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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
• Background– Importance of traffic modeling
– Goals of traffic modeling
– Preliminary knowledge
• Challenges & Current Status
• Our Work– Modeling single-layer video traffic
– Modeling multi-layer video traffic
• 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
• Background– Importance of traffic modeling
– Goals of traffic modeling
– Preliminary knowledge
• Challenges & Current Status
• Our Work– Modeling single-layer video traffic
– Modeling multi-layer video traffic
• 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
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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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coefficients (bytes)
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coefficients (bytes)
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coefficients (bytes)
Mixture-Laplacian
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coefficients (bytes)
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
n
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
Inter-GOP Correlation
Wavelet Domain Time Domain
Enhancement Layer Frame Size Modeling
Cross-layer Correlation
Single-layer & Base layer
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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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0 70 140 210 280 350
lag
corr
elat
ion
actual
our model
i.i.d methods
The correlation between and in Star Wars.
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Agenda
• Background– Importance of traffic modeling
– Goals of traffic modeling
– Preliminary knowledge
• Challenges & Current Status
• Our Work– Modeling single-layer video traffic
– Modeling multi-layer video traffic
• 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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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
n
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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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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bit
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atio
actual
synthetic
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4%
10 20 30 40
buffer capacity (ms)re
lati
ve e
rro
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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.
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