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Modeling Video Traffic from Multiplexed H.264

Videoconference Streams

Aggelos Lazaris

Departmentof Electronic and Computer Engineering

Technical University of Crete

Chania, Greece

Email: alazaris@telecom.tuc.gr

Polychronis Koutsakis

Department of Electrical and Computer Engineering

McMaster University

Hamilton, ON, Canada

Email: polk@ece.mcmaster.ca

Abstract—Due to the burstiness of video traffic, video modeling

is very important in order to evaluate the performance of future

wired and wireless networks. In this paper, we investigate the

possibility of modeling H.264 videoconference traffic with well-

known distributions. Our results regarding the behavior of single

videoconference traces provide significant insight and help to

build a Discrete Autoregressive (DAR(1)) model to capture the

behavior of multiplexed H.264 videoconference movies from VBR

coders.

I.INTRODUCTION

As traffic from video services is expected to be a substantial

portion of the traffic carried by emerging wired and wireless

networks [7][13], statistical source models are needed for

Variable Bit Rate (VBR) coded video in order to design

networks which are able to guarantee the strict Quality of

Service (QoS) requirements of the video traffic. Video packet

delay requirements are strict, because delays are annoying to a

viewer; whenever the delay experienced by a video packet

exceeds the corresponding maximum delay, the packet is

dropped and the video packet dropping requirements are

equally strict.

Hence, the problem of modeling video traffic, in general,

and videoconferencing, in particular, has been extensively

studied in the literature. VBR video models which have been

proposed in the literature include first-order autoregressive

(AR) models [2], discrete AR (DAR) models [1][3], Markov

renewal processes (MRP) [4], MRP transform-expand-sample

(TES) [5], finite-state Markov chain [6][7], Gamma-beta-auto-

regression (GBAR) models [8][9] (which capture data-rate

dynamics of VBR video conferences well but was found in [9]

to not be suitable for general MPEG video sources), discrete-

time Semi-Markov Processes (SMP) [10], wavelets [11],

multifractal and fractal methods [12].

In [14][15], different approaches are proposed for MPEG-1

traffic, based on the log-normal, Gamma, and a hybrid

Gamma/lognormal distribution model, respectively.

H.264 is the latest video coding standard of the ITU-T

Video Coding Experts Group (VCEG) and the ISO/IEC

Moving Picture Experts Group (MPEG). It has recently become

the most widely accepted video coding standard since the

deployment of MPEG2 at the dawn of digital television, and it

may soon overtake MPEG2 in common use. It covers all

common video applications ranging from mobile services and

videoconferencing to IPTV, HDTV, and HD video storage [18].

Standard H.264 encoders generate three types of video

frames: I (intracoded), P (predictive) and B (bidirectionally

predictive); i.e., while I frames are intra-coded, the generation

of P and B frames involves, in addition to intra-coding, the use

of motion prediction and interpolation techniques. I frames are,

on average, the largest in size, followed by P and then by B

frames.

Similarly to our recent work on modeling H.263

videoconference traffic [17], our present work initially focuses

on the accurate fitting of the marginal (stationary) distribution

of video frame sizes of single H.264 video traces. More

specifically, our work follows the steps of the work presented in

[3], where Heyman et al. analyzed three videoconference

sequences coded with a modified version of the H.261 video

coding standard and two other coding schemes, similar to the

H.261. The authors in [3] found that the marginal distributions

for all the sequences could be described by a gamma (or

equivalently negative binomial) distribution and used this result

to build a Discrete Autoregressive (DAR) model of order one,

which works well when several sources are multiplexed.

An important feature of common H.264 encoders is the

manner in which frame types are generated. Typical encoders

use a fixed Group-of-Pictures (GOP) pattern when compressing

a video sequence; the GOP pattern specifies the number and

temporal order of P and B frames between two successive I

frames. A GOP pattern is defined by the distance N between I

frames and the distance M between P frames.

In this work, we focus on the problem of modeling

videoconference traffic from H.264 encoders, which is a

relatively new and yet open issue in the relevant literature.

II.SINGLE-SOURCE H.264TRAFFIC MODELING

A. Frame-size histograms

In our work, we have studied two different long sequences

of H.264 VBR encoded videos in eighteen formats, from the

publicly available Video Trace Library of [19]. The selected

videos are of low or moderate motion (i.e., traces with very

similar characteristics to the ones of actual videoconference

traffic), in order to derive a statistical model which fits well the

real data.

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978-1-4244-2324-8/08/$25.00 © 2008 IEEE.

Page 2

The two traces are, respectively:

1) A demo from the Sony Digital Video Camera

2)An excerpt of NBC News

The length of the videos is 10 and 30 minutes, respectively.

The data for each trace consists of a sequence of the number of

cells per video frame and the type of video frame, i.e., I, P, or

B. Without loss of generality, we use 48-byte packets

throughout this work, but our modeling mechanism can be used

equally well with packets of other sizes. Table I presents the

trace statistics for each trace. The interframe period is 33.3 ms.

We have investigated the possibility of modeling the

eighteen traces with quite a few well-known distributions and

our results show that the best fit among these distributions is

achieved for all the traces studied with the use of the Pearson

type V distribution. The Pearson type V distribution (also

known as the “inverted Gamma” distribution) is generally used

to model the time required to perform some tasks (e.g.,

customer service time in a bank); other distributions which

have the same general use are the exponential, gamma, weibull

and lognormal distributions [20]. Since all of these distributions

have been often used for video traffic modeling in the literature,

they have been included in this work as fitting candidates, in

order to compare their modeling results in the case of H.264

videoconferencing.

The frame-size histogram based on the complete VBR

streams is shown, for all four sequences, to have the general

shape of a Pearson type V distribution. Fig. 1 presents

indicatively the histogram for the NBC News ([CIF, G16, B7,

F28]) sequence.

B.Statistical Tests and Autocorrelations

Our statistical tests were made with the use of Q-Q plots

[3][20], Kolmogorov-Smirnov [20] tests and Kullback-Leibler

divergence tests [21]. The Q-Q plot is a powerful goodness-of-

fit test, which graphically compares two data sets in order to

determine whether the data sets come from populations with a

common distribution (if they do, the points of the plot should

fall approximately along a 45-degree reference line). More

specifically, a Q-Q plot is a plot of the quantiles of the data

versus the quantiles of the fitted distribution (a z-quantile of X

is any value x such that P ((X ? x) = z). The Kolmogorov–

Smirnov test (KS-test) tries to determine if two datasets differ

significantly. The KS-test has the advantage of making no

assumption about the distribution of data, i.e., it is non-

parametric and distribution free. The KS-test uses the

maximum vertical deviation between the two curves as its

statistic D. The Kullback-Leibler divergence test (KL-test) is a

measure of the difference between two probability distributions.

The Pearson V distribution fit was shown to be the best in

comparison to the gamma, weibull, lognormal and exponential

distributions, which are presented here (comparisons were also

made with the negative binomial and Pareto distributions,

which were also worse fits than the Pearson V). However, as

already mentioned, although the Pearson V was shown to be the

better fit among all distributions, the fit is not perfectly

accurate. This was expected, as the gross differences in the

number of bits required to represent I, P and B frames impose a

degree of periodicity on H.264-encoded streams, based on the

cyclic GoP formats (therefore, this case is different than the

case of H.263 traffic we studied in [17], where the number of I

frames was so small in each trace that the trace could be

modeled as a whole).

Hence, we proceeded to study the frame size distribution for

each of the three different video frame types (I, P, B), in the

same way we studied the frame size distribution for the whole

trace. This approach was also used in [9][22].

TABLE I. TRACE STATISTICS

Video Name

[RES, G, B, F]a

Mean

(bits)

15816

1197

14632

1084

15081

1054

16624

1059

14067

954

12801

887

13129

898

Peak

(bits)

181096

28032

182520

28216

186872

29768

192272

31840

221664

23096

222888

23232

227680

25480

233296

28224

398544

143408

Variance

(bits2)

471117539

4925112

467920380

5007541

467131784

5179470

456464433

5246908

752947478

4693753

770225078

4856589

787021301

5243752

803054805

5818976

2684852964

327728805

NBC News

NBC News

NBC News

NBC News

NBC News

NBC News

NBC News

NBC News

Sony Demo

Sony Demo

Sony Demo

Sony Demo

Sony Demo

Sony Demo

Sony Demo

Sony Demo

Sony Demo

Sony Demo

[CIF, 16, 1, 28]

[CIF, 16, 1, 48]

[CIF, 16, 3, 28]

[CIF, 16, 3, 48]

[CIF, 16, 7, 28]

[CIF, 16, 7, 48]

[CIF, 16, 15, 28]

[CIF, 16, 15, 48]

[CIF, 16, 1, 28]

[CIF, 16, 1, 48]

[CIF, 16, 3, 28]

[CIF, 16, 3, 48]

[CIF, 16, 7, 28]

[CIF, 16, 7, 48]

[CIF, 16, 15b, 28] 14861

[CIF, 16, 15b, 48] 933

[HD, 12, 2, 48]

[HD, 12, 2, 38]

22513

7618

a. RES: Resolution, G: GoP Size, B: Number of B Frames, F: Quantization Parameters

b. When B=15 and G=16 there are no P frames in the trace sequence

Frame Size Histogram

0,E+00

1,E-05

2,E-05

3,E-05

4,E-05

5,E-05

6,E-05

7,E-05

8,E-05

9,E-05

1,E-04

0 50100 150 200

Frame Sizes (KB)

Frequency (Percentile of total frames)

Figure 1. Frame size histogram for the NBC News trace with parameters:

[CIF, G16, B7, F28].

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978-1-4244-2324-8/08/$25.00 © 2008 IEEE.

Page 3

Another approach, similar to the above, was proposed in

[14]. This scheme uses again lognormal distributions and

assumes that the change of a scene alters the average size of I

frames, but not the sizes of P and B frames. However, it is

shown in [4][15] that the average sizes of P and B frames can

vary by 20% and 30% (often more than that), respectively, in

subsequent scenes, therefore the size changes are statistically

significant.

The mean, peak and variance of the video frame sizes for

each video frame type (I, P and B) of each movie were taken

again from [19] and the Pearson type V parameters are

calculated based on the following formulas for the mean and

variance of Pearson V (the parameters for the other fitting

distributions are similarly obtained based on their respective

formulas).

The Probability Density Function (PDF) of a Pearson V

distribution with parameters (?, ?) is f(x)= [x-(?+1) e-?/x]/ [?-?

?(?)], for all x>0, and zero otherwise.

The mean and variance are given by the following

equations: Mean=?/(?-1), Variance=?2/[(?-1)2(?-2)]

The autocorrelation coefficient of lag-1 was also calculated

for all types of video frames of the eighteen movies, as it shows

the very high degree of correlation between successive frames

of the same type. The autocorrelation coefficient of lag-1 will

be used in the following Sections of this work, in order to build

a Discrete Autoregressive Model for each video frame type.

From the five distributions examined (Pearson V,

exponential, gamma, lognormal, weibull) the Pearson V

distribution once again provided the best fitting results for the

54 cases (18 movies, 3 types of frames per movie) studied.

In order to further verify the validity of our results, we

performed Kolmogorov-Smirnov and Kullback-Leibler tests for

all the 54 fitting attempts. The results of our tests confirm our

respective conclusions based on the Q-Q plots (i.e., the Pearson

V distribution is the best fit). Fig. 2 presents indicative results

from the KS-test. Regarding the KL-test, the results for the {I,

P, B} frames of the Sony Demo ([CIF, G16, B3, F48]) trace are

respectively, for the Pearson V distribution {0.364, 0.721,

0.432), for the Lognormal distribution {0.378, 0.864, 0.479},

for the Gamma distribution {0.387, 1.027, 0.543} and for the

Weibull distribution {0.453, 1.024, 0.533}.

Although controversy persists regarding the prevalence of

Long Range Dependence (LRD) in VBR video traffic

([25][26][27]), in the specific case of H.264-encoded video, we

have found that LRD is important. The autocorrelation function

for the NBC News ([CIF, G16, B7, F28]) trace is shown in Fig.

3 (the respective Figures for the other three traces are similar).

Three apparent periodic components are observed, one

containing lags with low autocorrelation, one with medium

autocorrelation and the other lags with high autocorrelation. We

observe that autocorrelation remains high even for large

numbers of lags and that both components decay very slowly;

both these facts are a clear indication of the importance of

LRD. The existence of strong autocorrelation coefficients is due

to the periodic recurrence of I, B and P frames.

Although the fitting results when modeling each video

frame type separately with the use of the Pearson V distribution

are clearly better than the results produced by modeling the

whole sequence uniformly, the high autocorrelation shown in

the Figure above can never be perfectly “captured” by a

distribution generating frame sizes independently, according to

a declared mean and standard deviation, and therefore none of

the fitting attempts (including the Pearson V), as good as they

might be, can achieve perfect accuracy. However, these results

lead us to extend our work in order to build a DAR model,

which inherently uses the autocorrelation coefficient of lag-1 in

its estimation. The model will be shown to accurately capture

the behavior of multiplexed H.264 videoconference movies, by

generating frame sizes independently for I, P and B frames.

Finally, it should be noted that in [16] we have successfully

modeled High Definition (HD) H.264 traces as a whole (i.e.,

with a similar approach to that of [17] for H.263 traces) and

used the result to propose an efficient MAC protocol for GEO

satellite networks. The Weibull distribution was shown to

provide the best results when modeling the traces as a whole,

slightly outperforming the Pearson V distribution. However, in

the case of the “Main Profile” traces from [19] (which consume

significantly smaller amounts of bandwidth than the HD ones)

the Pearson V distribution clearly excels as a fit both for the

whole trace and for the separate modeling of I, P, B frames.

0 0.10.20.30.4 0.5

Bytes

0.60.70.80.91

x 10

-3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Percentile

Kolmogorov - Smirnov Tests for B-sonyCIF-G16B3F48

Actual Trace

Exponential, D= 0.48555

Gamma, D= 0.35528

Lognormal, D= 0.34261

PearsonV, D= 0.30829

Weibull, D= 0.32609

Figure 2. KS-test (Comparison Percentile Plot) for the Sony Demo B

frames ([CIF, G16, B3, F48]).

Frame Size Autocorrelation

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 50 100150

Lag[frames]

ACC

Figure 3. Autocorrelation Coefficients of the NBC News trace ([CIF,

G16, B7, F28]).

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978-1-4244-2324-8/08/$25.00 © 2008 IEEE.

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III.

A Discrete Autoregressive model of order p, denoted as

DAR(p) [23], generates a stationary sequence of discrete

random variables with an arbitrary probability distribution and

with an autocorrelation structure similar to that of an

Autoregressive model. DAR(1) is a special case of a DAR(p)

process and it is defined as follows: let {Vn} and {Yn} be two

sequences of independent random variables. The random

variable Vn can take two values, 0 and 1, with probabilities 1-?

and ?, respectively. The random variable Yn has a discrete state

space S and P{Yn = i} = ?(i). The sequence of random variables

{Xn} which is formed according to the linear model:

Xn = Vn Xn-1 + (1- Vn) Yn

is a DAR(1) process.

A DAR(1) process is a Markov chain with discrete state

space S and a transition matrix:

P = ?I + (1-?) Q

where ? is the autocorrelation coefficient, I is the identity

matrix and Q is a matrix with Qij = ?(j) for i, j ? ?S.

Autocorrelations are usually plotted for a range W of lags.

The autocorrelation can be calculated by the formula:

?(W)= E[(Xi - ?)(Xi+w - ?)]/?2

where ? is the mean and ?2 the variance of the frame size for a

specific video trace.

As in [3], where a DAR(1) model with negative binomial

distribution was used to model the number of cells per frame of

VBR teleconferencing video, we want to build a model based

only on parameters which are either known at call set-up time

or can be measured without introducing much complexity in the

network. DAR(1) provides an easy and practical method to

compute the transition matrix and gives us a model based only

on four physically meaningful parameters, i.e., the mean, peak,

variance and the lag-1 autocorrelation coefficient ? of the

offered traffic (these correlations, as already explained, are

typically very high for videoconference sources). The DAR(1)

model can be used with any marginal distribution [24].

As already explained, the lag-1 autocorrelation coefficient

for the I, P and B frames of each trace is very high in all the

studied cases. Therefore, we proceeded to build a DAR(1)

model for each video frame type for each one of the eighteen

traces under study. More specifically, in our model the rows of

the Q matrix consist of the Pearson type V probabilities (f0, f1,

… fk, FK), where FK= ?k>K fk, and K is the peak rate. Each k, for

k<K, corresponds to possible source rates less than the peak

rate of K.

From the transition matrix in (2) it is evident that if the

current frame has, for example, i cells, then the next frame will

have i cells with probability ?+(1-?)*fi, and will have k cells,

k≠ i, with probability (1-?)*fk. Therefore the number of cells

per video frame stays constant from one (I, P or B) video frame

to the next (I, P or B) video frame, respectively, in our model

THE DAR (1) MODEL – RESULTS AND DISCUSSION

(1)

(2)

(3)

with a probability slightly larger than ?. This is evident in Fig.

4, where we compare the actual B frames sequence of the NBC

News ([CIF, G16, B15, F28]) trace and their respective DAR(1)

model and it is shown that the DAR(1) model’s data produce a

“pseudo-trace” with a periodically constant number of cells for

a number of video frames. This causes a significant difference

when comparing a segment of the sequence of I, P, or B frames

of the actual NBC News video trace and a sequence of the same

length produced by our DAR(1) model. The same vast

differences also appeared when we plotted the DAR(1) models

versus the actual I, P and B video frames of the other traces

under study.

0

100

200

300

400

050010001500

Frames

200025003000

Cells

Actual TraceDAR Model

Figure 4. Comparison for a single trace between a 10000 frame sequence of

the actual B frames sequence of the NBC News ([CIF, G16, B15, F28]) trace

and the respective DAR(1) model in number of cells/frame (Y-axis).

0

2000

4000

6000

8000

10000

050010001500

Frames

200025003000

C ells

Actual TraceDAR Model

Figure 5. Comparison for 30 superposed sources between a 3000 I frame

sequence of the actual NBC News ([CIF, G16, B1, F28)] trace and the

respective DAR(1) model in number of cells/frame (Y-axis).

0

500

1000

1500

2000

2500

3000

3500

010002000300040005000

Frames

600070008000900010000

Cells

Actual TraceDAR Model

Figure 6. Comparison for 30 superposed sources between a 10000 P frame

sequence of the actual NBC News ([CIF, G16, B1, F28)] trace and the

respective DAR(1) model in number of cells/frame (Y-axis).

0

200

400

600

800

1000

1200

010002000300040005000

Frames

600070008000900010000

C ells

Actual TraceDAR Model

Figure 7. Comparison for 30 superposed sources between a 10000 B frame

sequence of the actual NBC News ([CIF, G16, B1, F28)] trace and the

respective DAR(1) model in number of cells/frame (Y-axis).

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However, our results have shown that the differences

presented above become small for all types of video frames and

for all the examined traces for a superposition of 5 or more

sources, and are almost completely smoothed out in most cases,

as the number of sources increases (the authors in [3] have

reached similar conclusions for their own DAR(1) model and

they present results for a superposition of 20 traces). This is

clear in Figs. 5-7, which present the comparison between our

DAR(1) model and the actual I, P, B frames’ sequences of the

NBC News ([CIF, G16, B1, F28)] , for a superposition of 30

traces (the results were perfectly similar for all video frame

types of the other three traces; we have used the initial trace

sequences to generate traffic for 30 sources, by using different

starting points in the trace). The common property of all these

results (derived by using a queue to model multiplexing and

processing frames in a FIFO manner) is that the DAR(1) model

seems to provide very accurate fitting results for P and B

frames, and relatively accurate for I frames.

However, although Figs. 5-7 suggest that the DAR(1)

model captures very well the behavior of the multiplexed actual

traces, they do not suffice as a result. Therefore, we proceeded

again with testing our model statistically in order to study

whether it produces a good fit for the I, P, B frames for the

trace superposition. For this reason we have used again Q-Q

plots, and we present indicatively some of these results in Figs.

8-9, where we have plotted the 0.01-, 0.02-, 0.03-,… quantiles

of the actual B and I video frames’ types of the NBC News

trace versus the respective quantiles of the respective DAR(1)

models, for a superposition of 30 traces.

As shown in Fig. 8, which presents the comparison of actual

P frames with the respective DAR(1) models for the NBC

News ([CIF, G16, B3, F48]) trace, the points of the Q-Q plot

fall almost completely along the 45-degree reference line, with

the exception of the first and last 3% quantiles (left- and right-

hand tail), for which the DAR(1) model underestimates the

probability of frames with a very small and very large,

respectively, number of cells. The very good fit shows that the

superposition of the P frames of the actual traces can be

modeled very well by a respective superposition of data

produced by the DAR(1) model (similar results were derived

for the superposition of B frames), as it was suggested in Figs.

6, 7. Fig. 9 presents the comparison of actual I frames with the

respective DAR(1) model, for the NBC News ([CIF, G16, B7,

F48]) trace. Again, the result suggested from Fig. 5, i.e., that

our method for modeling I frames of multiplexed H.264

videoconference streams provides only relative accuracy, is

shown to be valid with the use of the Q-Q plots. The results for

all the other cases which are not presented in Figs. 8-9 are

similar in nature to the ones shown in the Figures.

One problem which could arise with the use of DAR(1)

models is that such models take into account only short range

dependence, while, as shown earlier, H.264 videoconference

streams show LRD. This problem is overcome by our choice of

modeling I, P and B frames separately. This is shown in Fig.

10. It is clear from the Figure that, even for a small number of

lags, (e.g., larger than 10) the autocorrelation of the

superposition of frames decreases quickly, for all the traces.

Therefore, although in some cases the DAR(1) model exhibits a

slower decrease than that of the actual traces’ video frames

sequence, this has minimal impact on the fitting quality of the

DAR(1) model. This result further supports our choice of using

a first-order model.

IV.CONCLUSIONS

In this paper, we have proposed and tested a new model for

traffic originating from VBR H.264 videoconferencing

sources. Models of video traffic will prove very important in

the immediate future, as networks will need to competently

handle video traffic (i.e., to guarantee its strict QoS

requirements despite its

Autoregressive model built in this work is shown to be highly

accurate and, to the best of our knowledge, is one of the first

works in the relevant literature to address the specific problem.

Based on the very good results of our study in modeling P- and

burstiness). The Discrete

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

80010001200 140016001800

Figure 8. Q-Q plot of the DAR(1) model versus the actual video for the P

frames of NBC News ([CIF, G16, B3, F48]), for 30 superposed sources.

4500

4700

4900

5100

5300

5500

5700

5900

6100

6300

6500

45005000550060006500

Figure 9. Q-Q plot of the DAR(1) model versus the actual video for the I

frames of NBC News ([CIF, G16, B7, F48]), for 30 superposed sources.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

050100 150200

Lag[frames]

ACC

Actual Trace

DAR Model

Figure 10. Autocorrelation vs. number of lags for the I frames of the actual

NBC News ([CIF, G16, B15, F28]) trace and the DAR(1) model, for 30

superposed sources.

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.

978-1-4244-2324-8/08/$25.00 © 2008 IEEE.

Page 6

B-frames’ sizes of multiplexed H.264 videoconference traces,

and the low complexity of our first-order model, we believe

that our approach is very promising for modeling this type of

traffic. However, since our modeling scheme shows relative

accuracy in modeling I -frames’ sizes, the use of wavelet

modeling for the I -frames’ size sequence may provide a very

competent solution, and our future work will be pointed

towards this direction.

ACKNOWLEDGMENT

This work has been funded, in part, by a grant from the Natural

Sciences and Engineering Research Council of Canada

(NSERC).

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Gamma-Based

for VBR-Video Traffic

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