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Our Work

Intra-GOP

Correlation

I-frame Size Modeling

P and B-frame Size Modeling






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Modeling P/B-Frame Sizes

• Assume that GOP structure is fixed, e.g., IBBPBBPBBPBB

• Definition: In the n-th GOP, – — the I-frame size

– — the size of the i-th P-frame

– — the size of the i-th B-frame

• For example, represents the size of the third P-frame in the 10-th GOP

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Intra-GOP Correlation

• Most previous work does not consider intra-GOP correlation and estimates P and B-frame sizes as i.i.d. random variables

• However, intra-GOP correlation is important and has similar structures between and , with respect to different i.

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Intra-GOP Correlation (cont.)

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lag

co

rrel

ati

on

cov(P1,I)

cov(P2,I)

cov(P3,I)

The correlation between different B-frame sequences and the I-frame sequence (left). That between different P-frame sequences and the I-frame sequence (right).

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lag

co

rrela

tio

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cov(B1,I)

cov(B2,I)

cov(B7,I)

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Modeling P-Frame Sizes

• The size of the i-th P-frame in the n-th GOP:

– Process and is independent of

– Parameters σP and σI are the standard deviation of and , respectively.

– Parameter is the lag-0 correlation coefficient.

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Performance Comparison

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lag

corr

elat

ion

actual

our model

i.i.d methods

The correlation between and in Star Wars.

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Agenda







• Conclusion

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Our Work

Intra-GOP

CorrelationI-frame

Size ModelingP and B-frame Size Modeling






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Modeling Enhancement Layer

• We estimate I-frame sizes in wavelet domain

• We estimate P and B-frame sizes using the cross-layer correlation:

– where is the size of the i-th P-frame, and is the size of the i-th B-frame

– Parameter is the lag-0 cross correlation coefficient, are the standard deviation of the enhancement layer sequence and its corresponding base layer sequence.

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Performance

The cross correlation in the original and synthetic The silence of the Lambs.

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lag

cro

ss c

orr

elat

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actual

our model

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lagcr

oss

co

rrel

atio

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actual

Zhao et al.

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Model Accuracy Study

• QQ plots— Verify the distribution similarity between the original traffic and the synthetic one

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original frame size

syn

thet

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original frame size

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QQ plots for the synthetic single-layer Star Wars (left) and the synthetic enhancement layer The Silence of the Lambs (right).

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Model Accuracy Study (cont.)

• Leaky-bucket simulation– Examine how well the traffic model preserves

the temporal information of the original traffic

– Implementation: Pass the original and synthetic traffic through a generic buffer with capacity cand drain rate d

– Evaluation metric:

• where p is the actual packet loss ratio and pmodelis the synthetic one.

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Model Accuracy Study (cont.)

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drain rate

bit

lo

ss r

atio

actual

synthetic

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1%

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4%

10 20 30 40

buffer capacity (ms)re

lati

ve e

rro

r

our modelNested ARGamma_AGamma_B

Comparison of several models in H.26L coded Starship Troopers

The loss ratio p of the original and synthetic The Silence of the Lambs enhancement layer

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Conclusion

• This paper proposes a traffic model applicable to both single-layer and multi-layer VBR video traffic.

• The presented traffic modeling framework captures both LRD and SRD properties of video traffic.

• This framework accurately describes the intra-GOP correlation and the cross-layer correlation.

Wavelet and Time -Domain Modeling of Multi -Layer VBR...

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