Control of Perceived Quality of Service in Multimedia Retrieval ...

Control of Perceived Quality of Service in Multimedia Retrieval Services: Prediction-based mechanism vs. compensation buffers Aurelio La Corte, Alfio Lombardo, Sergio Palazzo, Giovanni Schembra Istituto di Informatica e Telecomunicazioni, University of Catania V.le A. Doria 6 - 95125 Catania - ITALY

Abstract In multimedia systems end-to-end delay jitter has a great impact on the continuity of information playback. Therefore it is necessary to introduce appropriate mechanisms to compensate for delay variations, so that the intramedia and intermedia temporal relationships can be preserved. In this paper, two methods for compensation of the network delay jitter in a distributed multimedia retrieval service are compared: the first is based on prediction of the network delay jitter suffered by each information unit and retrieval time modification at the source site; the second is based on a compensation buffer at the destination site. Comparison is made by assuming a master/slave relationship between the monomedia streams composing the multimedia data flow.

Keywords: multimedia communications, intramedia and intermedia synchronization, jitter, skew

1. Introduction In traditional telecommunication services, user needs determine different performance requirements in terms of delay and packet loss according to the media supported. Audio services, for example, can tolerate packet loss and moderate delay with very limited jitter, whereas data services tolerate delay but require stringent packet loss parameters. With the advent of multimedia services the performance requirements users have to be provided with are becoming more and more constraining [1-4]. In a multimedia retrieval service, for example, the character streams concerning film subtitles have delay requirements similar to those of video or audio. This is due to the fact that the main characteristics of multimedia services are related to synchronization. A multimedia stream is, in fact, characterized by multiple monomedia streams related to each other by means of time relationships which must be preserved. Due to the various delays the monomedia streams may undergo during transmission in a high-speed integrated network, appropriate mechanisms must be introduced so as to meet both the requirements of each monomedia stream (intramedia synchronization) and those related to how the monomedia streams are integrated to form the multimedia stream (intermedia synchronization). In order to quantify these synchronization requirements and to implement the related control mechanisms, some Quality of Service (QoS) parameters have been defined [4-6]. These QoS parameters are basically linked to the delay jitter the information units of each monomedia stream undergo and the skew occurring in the multimedia stream, that is the difference between the instantaneous delays of information units belonging to two different monomedia streams. As measurements of human perception of the above parameters [6] have shown that monomedia streams may appear to be "in synch" if the jitter and skew are limited to appropriate values, the QoS parameters perceivable at the user interface, herein referred to as Perceived Quality of Service (P_QoS) parameters [7], can be expressed as restrictions on the statistics of the values assumed by the jitter and skew. In literature several mechanisms dealing with the problem of limiting delay jitter and/or skew in multimedia retrieval services have been presented [5-6][8-24]. Many of these mechanisms can be classified into two categories: the first one comprises mechanisms based on the use of buffers at the destination site, the second on modification of retrieval times at the source site so as to compensate for delay jitter. The application of buffering techniques requires the bounds of the delay jitter introduced by the network to be known a priori or estimated at the destination site [11-13]. These techniques are extremely simple to implement but the buffer needed to guarantee the synchronization requirements may be so big that it causes unacceptable delays. The second kind of technique uses mechanisms which reshape the probability density function (pdf) of the delay jitter at the destination site [14-18] by varying the information unit retrieval times at the source site. In this paper we compare the use of these two techniques; in particular, as far as the latter technique is concerned, an extension of the one presented in [17] is used. Comparison between the above two techniques is made by assuming a master/slave representation of the component monomedia streams [8]. The paper is organized as follows: Section 2 defines the synchronization problem, introducing the intra/intermedia synchronization conditions to be applied to each monomedia stream in terms of Perceived Quality of Service parameters. Section 3 introduces the proposed predictionbased delay jitter compensation mechanism. Section 4 shows how the P_QoS requirements are mapped on the parameters of the intra/intermedia synchronization mechanisms. Section 5 presents a case study which highlights the limits of the applicability and effectiveness of the two synchronization mechanisms by varying statistical properties of the network delay and the required P_QoS parameters. Finally, Section 6 summarizes the paper.

2. Definition of the problem End-to-end delay jitter has a great impact on the continuity of playback of information of each monomedia stream and on the concurrent playback of several monomedia streams. A system supporting multimedia retrieval services has to be equipped with functions which will guarantee intra/intermedia synchronization requirements by limiting variations in the delay jitter. To define the system environment in which these functions are to be located, let us consider the general data location model shown in Fig. 1. In this model several sources use a broadband integrated network to send pre-recorded multimedia data streams to a destination node. The sources can be either located in a single site or distributed over the network. A multimedia stream is therefore a combination of “N” monomedia streams which are retrieved by different sources and transported autonomously, for example through separate virtual channels. Below we assume that the technology used to transport information is the Asynchronous Transfer Mode (ATM), which, in the long term, is the most capable of supporting multimedia services. Each media stream, as shown in Fig. 2, is seen as being made up of an ordered sequence of Information Units (IUs) [10], containing a set of packets relating to the same media. The end-to-end delay between the sender and receiver of the monomedia streams consists of collection delay, which is the time needed at the source site to collect and prepare IUs for transmission, network delay and delivery delay, which is the time needed at the destination site to process and prepare IUs for playback [20]. In the following we only consider network delay. However, the same line of reasoning can be used to include the other two kinds of delay in solving the synchronization problem. Source #1

........

Source #2

channel #2 media #2 channel #1 media #1

Source #N

channel #N media #N

integrated network

... Destination

Fig. 1: Data location model for a multimedia retrieval service

IU 1 (n)

IU 1 (n-1)

IU 1 (n+1)

channel #1 time

IU 2 (n-1)

IU 2(n)

IU 2 (n+1)

channel #2 time

.......... IU N (n-1)

..........

..........

IU N (n)

IU N (n+1)

channel #N time

Fig. 2 : Information Units (IUs)

The IUs from the i-th media are retrieved and prepared for transmission at the source site at the time t_txi(n); they are subject in transmission to a variable delay and at the time t_rxi(n) are delivered to the destination site, where they are processed for playback to the user. We assume that clock ticks at the source site and at the destination site have the same advancement [12-13]. The time relationships between IUs belonging to the same monomedia are altered on account of the network delay jitter (henceforward simply called jitter), defined as ji(n) =t_rxi(n) - t_txi(n) - d i (1) where d i is the average network delay suffered by the i-th media. As ji(n) is a random process, the temporal relationships between the IUs of the i-th media are not maintained at the destination site. The time relationships between IUs belonging to different media are altered on account of the different starting times for the sources, sti, the different average delays and the jitters the IUs undergo. More specifically, we define the skew si,k(n) at the instant “n” between the n-th IUs of the media "i" and "k" as the displacement in time between the IUs belonging to "i" and "k": (2) si,k(n) = d i − d k + sti − stk + ji(n) − jk(n) As the first 4 terms of the above relation are constant and can easily be compensated for at the destination site by means of a buffer, without loss of generality, we assume that d i − d k + sti − stk = 0 The skew si,k(n) is therefore: si,k(n) = ji(n) − jk(n) (3) Again, as si,k(n) is a random process, the temporal relationships between the IUs belonging to media “i” and media “k” are not maintained at the destination site. A synchronization mechanism has to maintain the jitter and skew variations bounded within suitable values [6]. To achieve this goal it has to act on all the monomedia streams making up the multimedia stream. In particular, in a multimedia source there is one monomedia stream which is completely independent of the others, and the others are dependent only on the first. We will indicate the first as the master and the others as slaves [8][25]. The playback of the master can be spared from discontinuities. Whereas the master plays back at its natural rate, the slave streams can be subjected to skips and pauses, in order to remain synchronized with the master [8]. The Perceived Quality of Service the multimedia system has to provide the user with can therefore be defined in terms of the probability that the jitter suffered by the master stream and the skew occuring between each slave stream and the master stream will exceed certain maximum admissible values. Let us define the residual jitter j_ri(n) and the residual skew s_ri,k(n) as the jitter and the skew that occur at the destination site after applying the synchronization mechanism. The P_QoS the multimedia system has to provide the user with can be therefore specified as: p{ j_ rM ( n ) > J M ,max } ≤ ε M for the master (4a)

{

}

p s _ rS,M ( n ) > S S,max ≤ ε S

for the slaves

(4b)

where the symbol p{.} is used to indicate probability, the indexes "M" and "S" are used to indicate master and slaves, and JM,max and SS,max are the maximum admissible residual jitter and residual skew values respectively. Therefore a synchronization mechanism has to reshape the pdf’s of either the jitter of the master and the skew of the slaves with respect to the master in such a way that the above P_QoS requirements are met for each media. Let us note that if we assume that IUs are discarded when the residual jitter or the residual skew exceeds the maximum admissible value, the P_QoS can be specified equivalently as:

p(loss) ≤ ε M for the master (4a') p(loss) ≤ ε S for the slaves (4b') . In order to provide users with the P_QoS they require hereinafter we will use two different jitter compensation techniques. The first compensates for jitter at the source site through prediction and retrieval time variation; the second uses a compensation buffer at the destination site [13]. Henceforward, the size of this buffer, referred to as b i , where i=M and i=S indicate the buffers for the master and slave streams respectively, will be defined as the maximum IU jitter variation it can compensate for. As regards the first technique, in the following section we introduce an improvement of the technique presented in [17] and [18]. Subsequently we analyze the effectiveness of the two different techniques versus the statistical properties of the jitter and the different P_QoS requirements. 3. Source site jitter compensation by jitter prediction The jitter pdf can be reshaped by varying the information unit retrieval times at the source site. To do so, the retrieval times are modified in such a way as to compensate for the jitter values predicted at the source site. If we use ji ( n ) to indicate the jitter value of IUi(n) predicted at the source site and establish that the time instant at which IUi(n) is retrieved and prepared for transmission at the source site, t_txi(n), be replaced by [t_txi(n) - ji ( n ) ], the residual jitter, j_ ri ( n ) , is the jitter prediction error, that is: j_ ri ( n ) = e i ( n ) = j i ( n ) − j i ( n ) (5) At the source site the predicted jitter value can be calculated by an optimal predictor [26], that is, one which is able to minimize the prediction error variance. To achieve this, the predictor uses the values of the jitter the previous IUs underwent and the destination site therefore has to notify the source site of the arrival time, t_rxi(n), of each of the IUs it has received. The information units that the destination sends back to the source for this purpose are called Feedback Information Units (FIUs). More specifically, when the FIUi(n) arrives at the source site, the jitter that was suffered by the IUi(n) is calculated from relation (1) taking into account the variation that has been made on the retrieval time for IUi(n), that is: (6) ji(n) = t_rxi(n) - [t_txi(n) - ji ( n ) ]- d i On account of the propagation time for the IUs and corresponding FIUs, when the jitter for IUi(n+1) has to be predicted at the source site the jitter values for the IUs immediately preceding it may not be available. The predictor to be used has to be able, therefore, to make a prediction more than one step ahead. If, for example, when IUi(n+1) has to be emitted FIUs up to the (n-L)-th have been received, it will be necessary to make a prediction (L+1) jitter samples in advance. Obviously, the lower the value of L the more reliable the prediction will be [26]. The best prediction is obtained when L=0, i.e. when FIUi(n) arrives back at the source site before IUi(n+1) is retrieved. In this case a linear predictor can be used [26]. To achieve a certain prediction efficiency it may be necessary to limit the value of L. Assuming the processing times at the destination and source sites to be negligible, once the statistical features of the network delay have been fixed, this condition will have an impact on the “synchronization granularity” [10]. It imposes a constraint, in fact, on the minimum size of the IU and thus on the minimum time interval between the retrieval times of two consecutive IUs. It should be noted, however, that in any case an FIU received late at the source site is used to update the history of the jitter values and is then used in subsequent predictions. In the light of what has been said so far, for each media the steps of the prediction-based jitter compensation algorithm we propose are therefore the following:

• at the destination site, for each IU received, the arrival time is embedded in an FIU and fed back to the relevant source; • at each source site, the predicted jitter value is calculated on the basis of the jitter values available and the retrieval time of the next IU is calculated in such a way as to compensate for the predicted jitter value. Whenever an FIU arrives the predicted jitter value and the retrieval time are recalculated. If the jitter is a wide-sense stationary random process, the order of prediction is sufficiently high and an optimal predictor is used, the jitter prediction error, e i ( n ) , and therefore the residual jitter, can be regarded as white noise [26]; that is, it is practically uncorrelated, has a Gaussian pdf and the jitter prediction error variance, σ 2i,e , indicates achieved jitter pdf reshaping. 4. P_QoS control As we saw in Section 2, the P_QoS requirements are specified by parameters defined as: P_QoSM = [JM,max, εM] for the master P_QoSS = [SS,max, εS] for each slave To meet the P_QoS requirements, therefore, any jitter compensation mechanism has to take two steps: in the first it has to fit the master requirements defined by relation (4a) or (4a’); in the second it has to meet the slave requirements defined by relation (4b) or (4b’). In this section we discuss how to set the value of the parameters of the synchronization techniques we are dealing with, that is the compensation buffer size to be used and the jitter prediction error variance to be achieved. We consider the P_QoS requirements specified in (4), but the same line of reasoning can be followed starting from (4'). In addition, as far as the prediction-based mechanism is concerned, we will not consider different types of predictors since it is beyond the scope of this paper; we will only assume use of an optimal predictor, that is, one which is able to minimize the prediction error variance. Finally, as the effectiveness of the two jitter compensation mechanisms depends on the jitter statistical properties, we henceforward assume that the jitter has either a bell-shaped pdf that can be approximated with a Gaussian pdf, or a uniform pdf in the interval [-∆i, ∆i]. In any case, the reasoning followed below can easily be extended to other types of jitter pdf. Obviously it is not necessary to apply any jitter compensation mechanism to the master stream when the jitter jM(n) is such that relation (4a), calculated with j_rM(n)=jM(n), holds. In both the jitter pdfs considered, this is linked to the jitter variance σ 2M . In fact, when the pdf of the jitter suffered by the master is uniform in the interval [-∆M, ∆M], for the following relation to hold 2 ⋅ (∆ M − J M ,max ) p{ j M ( n ) > J M ,max } = 1 − ≤εM (7) 2 ⋅ ∆M

σ

2 M

≤

J 2M ,max

3 ⋅ (1 − ε M )

2

(8)

∆2M must be true, as the jitter variance σ = [26] 3 If, on the other hand, the jitter pdf is Gaussian, no synchronization mechanism need be applied when J  p | jM ( n )| > J M ,max = 1 − 2 ⋅ Φ M ,max  ≤ ε M (7’)  σM  2 M

[

x

]

2 1 e − y dy is the error function [27]. To solve the inequality in (7') on the basis of where Φ(x) = ∫ 2π 0 the jitter variance, an approximated expression of this error function has to be used. We use Gitnik’s

approximation [28], according to which the inequality 2 ⋅ Φ( x ) ≥ 1 − ε M can be replaced by 2 e −0.619536⋅x ≤ 2 ⋅ ε M − ε 2M in which the term of the second order is neglected. The inequality in (7') can therefore be rewritten as: −0.619536 ⋅ J 2M ,max σ 2M < (8’) ln(2 ⋅ ε M ) So, when the jitter variance is such that relation (8) or (8') does not hold, it is necessary to compensate jitter suffered by the master stream. The same can be said for the slave stream. In fact, according to the definition of skew given in Section 2, the residual skew is the difference between the residual jitter of the master and the slave. Assuming that the jitters the different media undergo are statistically independent of each other, the residual skew pdf is given by the convolution between the residual jitter pdf's of the master and the slave. So, to guarantee the P_QOSS requirements, i.e. relation (4b), the following relation must hold + S S ,max +∞   p | sS,M ( n)| ≤ S S,max = ∫  ∫ f j_ rM (τ ) ⋅ f j_ rS (x + τ ) ⋅ dτ  ⋅ dx > 1 − ε S (9) − S S ,max  −∞  If relation (9), calculated with j_rS(n)=jS(n), does not hold, it will be necessary to apply a mechanism to compensate for the jitter the slave stream undergoes.

[

]

4.1 Intramedia synchronization of the master Let us suppose that the conditions defined by relation (8) or (8’) do not occur. In this case it is necessary to introduce a compensation buffer and/or reshape the jitter pdf by jitter prediction in such a way that the residual jitter satisfies relation (4a). Let us note that the residual jitter suffered by the master is: (10) j_ rM ( n ) = e M ( n ) = j M ( n ) − j M ( n ) when only the prediction-based mechanism is used, 0 if j M ( n ) ≤ 0.5 ⋅ b M  j_ rM ( n ) =  j M ( n) − 0.5 ⋅ b M if j M ( n ) > 0.5 ⋅ b M (11)  j ( n) + 0.5 ⋅ b if j M ( n ) < −0.5 ⋅ b M M  M when only the compensation buffer-based mechanism is used, and finally 0 if e M ( n ) ≤ 0.5 ⋅ b M  j_ rM ( n ) = e M ( n ) − 0.5 ⋅ b M if e M ( n ) > 0.5 ⋅ b M (12) e ( n ) + 0.5 ⋅ b if e M ( n ) < −0.5 ⋅ b M M  M where e M ( n ) = j M ( n ) − j M ( n ) , when the prediction-based mechanism followed by the compensation buffer is used. Below we discuss how to set the compensation buffer size to be used and/or the jitter prediction error variance to be achieved in order to meet the P_QoS requirements. Jitter Compensation by means of a Buffer

Fig. 3 is a schematic representation of the effect of the compensation buffer on the jitter pdf in the two cases considered - uniform pdf and Gaussian pdf. If the jitter pdf is uniform, the residual jitter pdf for the master, j_rM(n), is given by:  bM if x = 0 2 ⋅ ∆  M f j_ rM (x) =   1 if 0 < x ≤ (∆ M − 0.5 ⋅ b M )  2 ⋅ ∆ M where bM is the size of the compensation buffer inserted into the master stream and, obviously, ∆ M > 0.5 ⋅ b M . Therefore, for the following relation to hold: p{ j_ rM ( n ) > J M ,max } = 1 − bM ≥ 2 ⋅

[

0 .5⋅b M

∫f

j _ rM −0 . 5⋅b M

( x)dx ≤ ε M

3 ⋅ (1 − ε M ) ⋅ σ M − J M ,max

]

(13)

must be true. If, on the other hand, the jitter pdf of the master is Gaussian, the residual jitter pdf is given by:   bM  if x = 0  2 ⋅ Φ 2 ⋅ σ   M  f j_ rM (x) =  ( x + 0.5⋅b M )2  1 e 2⋅σ M if x ≠ 0   2π ⋅ σ M So, to obtain + 0.5 ⋅ b M  J p | j_ rM ( n )| > J M ,max = 1 − 2 ⋅ Φ M,max  ≤ εM σM   again using Gitnik's approximation [28], simple calculations yield

[

]

f jM ( x )

f j _ rM ( x)

(a) −∆Μ

∆Μ -0.5·bM

0.5·bM

f jM ( x )

-0.5·bM

−∆Μ+0.5·bM

∆Μ−0.5·bM

compensation buffer

f j _ rM ( x )

(b)

0.5·bM

Fig. 3: jitter pdf - f jM ( x ) - and residual jitter pdf - f j _ rM ( x ) - after buffer compensating for all the jitter values of the IUs contained in the interval [-0.5·bM, 0.5·bM], when the jitter pdf is uniform (a) and Gaussian (b).

f j _ rM ( x )

f jM ( x )

−∆ Μ

∆Μ

f jM ( x )

−∆ Μ

prediction-based jitter compensation mechanism

∆Μ

f j _ rM ( x )

Fig. 4: jitter pdf - f jM ( x ) - and residual jitter pdf - f j _ rM ( x ) - after application of the predictionbased jitter compensation mechanism.

 ln(2 ⋅ ε M )  bM ≥ 2 ⋅  ⋅ σ M − J M ,max  (13')  −0.619536  As can be observed from relations (13) and (13'), the compensation buffer size needed for the P_QoSM requirements to be met is smaller in the case of a uniform jitter pdf than in the case of a Gaussian jitter pdf, provided that εM is less than 10-1. Jitter Compensation Using the Prediction-based Mechanism As we said above, if the jitter is a wide-sense stationary process, an optimal predictor is used and the order of prediction is sufficiently high, the jitter prediction error eM(n) can be regarded as white noise, that is, the residual jitter of the master is practically uncorrelated and has a bell-shaped pdf which can be approximated by a Gaussian pdf despite the initial shape (as in Fig. 4). So, in the case of both jitter with a uniform pdf and jitter with a Gaussian pdf, the residual jitter pdf is given by: x2

f j _ rM ( x ) =

1 2⋅σ e M ,e 2π ⋅ σ M ,e

where σ 2M ,e is the jitter prediction error variance. To satisfy relation (4a), the following must hold: J  p | j_ rM ( n )| > J M ,max = 1 − 2 ⋅ Φ M ,max  ≤ ε M (14)  σ M ,e  The problem of guaranteeing a certain P_QoS for master intramedia synchronization can be replaced by the problem of reshaping the jitter pdf of the master in such a way that the jitter prediction error variance, σ 2M ,e , is such as to satisfy relation (14). Again using the Gitnik’s approximation of the error function, from (14) we obtain that the prediction error variance to be achieved has to be: −0.619536 ⋅ J 2M ,max 2 σ M ,e ≤ (15) ln(2 ⋅ ε M )

[

]

Jitter Compensation Using the Prediction-based Mechanism and the Buffer Use of the compensation buffer alone may lead to excessively long buffers and unacceptable end-to-end delays. On the other hand, the effectiveness of the prediction technique depends on both the jitter correlation degree [26] and the network delay because, as we said, the latter determines how far in advance prediction needs to be made (i.e. the value of L). Both factors are decisive for the value of the jitter prediction error variance, σ 2M ,e , that the prediction-based mechanism can reach. For this reason it may be necessary to combine the two techniques by introducing a compensation buffer after the prediction-based jitter compensation mechanism. In this case the residual jitter pdf is of the kind shown in Fig. 5. It is expressed by:   bM   if x = 0 2 ⋅ Φ  2 ⋅ σ M ,e   f j_ rM (x) =  ( x + 0.5⋅b M )2  1 2⋅ σ M , e e if x ≠ 0   2 π ⋅ σ M ,e To meet the P_QoS requirement for the master intramedia synchronization, i.e. to meet relation (4a), the following must hold: J + 0.5 ⋅ b M  p | j_ rM ( n )| > J M ,max = 1 − 2 ⋅ Φ M,max  ≤ εM σ M ,e  

[

]

Again using the Gitnik’s approximation, we obtain that the jitter prediction error variance σ 2M ,e and the size of the compensation buffer bM now have to satisfy the relation: 2 −0.619536 σ 2M ,e ≤ J M ,max + 0.5 ⋅ b M ) (16) ( ln(2 ⋅ ε M ) So the value of bM in (16), that is, the size of the buffer that has to be inserted on the master stream, has to be chosen in such a way that the prediction-based mechanism is able to supply a value for σ 2M ,e which will satisfy relation (16). Of course, the larger the compensation buffer the greater the admissible value for σ 2M ,e , and therefore the less pdf reshaping the prediction-based mechanism has to do, and vice versa. It is worth remarking that in some cases the prediction-based mechanism does not reduce the

f jM ( x ) feM (x)

f j _ rM ( x )

compensation buffer

(a)

f jM ( x )

prediction-based technique

-0.5·bM

0.5·bM

(b)

(c)

∆Μ

-∆Μ

(a)

Fig. 5: jitter pdf - f jM ( x ) - (a), jitter prediction error pdf - f e M ( x ) - (b), residual jitter pdf f j _ rM ( x ) - after the compensation buffer (c).

compensation buffer size, so it is counterproductive. This happens when the jitter prediction error variance is greater than the jitter variance or when, with bounded jitter, the effect of prediction is an increase in the bounds of the jitter which is not compensated by an adequate reduction in the jitter prediction error variance. These occurrences depend on the level of correlation of the jitter, on its pdf and, if the latter is bounded, on the values of the P_QoS requirements. In fact, with reference to the two jitter pdf's considered, the prediction-based mechanism is counterproductive when: 2 −1.8586 ⋅ (1 − ε M ) 2 σ M,e ≥ σ 2M if the jitter pdf is uniform (17) ln(2 ⋅ ε M )

σ 2M , e ≥ σ 2M

if the jitter pdf is Gaussian

(17')

4.2 Intermedia synchronization between master and slaves After meeting the P_QoS requirements for master intramedia synchronization, the jitter compensation mechanisms have to act in such a way as to ensure the P_QoS requirements concerning the skew between the master and the slaves. As in the case of intramedia synchronization for the master, this is achieved by reshaping the slave jitter pdf introducing a compensation buffer and/or using the prediction-based jitter compensation mechanism so that relation (4b) is met. The aim of this section is to identify, for each slave, the jitter prediction error 2 and/or the size bS of the compensation buffer to be introduced in order to meet variance σ S,e relation (4b). Table 1 summarizes the pdf of the residual jitter after application to both the master or the slave of the compensation buffer alone, the prediction-based jitter compensation mechanism alone, or both techniques, in the two jitter pdf cases hypothesized. As mentioned previously, according to the definition of skew given in Section 2 and assuming that the jitters the different media undergo are statistically independent of each other, the residual skew pdf of the slave with respect to the master is given by: fs _ rS, M ( x ) =

+∞

∫f

j _ rM

(τ ) ⋅ f j _ r ( x + τ ) ⋅ dτ S

(18)

−∞

To guarantee the P_QOSS requirements, i.e. for relation (4b) to hold, relation (9) must hold. Since the jitter pdf reshaping and/or the compensation buffer related to the master have already been determined in such a way that the P_QoSM requirements are met, the integral in relation (9) can be solved numerically, thus determining the values of the jitter prediction error variance, σ 2S, e , and/or the size, bS, of the compensation buffer to be applied to the slave stream so as to ensure that the P_QoSS requirements are met. If the residual jitter pdf of the master and slave are both Gaussian, as for instance when the prediction-based mechanism alone is used for both the master and the slave, it is possible to obtain an approximate analytical expression of the integral in (9). In fact, from (9) we have [27]:  S S,max   > 1− εS P | sS, M ( n)| ≤ S S,max = 2 ⋅ Φ (19)  σ M ,e + σ S,e  from which we obtain the prediction error variance of the slave jitter as a function of both the prediction error variance of the master jitter and the maximum value of skew defined in (4b), that is:

[

]

2

 − 0.619536 ⋅ SS2 ,max  σ <  − σ M ,e  (20) ln(2 ⋅ ε S )   So, to meet the P_QoS requirements for intermedia synchronization, in the case being examined it is necessary to reshape the slave jitter pdf in such a way that the prediction error variance meets relation (20). 2 S ,e

5. A case study In order to gain a clearer understanding of how to apply the two synchronization mechanisms so as to guarantee the P_QoS requirements, and show up the application limits of the two mechanisms, we will now discuss a case study. We will refer to a generic multimedia retrieval service comprising a master and a slave stream and, as in the previous sections, we will consider two kinds of jitter pdf - uniform and Gaussian. We assume that the jitter autocorrelation sequence for both streams has an exponential trend, that is R ii ( m) = σ 2i ⋅ α im , i=S,M, with 0 < α i < 1 An exponential autocorrelation sequence was used to make the long-term prediction error variance, σ 2i,e , independent of the prediction order when a linear predictor is used. In this case it is [26]: σ 2i, e = σ 2i ⋅ (1 − α 2i )

i=M,S

(21)

and is the minimum jitter prediction error variance value that the prediction-based mechanism can reach. In (21) the value of αi can be set so as to represent various levels of jitter correlation (e.g. αi=0.9 for a highly correlated jitter, αi=0.75 for a jitter with medium correlation and αi=0.5 for a jitter with low correlation). First of all let us deal with the problem of intramedia synchronization of the master stream. In the case of uniform jitter pdf, from relations (15) and (21) it is seen that the prediction-

uniform jitter pdf compensation buffer

prediction-based mechanism prediction-based mechanism + compensation buffer

 bi 2 ⋅ ∆  i f j_ ri (x) =  1   2 ⋅ ∆ i

if x = 0 if 0 < x ≤ (∆ i − 0.5 ⋅ bi )

Gaussian jitter pdf   bi  if x = 0  2 ⋅ Φ  2 ⋅ σi   f j_ ri (x) =  ( x + 0.5⋅ b i ) 2  1 e 2 ⋅σ i if x ≠ 0  π ⋅ σ 2  i x

f j _ ri ( x) =

2

1 2 ⋅σ e i,e 2π ⋅ σ i, e

  bi   2 ⋅ Φ  2 ⋅ σ i ,e   f j_ ri (x) =  ( x + 0.5⋅b i )2  1 2 ⋅σ i , e e   2 π ⋅ σ i ,e

if x = 0 if x ≠ 0

Table 1: residual jitter pdf after application of the compensation buffer, the prediction-based jitter compensation mechanism or both (i=M,S).

based mechanism would in no case be able to guarantee the master synchronization requirements on its own, i.e. it would never be able to supply a jitter prediction error variance value such as to meet relation (4a), when: −0.619536 ⋅ J 2M ,max 2 αM < 1− (22) σ 2M ⋅ ln(2 ⋅ ε M ) If, on the other hand, −0.619536 ⋅ J 2M ,max α 2M ≥ 1 − (23) σ 2M ⋅ ln(2 ⋅ ε M ) the prediction-based mechanism alone may be able to guarantee the master synchronization requirements as long as the predictor can supply a jitter prediction error variance that meets relation (15). Still in the case of uniformly distributed jitter, from relations (17) and (21) it can be seen that the compensation buffer alone must be used to meet the P_QoSM parameters when: 2 . −18586 ⋅ (1 − ε M ) 2 (24) αM ≤ 1− ln(2 ⋅ ε M ) From Table 2, which gives some αM values for various εM according to relation (24), it can be observed that it is always necessary to use the compensation buffer alone, unless the jitter is highly correlated or high εM values are admitted. εM=10-1 εM=10-2 εM=10-3 εM=10-4 εM=10-5 εM=10-6 εM=10-7

αM αM αM αM αM αM αM

≤ ≤ ≤ ≤ ≤ ≤ ≤

0.254 0.731 0.837 0.884 0.910 0.926 0.938

Table 2: αM values for which it is convenient to use the compensation buffer alone when the jitter pdf is uniform.

Again in the case of uniform jitter pdf, when 2 . −0.619536 ⋅ J 2M ,max −18586 ⋅ (1 − ε M ) 2 1− 1 < αM < − ln(2 ⋅ ε M ) σ 2M ⋅ ln(2 ⋅ ε M ) it is useful to use a combination of the two techniques to guarantee the intramedia synchronization requirements for the master. If, on the other hand, the jitter pdf is approximated with a Gaussian pdf, from relations (17') and (21) we deduce that the prediction-based jitter compensation mechanism always has a positive effect. The prediction error variance is, in fact, always lower than the jitter variance [26]. By way of example, let us consider a master stream which undergoes a jitter with a Gaussian pdf and a variance of σ 2M =100 ms2. If we chose to use the buffer-based jitter compensation mechanism alone to obtain JM,max=30 ms and εM =10-3, εM =10-4 or εM =10-5, from relation (13') we would obtain the following compensation buffer size values: εM =10-3 bM≥3.4 ms

εM =10-4 bM≥14.2 ms

εM =10-5 bM≥23.6 ms

It is pointed out that the compensation buffer size obviously does not depend on the level of jitter

correlation. If, on the other hand, the prediction-based mechanism alone is used to obtain the same values for JM,max and εM, from relation (15) the residual jitter variance, i.e. the jitter prediction error variance, must be: εM =10-3 σ 2M ,e ≤89.7 ms2

εM =10-4 σ 2M ,e ≤65.5 ms2

εM =10-5 σ 2M ,e ≤51.5 ms2

From relation (22) it can be deduced that by means of an optimal predictor it is possible to obtain these desired values for σ 2M ,e , in the three cases considered if αM=0.9 or αM=0.75. If, on the other hand, αM=0.5 and εM =10-4 or εM =10-5, the prediction error variance cannot be lower than the values indicated above so it is necessary to use a compensation buffer as well. Relation (16) provides the relation between the size of the compensation buffer and the jitter prediction error variance needed to guarantee the P_QoSM requirements. For example, if αM=0.5 and we choose a single σ 2M ,e value and varying εM value, possible choices would be those given in the following.

σ 2M ,e ≤76 ms2

εM =10-4 bM=4.6 ms

εM =10-5 bM=13 ms

σ 2M ,e ≤85 ms2

bM=8.4 ms

bM=17 ms

σ 2M ,e ≤90 ms2

bM=10.4 ms

bM=19.4 ms

σ 2M ,e ≤95 ms2

bM=12.2 ms

bM=21.4 ms

σ 2M ,e ≤99 ms2

bM=13.8 ms

bM=23.2 ms

Similar considerations are valid if we consider a uniform jitter pdf. If, for instance, the jitter variance is σ 2i,δ =2700 ms2 and we want to obtain JM,max=60 ms, from relations (13), (15) and (16) we obtain the jitter prediction error variance and compensation buffer size values given in Table 3. In the table null bM values mean that the necessary reshaping of the jitter pdf can only be achieved by the prediction-based jitter compensation mechanism. The rows in which only bM appears indicate the value bM needed to guarantee P_QoSM requirements with the compensation buffer alone. Cells marked with "--", on the other hand, indicate cases in which the prediction-based mechanism cannot be used. By using the compensation buffer alone it results from (13), in fact, that bM = 42 ms if εM =10-1, bM = 58 ms if εM =10-2, and bM ≅ 60 ms if εM ≤10-3. The jitter prediction error variance that the predictor is able to supply depends not only on the degree of jitter correlation but also on how far in advance the prediction has to be made, i.e. on the value of L [26]. In general, once the statistical properties of the jitter have been fixed, if a certain jitter prediction error variance value is to be obtained it is necessary to limit the value of L [26]. If the prediction is to be made at most L samples ahead, the FIUM(n) has to arrive before IUM(n+L) is retrieved. In this case, assuming for the sake of simplicity that the network delay between the source and the destination sites is the same as that between the destination and source, i.e. that the network delay a generic IU undergoes is the same as that suffered by the corresponding FIU, the following must hold: L

∑T i =1

IU M

( n + i) = t _ tx M ( n + L ) − t _ tx M ( n ) ≥ 2 ⋅ d M + e M ( n ) + jM ( n ) + jM ( n + L )

(25)

-1 εM = 10 bM=0 σ 2M ,e ≤1385.8

αM=0.9

bM=0

σ 2M ,e ≤756

bM=18.2

σ 2M ,e ≤756

bM=54.2

σ 2M ,e ≤1385.8

bM=0

σ 2M ,e ≤864

bM=27.6

--

--

σ 2M ,e ≤1647

bM=10.8

--

--

--

--

σ 2M ,e ≤2403

bM=38

--

--

--

--

--

bM≥60 --

≤1385.8

bM≥42 bM=0

σ

≤1215

bM≥58 bM=55.2

σ 2M ,e ≤1385.8

bM=0

σ 2M ,e ≤1242

bM=57.2

--

--

σ 2M ,e ≤1385.8

bM=0

--

--

--

--

σ 2M ,e ≤1782

bM=16

--

--

--

--

σ 2M ,e ≤2457

bM=39.8

--

--

--

--

bM≥42 bM=26

--

bM≥58 --

--

bM≥60 --

σ 2M ,e ≤2295

bM=34.4

--

--

--

--

σ 2M ,e ≤2430

bM=39

--

--

--

--

2 M ,e

σ αM=0.5

-3 εM = 10 bM=27.2 σ 2M ,e ≤540

σ 2M ,e ≤1385.8

σ αM=0.75

-2 εM = 10 bM=0 σ 2M ,e ≤570.1

2 M ,e

≤2052

bM≥42

2 M ,e

bM≥58

bM≥60

Table 3: Jitter prediction error variance and compensation buffer size necessary to guarantee the P_QoSM requirements with various correlation levels when the jitter pfd is uniform (σ 2M =2700 ms2 and JM,max=60 ms).

This condition therefore affects the value of the interarrival time at the source site for IUs, and thus the size of the IUs. If we consider that the master stream is a continuous media [6], i.e. that TIU M ( n) = cons tan t = TIU M , relation (25) is equivalent to: 2 ⋅ d M + e M ( n ) + jM ( n ) + jM ( n + L) TIU M ≥ (26) L Obviously, the higher the value of L the higher the prediction error variance that the predictionbased mechanism is capable of supplying. For example, in the case of jitter with a Gaussian pdf, a variance of σ 2M =100 ms2 and an average degree of correlation (αM=0.75), if relation (26) is satisfied with L=1, from relation (22) it is possible to obtain a jitter prediction error variance value of σ 2M ,e =45 ms2; if, on the other hand, relation (26) holds for L=2, by means of an 8th-order predictor [26] we would get σ 2M ,e =63 ms2. In the first case the prediction-based mechanism alone can guarantee P_QoSM=[JM,max=30, εM =10-5], whereas in the second case it is necessary to introduce a compensation buffer such that bM = 8 ms. We will now analyze intermedia synchronization between the master and the slave. As we saw in the previous section, guaranteeing intermedia synchronization requirements means reshaping

the jitter pdf for the slave, taking into account what has been done to the master. In other words, having fixed the values of P_QoSS=[JS,max, εS], the synchronization mechanisms, the predictionbased mechanism and/or the compensation buffer-based one have to perform reshaping in such a way that relation (9) is satisfied. For this reshaping the considerations made for the master stream still hold, i.e. intermedia synchronization is ensured by the intramedia synchronization of the slave stream. It should, however, be pointed out that the same P_QoSM parameters can be obtained by choosing different combinations of jitter prediction error variance and compensation buffer size values for the master stream, correspondingly, the same P_QoSS parameters can be obtained by choosing different combinations of jitter prediction error variance and compensation buffer size values for the slave stream, the values of which depend on what was done to the master stream. As we have defined the compensation buffer size as the maximum IU jitter variation it can compensate for, it is obvious that, for a given bi, i=S,M, the size of that buffer in cells is greater the higher the average bit rate of the source is. So, in making the choice it is necessary to consider that if, for example the average bit rate of the slave is much greater than the average bit rate of the master, the choice of a smaller compensation buffer on the slave has the advantage of breaking down the size of the buffer for the monomedia stream with the greatest load.

6. Conclusions In this paper we have discussed two different techniques for jitter compensation aiming at guaranteeing intra/intermedia synchronization requirements in a distributed multimedia retrieval service: the first is based on prediction of the jitter suffered by each information unit and the second on a compensation buffer at the destination site. A comparison between the two techniques has been made, in a scenario in which monomedia streams are represented by one master stream and one or more slave streams. Moreover, the use of the two techniques combined has been studied.

ATM di ∆i ei(n) εM εS FIU FIUi(n) Φ(x) i IU IUi(n) bi ji(n) j_ri(n) j ( n) i

JM,max

List of acronyms and symbols Asynchronous Transfer Mode average network delay of the i-th media maximum delay jitter provided by the network (i=M master, i=S slave) when the jitter pdf is uniform prediction error of network delay jitter suffered by the n-th IU of the i-th media maximum admissible probability that jitter will exceed JM,max maximum admissible probability that skew will exceed SS,max Feedback Information Unit n-th FIU of the i-th media error function index of the generic i-th media. i=M means master stream, i=S means slave stream Information Unit n-th IU of the i-th media size of the compensation buffer (i=M master, i=S slave) network delay jitter of the n-th IU of the i-th media residual jitter of the n-th IU of the i-th media the predicted network delay jitter value of the n-th IU of the i-th media maximum admissible network delay jitter for master

N P_QoS P_QoSi Rjj(m si,k(n) s_ri,k(n) sti SS,max σ 2i σ 2i , e t_rxi(n) t_txi(n)

number of monomedia stream which make up the multimedia stream Perceived Quality of Service Perceived Quality of Service parameters (i=M master; i=S slave) autocorrelation sequence of the jitter of the i-th media skew between the n-th IUs of the media "i" and "k" residual skew between the n-th IUs of the media "i" and "k" starting times for the i-th source maximum admissible skew between master and slave variance of the network delay jitter suffered by IUs of the i-th media long term jitter prediction error variance of the i-th media delivery time of the n-th IU of the i-th media at the destination site retrieval time of the n-th IU of the i-th media when no jitter compensation mechanism is used

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