ADMISSION CONTROL FOR VIDEO TRAFFIC STREAMS WITH SCALING CHARACTERISTICS *

/ Abstract The impact of time-dependence or scaling char­ acteristics on video acceptance regions is examined on this paper. We considered two different Call admission control (CAC) mechanisms; i) a descriptor-based CAC (DBCAC) mechanism and ii) a measurement-based CAC (MBCAC) mechanism. The proposed MBCAC is a hybrid measure­ ment scheme that includes a Kalman filter and a real-time Hurst estimation based on wavelets. We investigated several buffer sizes and video sequences with different dependence degrees. Furthermore. for the accuracy of the Hurst (H) esti­ mation. we developed a Hurst Estimator Package (HEP). This package consists of the estimators: Rescaled adjusted range (RlS). Higuchi and Abry-Veitch wavelet (AV). An important result showed that video traffic connections with long-range dependence (LRD) and short-range dependence (SRD) have similar admission regions.


INTRODUCTION
Call admission control or time-dependent or scaling video connections is still an important issue for network traffic engineering.This dependence degree is expressed by the Hurst parameter.Video streams have an inherent time dependence due to the encoding process.The presence of time-dependence or scaling characteristics were observed on different traffic streams [15. 8. 4. 16. 6].The performance of time-dependent traffic is a hot research topic specially when considering streams with long-range dependence or H > 1/2.The stream dependence impact on buffer dimen sioning and network performance is still under discussion [28.24J and the matter is not closed.In this paper.we exam ined the impact of the video connections scaling ((J < H < 1) on admission regions.
As we are dealing with time-dependent connections we need an accurate Hurst estimation to determine the admis sion regions.Different estimation methods shall he applied to achieve this estimation accuracy.The methods proposed in the literature were developed considering different samples distributions and characteristics.For instance.the Higuchi method is better for fractal samples.The AV filtering pro cedure is not interesting for short samples sequences.i.e.. less than 1000.Wc developed a package named Hurst Esti mator Package (HEP) consisting of the estimators.RIS [II].
Higuchi [29] and AV [nJ (wavelet).The time-dependence analysis is then presented for these three estimators.
The CAC function determines the acceptance or rejection of a new connection and guarantees the required quality-of service (QoS) of all connections.We focused on CAC mech anisms based on the effective bandwidth (EB) decision crite ria.The EB theoretical results were evaluated from the Nor ros equation [20].We examined two different CAC mecha nisms: i) a descriptor-based CAC (DBCAC) mechanism and ii) a measurement-based CAC (MBCAC) mechanism, Both CAC approaches were proposed to deal with time-dependent video sources.The main limitation of the DBCAC mech anisms is that the EB calculus is based on the traffic de scriptors.Declaration errors lead to incorrect CAC decisions.MBCAC mechanisms [7.9J that estimate real network re sources and parameters were proposed to avoid these limita tions and so.ensure accurate CAC decisions.
We propose a new MBCAC for streams with time dependence or scaling characteristics.Consequently.for this the MBCAC the EB is dynamically re-evaluated using the measured parameters including the time-dependence or Hurst degree.The AV [26. 27] estimator was added to the MBCAC mechanism to provide the on-line Hurst estimation.We de Admission Control for Video Traffic Streams with Scaling Characteristics note this on-line implementation of AV estimator as A FRY (real time AV estimator).Hence.for the MBCAC the EB re sults are continuously changing.This is also function of the connections input/output process and the available network ressources.
The acceptance regions were obtained for video connec tions where the scaling was modeled by a fractional Brow nian motion [19] (fBm) process and also for real MPEG-I sequences.The 113m choice is explained by the fact that it is the only stochastic process that is able to represent the whole scaling degree range (0 < H < 1).Moreover.fBm is known as the uniqu€g;-ussian H-sssi.i.e .. self-similar with self-simi larity parameter and stationary increments [18.211.
The M/G/x model proposed in [14] has a restricted scal ing representation.It generates samples with autocorrelation function defined by e-3Vk besides the model remains SRD.
The fractional Gaussian noise (fGn) is the fBm increment process and it captures only LRD (H > ±).Furthermore.
it is not able to well represent SRD connections r17].The EB and admission regions results are presented for arrival pro cesses with different scaling degrees (0 < H < 1) and buffer sizes.A set of simulations were performed to verify the an alytical results.We also presented the bounds of the NOITOS EB equation to deal with video traffic.
The rest of this paper is organized as follows.Sec tion 2, describes the scaling model for representing the time dependence of the video sequences and the EB evaluation.Section 3 briefty presents the Hurst parameter estimators ex amined on this work.Section-t show a description of the pro posed MBCAC mechanism including the on-line estimator of the Hurst parameter.In Section :' i the main results concerning the Hurst estimation.EB.DBCAC and MBCAC regions are presented and discussed.Finally.Section 6 is devoted to the conclusions of this work.

THE SCALING MODEL AND THE EB EVALUATION
The scaling or dependence degree is here represented by the Hurst parameter.The traffic scaling evolution can be oh served hy the asymptotic hehavior of its correlation function For traffic with LRD characteristics we have L~-x p(k) = x.For anti-persistent or negative dependent processes (0 < H < 1) we have L~-x p(k) = O.And. for SRD pro cesses (H = h) the correlation function hehavior is such that L~-"JG p(kf = c.where c > 0 is a finite constant (e.g .. pure Brownian motion and Poisson processes.).For traffic engi nceering the term SRD is related to the exponential decaying characteristic of the autocorrelation function of the Markov models.Some authors denote all processes with H -S ±as

SRD.!
In this work.the video sequences scaling was modeled by the fBm stochastic process.The fBm is a family of Gaussian random vari ab les (XH (t)) indexed in 5ft with zero mean and -:,lntinuous sample paths (null at time 0).The variance of its independent increments is proportional to its time intervals accordingly to the expression for O -S tt -S t-i -S 1. Xrr(t) is considered a self-similar pro cess if its statistical characteristics:' hold for any time scale.
Thus. for any to and i > 0 we have X' (0 ".

d -H[" (
_'eHl.t+T-Htjj,'>O==r -'eHt+ where the increments are stationary, self-similar and r is the process re-scaling factor.As we note.the characteristics of the XH(t) process varies according to the H values. Norros [20] proposed a discretization procedure of a ffim process to represent a traffic stream with scaling characteristics.Denote A( t) as the number of received packets by a multiplexer up to time t.We have. ( where m is the mean rate of the arrival process and

THE EFFECTIVE BANDWIDTH EVALUATION
Consider a queue system with deterministic service and in finite buffer Q. Norros [20] proposed an analytical approx imation to evaluate the required bandwidth c.-\ ('II). of 1/ ho mogeneous 113m sources.For a detailed description of EB definitions and formulations the reader should refer to [12].Suppose that each connection has mean (m), variance (0) and dependence degree (H) parameters.If f = P( Q > B) is the probability that a buffer of size Q becomes larger than a limit B. the required bandwidth C 4 (n) for an aggregate of II con nections is defined as where h'(H) = HH(1 -H)l-H.Hence, the EB of each connection is Suppose that n connections were previously admitted in a link with capacity C. When a new connection request is received, the EB for this new connection (1/ + 1) is evaluated by Ce(n + 1) = C-\(n + 1)/(n + 1).The new connection is accepted by the CAe only if Otherwise.the connection request is rejected.

ABRY-VEITCH ESTIMATOR
To determine the impact of the scaling on the admission re gions we need accurate Hurst estimation.Hence.we should examine different Hurst estimators.A brier description of the the main estimators included in the HEP"' is next presented.
They are the R/S (Rescaled Adjusted Range) statistic.the Higuchi and the wavelet-based Abry-Veiteh (AV) estimators.

R/S STATISTICS
Consider a sequence of random samples {X,} with par tial sums Y(n) = =;'=1 X, and sample variance S2 where ~. is a positive constant.The Hurst parameter is then ob .ainedby a linear regression in a log-log plot of R(II)/S(n) '. ersus n.The main advantage of the RlS statistics is its in ~.:pendence from the stream marginal distribution under esti :--ation.

. + XIII'
\\'e can get the following sample sequences where k = 1.2..... N. rn = 1.2..... k. and the operator J~ stands for the largest integer smaller than u.For each sequence Ze.we evaluate the normalized curve length and define the curve length L(I.) for each lag l: as 1 I. 4A detailed definition of fractal dimension can be found in [3J.Chapter V. pp.17 1-20-.1.

L(k)
The AV estimator" uses the discrete wavelet transform (DWT) to successively decompose a sequence of samples in approximation (o(j.k)) and detail (rlU k)) coefficients.
These coefficients are indexed by its decomposition scale j and time k: The authors showed the relation between these detail coefficients and the Hurst parameter.The AVestima tion can be described in three phases: 1. Wavelet decomposition: the DWT is applied to the sam ple data generati ng the detail coefficients d(j.h.).

2.
Variance estimation of the detail coefficients: for each scale J. we evaluate the variance fJ. ) where II) is the number of available coefficients for each scale j. J.
The AV estimator is robust to polynomial trends added to the process under analysis.Moreover.the AV is appropriate for real time estimation [27] and so. to deal with transient situ ation.This real time estimator (A.I "RT) was included in the proposed MBCAC mechanism presented in Section 4.

MBCAC FOR TIME-DEPENDENT VIDEO CONNECTIONS
The proposed MBCAC is based on a previous work pre sented in [7].In this earlier approach a Kalman filter was used to achieve the mean and variance estimation of the aggregated traffic.In our proposal.we included the A I FiT estimator and also an algorithm that dynamically evaluates the EB of the connections using the measured (m.r.H) parameters.Fig ure I illustrates the proposed hybrid MBCAC mechanism.
The EB evaluation for the time-dependent streams was de termined as presented in Section 2.1.The main difference is that the EB is now evaluated with the real-time estimated parameters.In our proposition.the EB is re-evaluated only when a connection leaves the network.This procedure allows faster decisions by the CAC mechanisms.
The measured mean and variance of the aggregated traffic represents a state vector XI, of the Kalman filter.A state changing occurs each time a connection enters or leaves the network.For each state.k. the Kalman filter stage gives an estimation of the mean JJ" and variance Ii of the aggregated traffic.The main function of the Kalman fiIter is to provide a weighted estimation between the declared and the measured parameters  The fl) parameters are re-evaluated at any time where ji) = S) /71).These ~j) values enables the weighted regression to obtain the Hurst estimation.The input traffic samples AU). are obtained at constant sampling intervals till' The choice of this sampling interval is very important to the measurement process.In our investigation we adopted the definition pre sented in [13].The sampling interval must be in the range ;) where (Lila;) is the largest delay in the system.given by elm(JJ = B / C.These are the timescales of interest for a measurement process in a queue-server sys tem with capacity C and finite buffer B.

RESULTS AND DISCUSSIONS
In this section we present the main theoretical and sirnula tions results.These results concerns the scaling or H estima tion (Section 5.2). the EB and DBCAC obtained regions (Sec tion 5.3) and finally, the MBCAC admission regions (Sec tion 5.4).

ANALYSIS ENVIRONMENT
To evaluate the admission regions for the DBCAC and MBCAC mechanisms we considered the real video se quences Table-TTennis.Salesman.Bond and Race.The Table-Tennis and Salesman standard sequences [5] were en coded in MPEG-2 and H.26l with sampling rate of 50 frames/sec and :360 GOB/sec 6 • respectively.The Bond and Race sequences [25] were MPEG-I encoded with sampling rate of 2.') frames/sec.The Table-Tennis and Salesman se quences were originally packetized in cells (1 cell=424 bits).For simplicity, the original MPEG-I traces were converted to cells/frame.Table I presents the mean (171) and standard deviation (a) of these sequences.These values are shown for the sampling period of each the sequence.These sta tistical parameters were considered as traffic descriptors by the DBCAC mechanism.The fBm process was generated

HURST ESTIMATION RESULTS
As mentioned before.to examined the impact of the video sequences scaling on the admission regions we need an ac curate Hurst estimation, Thus, in this section we show the results of the video connections off-line scaling estimation for the RlS.Higuchi and AV methods (see Table 2).These H results are considered for the EB evaluation and the DB CAC regions.Figure 3 also depicts an example of a Hurst estimation of the Tleunis sequence of each method.
From Table 2 we note the importance of using different es timators to obtain an accurate seal ing characterization.These estimators were concieved based on different assumptions  concerning the samples distrihution.We can see that the esti mators presented similar results for the sequences generated from the tBm process.However.there is a difference in the estimation results for the real MPEG-I sequences (Bond and Race).This fact can he explained by the high scaling vari ability.the short-lime duration and non-gaussian distribution of these sequences.The scale choice of an AV off-line es timation is more complex when dealing with samples with high scaling variability ou multi-scaling characteristics.An example of this scale choice complexity is illustrated in Fig ure 4 for the Race sequence.In Section 5.4, we will see that the A 1 RT achieved better accurate results for on-line or con tinuous estimation.An incorrect estimators choice leads to erroneous traffic scaling interpretation and so.CAe decisions.This reinforces the idea that different estimators should be used to decide the scaling degree to be considered by the CAC mechanism.In this work we adopted the RlS H values since we had similar results for the ffim sequences for all estimators.Moreover.for the real MPEG-l Bond and Bond sequences the Higuchi and AV methods did not present accurate results.If no knowl edge about the samples distribution is available we should use an average Hurst value from the obtained resulLs considering a certain confidence interval.

EB AND DBCAC REGIONS RESULTS
Several simulations were run to validate the EB theoreti cal results (see Eq. 3) and the DBCAC acceptance regions.For the EB analysis we considered that the video sources were multiplexed in a finite queue with deterministic ser vice (C = 15') Mbps) to obtain the maximum number of calls considering a CLR = 1O-~ (::::::  -----------  ing the anti-persistence effect or negative correlation [4,16].are strongly centered around the mean rate.Generally.this anti-persistent traffic presents better queueing performance compared to sources with LRD characteristic.Moreover.small buffer is a major req uirement when considering real time video applications, Hence.a new EB equation should be investigated for H < 1/2 and small buffers.Figure 5 illustrates the DBCAC admission regions obtained by the up perbound linear!method considering different buffer sizes, As we observe.the admission regions for LRD connec tions are close to SRD connections even for large buffer sizes (B = 10000 cells).as shown in Figures 5.c --,-------,---------,-----  results confirm the conclusions presented by Ryu [28] where he showed that LRD has no significant impact on network performance.However, this does not mean that the seal ing characteristics has no importance for traffic engineering.For exemple, in [30] the authors showed that the scaling de gree knowledge can improve the performance of rate-based feedback mechanisms.We extended the analysis for the real MPEG-l Bond sequence.The main objective was to ver ify the impact of other distribution.i.e.. non-gaussian.on the admission regions.Figure 6 shows the analytical (Lin ear method) and simulation results for Soles1710n02 and Bond sources.considering C = 155Mbps and B = 1000 cells, As we previously observed.the regions were similar when con sidering only the fBm sources.Here.however.the admission regions were more sensible to the traffic distribution than the scaling degree even for large buffers.We note that when the number of Bond sources increases this difference becomes larger.This means that the marginal distribution was respon sible for the impact on the number of admitted connections.
In an ongoing paper [10] we show that compared to scaling characteristics the video heavy-tail distribution has greater impact on network performance and so admission regions.In the dependence degree over four or five time scales.A further research should investigate if these time scales are sufficient to enable the analysis of the impact of the dependence degree on CAC regions.

MBCAC AND ON-LINE SCALING ESTIMATION RESULTS
To examine the performance of the MBCAC mechanism.we implemented a connection input/output algorithm.We ass Lime a constant time interval T~: between transitions i.e .. arrival and departure of a connection.When a connection leaves the net work.the EB is re-evaluated based on the esti mated parameters (ti: "..!'t,.ih).Then. the maximum number of admitted connections is computed.
We inserted an error in the mean and variance declared de scriptors to verify the MBCAC performance.We considered that each connection declares parameters 20'X bellow its real values.e.g.real mean TIl = 480 cells/frame and declared mean lf1d = :384 cells/frame for the Tlennis sequence.

_0
.o-: ---",-- The presence of this multi-scaling behavior on network traf fic is discussed in [22].Hence, the Hurst value should not be considered as constant for a long period of time.Only a real time estimation is able to detect this multi-scaling variation.This variation can change the EB results and so. the admis sion regions.The A1'RT also showed good performance for individual source Hurst estimation when considering the in put/output of other video connections.
The individual mean and variance measurements are de picted in Figure 8  This smoothing characteristic of the anti-persistent (H < ~ l traffic is very interesting for network performance and buffer dimensioninz.In the case of SRD traffic (H = 4).~ the variance is constant and similar to the original value (Fig ure ::I.b).For LRD traffic.the variance increased with the ag gregation of connections but no impact was detected due to this variance increasing.This agreggation effect is detected by the MBCAC mechanism.Once more. it is demonstrated the importance of measurement based procedures usage.
Figure 9.a presents the results obtained by the EB stage with the estimated parameters of the MBCAC for a LRD Salesman sequence.The EB results are continuously updated as the measurements are obtained from the MBCAC.The maximum number of admitted connections considering the EB results is presented in Figure 9.h.A high number of con nections (~ :390) could be admitted by the CAC mechanism if the EB is based on traffic descriptors.However, when EB is re-evaluated.i.e .. using the measurement parameters.the admission region changes roughly.Another interesting result reinforces that the number of admitted connections were very close despite of the dependence degree.Admission regions for declared and estimated parameters are shown in Figure 10 for different Salesman sequences.As we see, traditional DBCAC mechanisms arc not able to de tect declaration errors leading to wrong CAC decisions.This proves that broadband packet networks should adopt mea surement based procedures for traffic with scaling character istics.

CONCLUSIONS
The impact of the time-dependence or scaling degree on video admission regions has been evaluated in this paper.We investigated two different CAC approaches.The first ap proach was based on a DBCAC mechanism where the EB evaluation was based on the video traffic descriptors.A sec -nd approach named MBCAC was proposed to deal with net work measured parameters including an on-line scaling de gree estimator.This on-line Hurst estimation improved the EB accuracy and hence the CAC decisions.
The off-line Hurst estimation results have demonstrated .hat the RJS estimator is accurate and robust for processes with any marginal distribution.We also showed that only an on-line estimation is able to detect the traffic scaling varia tion.
This study has also showed that the dependence or scaling degree has no significant impact on the admission regions.Furthermore.we noticed that the traffic marginal distribution :orovoke more impact on the CAC regions.
Further research should include markovian models that represents the scaling degree during some scales as well as :'1: use of the scaling degree knowlegde to improve network conrrol performance,

2By
statistical characteristics.we mean marginal distribution and de '=:' " Brran.Statisticsfor Long-Mrnmr: Processes.Chapman 6. Hall.pendence degree.Only in this case a proces-should be considered as self similar.

Figure 1 .
Figure 1.General diagram of the proposed hybrid MBCAC.

Figure 2 .
Figure 2. Filter bank stages for the A l RT estimator.

'Figure 6 .
Figure 6.Admission regions for connections with different marginal distributions.

Figure 7 .
Figure 7. On-line Hurst estimation with different t m

Figure 9 ,
Figure 9, (a) Effective bandwidth (b) the max, number of connections for different H values, for the Salesman sequences with different Hurst values.The curves were obtained from a simulation set of 20 homogeneous sources, T; = 25s and t m = 0.02s.The curves presenting the mean measurements (Figure 8.a) show a slower convergence for LRD sources.For all cases, the MBCAC mechanism detected the declaration errors and the estimation achieved the correct mean value.The variance curve (Figure S.b) indicates the aggregation effect of connec tions with different dependence degrees.For anti-persistent traffic, the variance decreases with the video connections ag gregation.

Volume 17 ,Figure 10 .
Figure 10.Admission regions for declared and estimated pa rameters.
Hurst parameter estimation: we plot.1}J= log~ (VI) by j.Using a weighted linear regression.we get the slope (\ of the plot and the H parameter is estimated as H

Table 1 .
Parameters of the video sequences.
considering the m and (J parameters obtained from the real Table-Tennis and Salesman sequences.These fBm sequences have also different H values. e.g.H = 0.2.H = Cl..'i and H = 0.8.These three H values represent streams with anti persistence.SRD and LRD.respectively.For the theoretical admission regions evaluation we considered the upperbound linear approximation.

Table 3 .
Number of admitted connections-analytical & simulation results.