- Email: [email protected]
Adaptive traffic smoothing for live VBR MPEG video service
Computer Communications 21 (1998) 644–653
Adaptive traffic smoothing for live VBR MPEG video service Jin-soo Kim*, Jae-kyoon Kim Department of Electrical Engineering, KAIST 373-1 Kusong-dong, Taejon 305-701, South Korea Received 31 October 1997; received in revised form 16 January 1998; accepted 16 January 1998
Abstract In this paper, we propose an online source traffic smoothing algorithm, that can be effectively used in live video applications such as visual lectures or television news. For a practical implementation, firstly, we describe the constraints imposed by the delay bound at the sender side, and by the sender/receiver buffer sizes. Then, by using these constraints, the proposed algorithm is designed in such a dynamic way as to smooth maximally the transmission rate. Through experimental results, it is shown that the proposed scheme is effective in reducing the peak rate, temporal variations, and effective bandwidth of a given video stream. Particularly, it is noted that the proposed algorithm can be used in some applications where overall buffer sizes are finite or asymmetrically located. q 1998 Elsevier Science B.V. Keywords: Online traffic smoothing; Buffer constraints; Live VBR MPEG video
1. Introduction In the near future, it is expected that many emerging multimedia applications will rely on the efficient transmission of VBR-coded MPEG video streams. Recently, as one way to provide VBR-coded services, some works have dealt with source traffic smoothing methods [1–12], which are based on the introduction of delay and rate buffering between the video encoding and decoding processes. In Ref. [2], the problem of online traffic smoothing satisfying a delay bound was analyzed, assuming that all coded-frame sizes are known a priori. Based on Ref. [2], the improved algorithm in Ref. [3] was developed using a lookahead parameter and the number of frames with known codedframe sizes as well as frame delay at the sender, but this algorithm didn not consider buffer sizes at the sender and receiver sides. On the other hand, several transmission techniques of a prerecorded video source such as VoD applications have been addressed in Refs. [8–12]. In these applications, by capitalizing on prior knowledge of the coded-frame sizes for the entire video, these techniques can smooth traffic on a large time scale by prefetching frames into a receiver buffer in advance of bursts of large frames. In contrast to prerecorded video applications, live video services such as visual lectures or television news typically have the limited * Corresponding author. Tel.: 0082 42 869 5418; fax: 0082 42 869 8018; e-mail: [email protected]
0140-3664/98/$19.00 q 1998 Elsevier Science B.V. All rights reserved PII S 01 40 - 36 6 4( 9 8) 0 01 3 5- 2
knowledge of coded-data sizes and finite buffer sizes in the sender and receiver sides. As a result, live video applications require dynamic techniques that can react to changes in coded-frame sizes and the available buffer sizes. For live VBR video services, Reibman and Haskell studied constraints imposed by buffer sizes and transmission rates in Ref. [1]. But, they focused on the encoder rate control to prevent overflow and underflow at the sender and receiver buffers. In this paper, based on the works in Refs. [1,3,6], we develop an online traffic smoothing algorithm that can be effectively applicable for delaytolerant live video services such as visual lectures or television news. In these applications, receivers may be willing to tolerate a playback delay of several seconds in exchange for a smaller bandwidth requirement. First, for practical implementations, we describe constraints imposed by the delay bound, and by the sender/receiver buffer sizes. Then, by using these constraints, we propose an online source traffic smoothing algorithm that makes transmitted data maximally smooth, while dynamically controlling the data so that overflow and underflow may be avoided [13]. This paper is organized as follows. In Section 2, we present the system model and the notations used in this paper, and briefly review relationships between the buffer sizes and the transmitted data sizes. In Section 3, first we describe constraints imposed by the receiver buffer size, the delay bound, and the sender buffer size on the transmitted data sizes. Then, based on these constraints an online traffic smoothing algorithm which control adoptively the outgoing
J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
645
Fig. 1. An overview figure for adaptive source traffic smoothing.
transmission rate of the sender buffer. In Section 4, the experimental results are presented and it is shown that the proposed algorithm are effective at reducing the peak rate, coefficient of variation, and effective bandwidth of a live VBR coded-MPEG stream. Finally, a conclusion is given in Section 5.
2. Basic assumptions and notations
j X i¼1
1
s(i) ¹
j X
r(i), for j . 0
¼
j X
Xj
i ¼ 1 r(i)for0
r(i) ¹
jX ¹ Dr
. j # Dr
(2)
s(i) for j . Dr
i¼1
i¼1
From Eqs. (1) and (2), two different forms of B r(j) can be written for j . D r as follows j X
Br (j) ¼
In Fig. 1, the situation in an online traffic smoothing system is shown as a simplified block diagram. Let s(j) be the number of generated bits in the interval [(j ¹ 1)Dt, jDt), where Dt is the duration corresponding to one uncoded frame interval. It is assumed that s(i) is uniformly fed to the sender buffer during this time interval. Additionally, the size of decoding data package(receiver buffer readout package) is assumed to be same as the generated-data size by encoding per frame. Similarly, let r(j) be the number of bits that are uniformly transmitted into the network in the interval [(j ¹ 1)Dt, jDt). The value of r(j) depends on the nature of the sender and receiver buffer fullness, as well as the delay bound. Let us define D sDt as the allowable delay bound with which a specific coded-frame data can be stayed in the sender buffer [1]. It means that the sender side must terminate transmitting a specific coded-frame data within D sDt into network, after the first bit of that data is generated. Let us define D rDt as the decoding startup latency at the receiver side1. As expressed in Ref. [1], based on the above definitions and assumptions, the sender and receiver buffer fullness at time jDt; B s(j) and B r(j) can be expressed as Bs (j) ¼
Br (j) ¼
s(i) ¹ Bs (j)
(3)
i ¼ j ¹ Dr þ 1 j X
¼
r(i) ¹ Bs (j ¹ Dr ), for j . Dr
(4)
i ¼ j ¹ Dr þ 1
We note that in order to guarantee lossless online smoothand 0 # Br (j) # Bsize ing, the conditions of 0 # Bs (j) # Bsize s r size must be satisfied for all j, where Bs and Bsize represent the r sizes of sender and receiver buffers, respectively. Hence, from Eqs. (3) and (4), we obtain simple boundaries of partial sums over D rDt intervals. j X
size s(i) # Bsize s þ Br
(5)
size r(i) # Bsize s þ Br , for j $ Dr
(6)
i ¼ j ¹ Dr þ 1 j X i ¼ j ¹ Dr þ 1 size must be large It means that overall buffer size Bsize s þ Br enough to absorb the variability of data generated, or transmitted during the delay bound. In other words, a larger value of D r facilitates a smoothing transmission of the given video, at the expense of a larger buffer requirement at the sender and receiver sides.
(1)
i¼1
In this paper, it is assumed for clarity that D s and D r are integer values(D r $ D s $ 1). In practice, since the largest expected network delay (t) should be considered, we assume that D r ¹ D s . t is satisfied. The network jitter can be considered by introducing additional buffer space at the receiver.
3. Proposed source traffic smoothing algorithm For a live video service, the sender side cannot perform traffic smoothing over the entire video stream. Because the amount of smoothing is limited by the coded-frame data in the given delay bound as well as the sizes of the sender and receiver buffers. From Eq. (4), it is shown that the
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transmission rate, r(j), depends on the past informations of r(j) as well as the sender and receiver buffer occupancies. From these points of view, we describe in detail the constraints imposed by: (i) the receiver buffer size; (ii) the delay bound; and (iii) the sender buffer size. Based on these constraints, a new dynamic r(j) decision algorithm is designed. 3.1. Constraint imposed by the receiver buffer size If the receiver buffer size is sufficiently large, the selection range of r(j) can be wide. But, in the real case that the receiver buffer size is small and fixed, the maximum value of r(j) is restricted by the overflow prevention condition of must be the receiver buffer. From Eq. (4), since Br (j) # Bsize r satisfied for all j, that is, j X
r(i) ¹ Bs (j ¹ Dr ) # Bsize for all j r
(7)
i ¼ j ¹ Dr þ 1
must be maintained. Hence, the maximum value of r(j) is bound as follows, ( ) jX ¹1 max size r(i), 0 r (j) ; max Br þ Bs (j ¹ Dr ) ¹ i ¼ j ¹ Dr þ 1
(8) or by using Eq. (1) in Eq. (8), ( rmax (j) ; max þ
Bsize r Bs (j ¹ 1) ¹
jX ¹1
departure time ¹ buffer entering time # Ds Dt Therefore, (j ¹ 1)Dt þ
s¯(j ¹ J) Dt ¹ bj ¹ J Dt # Ds Dt r(j)
(j ¹ 1)Dt þ
s(j ¹ J þ 1) s¯(j ¹ J) Dt ¹ bj ¹ J þ 1 Dt # Ds Dt Dt þ r(j) r(j) (11)
By extending this procedure to p frame data, a lower inequality for r(j) can be formally defined as s¯(j ¹ J) Ds þ bj ¹ J ¹ j þ 1
(9)
i ¼ j ¹ Dr þ 1
The underflow prevention of the receiver buffer can be replaced by the constraint on the delay bound, as explained in the next subsection. 3.2. Constraint imposed by the delay bound Fig. 2 shows the queueing structure in the sender buffer at time (j ¹ 1)Dt. The coded-frame data that waits for transmission in the sender buffer cannot wait longer than the delay bound (D sDt). In other words, the time interval for each batch of coded-frame data, between the time of the first bit entering the sender buffer and the time of last bit
(10)
where the new symbols are defined as follows: J is a value an integer less than D s and represent the queueing length at time (j ¹ 1)Dt in the sender buffer (see Fig. 2); s¯(j ¹ J) is the first data size which will be transmitted at (j ¹ 1)Dt and the remainder of s(j ¹ J) which was not transmitted before (j ¹ 1)Dt; b j¹j Dt represents the instantaneous time when the first bit of s¯(j ¹ J) has begun entering the sender buffer. The departing time of s¯(j ¹ J) may be the transmission starting time of s(j ¹ J þ 1). As soon as the transmission of s¯(j ¹ J) is terminated, in order to transmit s(j ¹ J þ 1) continuously at the same rate, r(j) the following inequality must be simultaneously satisfied as follows.
rL1 (j, 0) ;
) s(i), 0
departing the buffer must be less than D sDt, as specified in Section 2, i.e.
s¯(j ¹ J) þ r (j, p) ;
iX ¼p
Ds þ bj ¹ J þ p ¹ j þ 1
, 1 #p # J ¹1
iX ¼p
sˆ(j ¼ J þ i) , J#p Ds þ bj ¹ J þ p ¹ j þ 1
Bs (j ¹ 1) þ rL1 (j, p) ;
s(j ¼ J þ i)
i¼1
L1
(12)
i¼J
(13)
where, if p is equal to or greater than J, sˆ(j ¹ J þ p) is a value which is estimated by using the characteristics of pseudoperiodic patterns in the MPEG-coded video sequence. The coded-data size estimation method is proposed in detail in Section 3.4.
Fig. 2. Queueing structure in the sender and receiver buffers.
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3.3. Constraint imposed by the sender buffer In deciding the transmission rate, it is required that the sender buffer overflow and underfiow should be avoided. For these purposes, we describe the constraints imposed by the sender buffer size. Eq. (1) can be recursively written as Bs (j) ¼ Bs (j ¹ 1) þ sˆ(j) ¹ r(j), for j . 0
# r(j) # Bs (j ¹ 1) þ sˆ(j) Bs (j ¹ 1) þ sˆ(j) ¹ Bsize s
(15)
To obtain an identical transmission rate for the incoming hDt intervals, the following inequalities should be simultaneously satisfied. Bs (j ¹ 1) þ
hX ¹1
hX ¹1
$ max;h Bsize s
h¹1 Ds ¹ 1 X s(j þ k) h k¼0
The proof is completed. A Lemma 2. If the following inequality, that is, ( ) j X size sk , ;j Br $ max k ¼ j ¹ Dr þ 1
is satisfied, r ðj; hÞ # r max ðjÞ holds for ;h $ 1: Similarly, this proof is straightforward from Eqs. (9) and (18).
sˆ(j þ k) ¹ Bsize # h·r(j) # Bs (j ¹ 1) s
sˆ(j þ k), h $ 1
ð16Þ
k¼0
For convenience of explanation, from Eq. (16) let us define the upper bounds and the second lower bounds of r(j), which are a function of lookahead interval h, respectively. 9 8 hX ¹1 > > > > > > sˆ(j þ k) ¹ Bsize > > Bs (j ¹ 1) þ s = < k¼0 L2 , 0 , r (j, h) ; max > > h > > > > > > ; : h$1
ð17Þ
Bs (j ¹ 1) þ rU1 (j, h) ;
$ (j ¹ 1) should be satisfied for all j, the above Since Bsize s expression is written by
U1
k¼0
þ
respectively. Accordingly, in order that rL1 (j,p) $ r L2(j,h) is satisfied in all regions of h $ 1, we can obtain ( ) hX ¹1 Ds ¹ 1 size {B (j ¹ 1) þ s(j þ k)} Bs $ max;h Ds ¹ 1 þ h s k¼0
(14)
where sˆ(j) is a estimate value of s(j). Since 0 # Bs (j) # Bsize s must be satisfied for all j, the following inequalities can be written by
647
hX ¹1 k¼0
h
sˆ(j þ k) , h$1
(18)
where {ˆs(j þ k), k ¼ 0, 1, …} are estimated values by using the proposed method described in detail in the next subsection. It is noted that as h increases, the effect of the sender buffer size disappears gradually and r L2(j,h) get closer to the value of r U1(j,h). Additionally, in the case that Bsize is s not sufficiently large, r L2(j,h) tends to be more dominant than r L1(j,p) as h increases. But, in some applications with a sufficiently large sender buffer size, r L1(j,p) is always greater than r L2(j,h) for all p and h. From the above constraints, the following lemmas can be remarked. Lemma 1. If the inequality, that is, L1 L1 $ (D ¹ 1)max {s(j)} is satisfied, r (j,p) $ r (j,h) Bsize s s ;j holds for p $ J and h $ 1. Proof. From Eqs. (13) and (17), it is directly expressed as p ¼ h þ J ¹ 1 and bj ¹ j þ p Dt ¼ (h þ j ¹ 2)Dt for h $ 1,
3.4. The proposed coded-frame size estimation In this paper, it is assumed that {s(j þ k),k $ 0} are not known at time (j ¹ 1)Dt. Accordingly, in order to efficiently estimate the coded-frame sizes for future frames in Eqs. (13), (17) and (18), k-step linear predictor is used [15]. That is, s(j þ k) is estimated by using a linear combination of the previous values of s(j). Let us denote the value as sˆ(j þ k). Thus, Lth order linear predictor has the form: sˆ(j þ k) ¼
LX ¹1
w(l)s(j ¹ l)
(19)
l¼0
where w(l), for l ¼ 0,1,…,L-1, are the linear prediction filtering coefficients. The optimal linear predictor in the mean square sense is one which minimizes the mean square error, E{s(j þ k) ¹ sˆ(j þ k)}. The {w(l)} l¼0,…,L¹1 is found by adoptively solving the Wiener–Hopf equations at time (j ¹ 1)Dt [15]2. Since I, P, and B frame types have different statistical characteristics, we separate them and estimate s(j þ k) based on the each frame type. Besides, in the MPEG compression sense, since P and B frames exploit causal-temporal redundancies and noncausal temporal redundancies as well as spatial ones, respectively, the characteristics of bit rate may be significantly affected by a scene changed frame. Accordingly, in order to obtain the exact rate bounds for new coming P or B frames, it is necessary to detect whether scene change has occurred or not in s(j ¹ 1) at time (j ¹ 1)Dt (Fig. 3). There are many ways to detect a scene-changed frame from the past statistical informations [16,17]. But, in this paper, to facilitate implementation and reduce the computation 2 In this paper, to reduce computation load, we fixed L ¼ 3 for all experiments.
648
J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
Fig. 3. Typical example for four rate bounds.
complexity, the following simple decision method is used. if 0:85 3 Idata , s(j ¹ 1), else
scene changed not changed
where Idata is the data size generated by the most recently encoded I frame. Once s(j ¹ 1) is detected as a scenechanged frame, this data would not be used in estimating the coded-data sizes of new coming frames. 3.5. The proposed r(j) decision algorithm
else r min(j) ¼ max{r L1(j,p),p ¼ 0,…,J ¹ 1} and go to Step 2. Step 2. Let us define r L(j,h) ; max{r L1(j,J þ h ¹ 1), r L2(j,h),r min(j)} and r U(j,h) ; min{r U1(j,h), r max(j)}, respectively. If r L(j,1) . r U(j,1), then r(j) ¼ r max(j) and stop. else go to Step 3. Step 3. Find the largest integer H( , GOPsize) such that max rL (j, h) # min rU (j, h)
1#h#H
The proposed algorithm consists of two parts. First, the data which await for transmission within the sender buffer have to satisfy the delay constraints as well as the receiver buffer constraints. Second, the data which will arrive at the sender buffer does not have to give rise to overflow and underflow. In a dynamic way, a new r(j) decision rule is designed by using Eqs. (8), (12), (13), (17) and (18) as follows. Step 1. If there exists p satisfying r max(j) , r L1(j,p), as p increases from 0 up to J ¹ 1, let us denote P ¼ p,r P ¹ 1} and go to Step 2.
min
L1
(j) ¼ max{r (j,p),p ¼ 0,…,
1#h#H
If H ¼ GOPsize, then go to Step 4. else if max 1 # h # H r L(j,h) . r U(j,H þ 1), then r(j) ¼ max r L (j, h) 1#h#H
(20)
else r(j) ¼ min r U (j, h) 1#h#H
and stop.
(21)
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J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
Step 4. If r(j ¹ 1) # max 1 # h # GOPsizer L(j,h), then r(j) ¼
max
1#h#GOPsize
rL (j, h)
(22)
else if max 1 # h # GOPsizer L(j,h) # r(j ¹ 1) # min 1 # h # GOPsizer U(j,h), then r(j) ¼ r(j ¹ 1)
(23)
else r(j) ¼
min
1#h#GOPsize
rU (j, h)
(24)
and stop. In Step 1, a maximum value of r(j) is found based on the receiver buffer sizes and the delay bound constraint. In Step 3 and 4, a maximally smoothed value of r(j) is selected as shown in Fig. 4. That is, at every frame starting point, the proposed algorithm determines the longest trajectory for arrived and incoming coded-frames. Cosequently, this method results in a transmission trajectory that has the smallest possible peak rate requirement and the smallest rate change between adjacent different transmission rates.
The proposed algorithm is simple to implement for a practical application. But, as the value of D r increases, the computation burdens are increase linearly. From Eqs. (8), (9), (12), (17) and (18), it is easily found that the required computation burdens in the worst case are (3GOPsize þ 2D r þ 1) additive operations and (3GOPsize þ D r þ 1) multiplicative operations. Additionally, the computation burdens for finding the coded-frame sizes estimates by using Eq. (19) in the worst case are GOPsize·(3 3 3 matrix inversion þ 18 multiplicative þ 8 additive) operations are required. For a practical situation where the computation burden is extremely limited, it is necessary for the sender side to balance the trade-off between the computation loads and the efficiency in the bandwidth requirements. But, in the case that the sender and/or receiver buffer sizes are restricted on the above Lemma 1 and 2, it is noted that the proposed r(j) decision rule can be simplified.
4. Experimental results and performance evaluation 4.1. The experimental conditions The trace used in our experiments is the ‘news’ sequence which is composed of 40 000 frames [18]. The GOP pattern is given by (GOPsize, P-frame period) ¼ (12,3) where GOPsize is the distance between two successive I frames and P-frame period is the distance between I or P frame and the subsequent P frame. For more details about the encoder parameters, one may refer to Ref. [18]. In this paper, we conduct all experiments under the condition of D s ¼ D r ¹ 1, although various experimental situations can be established for performance evaluations. For a given D r, this paper determines the sender buffer size size, Bsize s , and the receiver buffer size, Br , by using the following relations: nXj (25) Bsize s ¼ as · max;j i ¼ j ¹ Dr þ 1 s(i)g, 0 , as # 1 ( Bsize r
¼ ar · max ;j
j X
) s(i) , 0 , ar # 1
i ¼ j ¹ Dr þ 1
where s(i) is the coded-frame data size of the ith frame in the given video trace. a s and a r represent the buffer multiplicative factors, which are introduced to investigate the smoothing effects that arise by changing the sender and receiver buffer sizes. As expressed in Eq. (5), we select a s, a r such that a s þ a r $ 1 should be satisfied. 4.2. The effects of buffer size
Fig. 4. Rate decision methods for Step 3 and 4 in proposed algorithm: (a) Eq. (20) in Step 3; (b) Eq. (21) in Step 3; (c) Step 4.
Fig. 5 demonstrates the benefits of increasing the buffer sizes in smoothing VBR MPEG video streams. As expected, this figure shows that under large buffer sizes a bursty behavior of the original traffic is significantly smoothed, since the smoothing ability can be extended as large as
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J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
Fig. 5. One segment of smoothed traffic.
the additional buffering space. These facts are obvious, especially in the regions that original stream has peaks in the same scene. In order to investigate the effects of the buffer sizes, we establish two different experimental scenarios: (i) the sender buffer size is fixed (a s ¼ 0.9) and the receiver buffer size is varying; (ii) the receiver buffer size is fixed (a r ¼ 0.9) and the sender buffer size is varying. Fig. 6 shows the experimental results obtained by using the proposed algorithm with D r ¼ 150. 4.2.1. The peak-to-average ratio (PAR) The PAR or peak rate is one of the measures that determines the worst-case bandwidth requirement for a piecewise CBR service. As shown in Fig. 6(a), the PAR is decaying for the increase of the sender and receiver buffer sizes and gets closer to a constant value which is independent of the buffer sizes. In extremely small buffer sizes (a s , 0.7, a r , 0.4), it is noted that the dependency of PAR on the sender buffer sizes is larger than the receiver buffer size. This is because the small sender buffer size the PAR is directly affected by the abrupt coded-frame sizes changes such as fast moving frames or scene changed frames. 4.2.2. The coefficient of variation(COV) The coefficient of variation (COV) is introduced as a measure to investigate and evaluate the temporal variations of the transmission rate around mean rate [3,5,14]. Fig. 6(b)
shows the characteristics of COV obtained from the above experiments. The decaying behavior of COV is similar to that of PAR and get to be independent of the buffer size in the large buffer size region, since the delay bound (r L1(j,p) in Section 3) becomes the major limitation on the ability to determine r(j). In the above experiments, it is observed that in the cases of extremely small buffer sizes(a s , 0.7, a r , 0.4), the buffer overflow is incurred mainly owing to the abrupt rate increases and the loss rates are in the range of 10 ¹4,10 ¹6. For more related results, one may refer to Ref. [6]. 4.3. The effects of delay bound In this subsection, the performance characteristics of a smoothed traffic in the proposed algorithm are investigated as a function of the delay bound. As we mentioned in Section 1 that the online smoothing scheme can achieve a smaller bandwidth requirement by introducing a large delay bound (D r), even with D r ¼ 30, a s ¼ a r ¼ 0.8, the proposed scheme reduces the PAR by 23.3% and the COV by 51.4%, respectively, over the original unsmoothed video stream. For performance comparisons of the proposed scheme, we consider the sliding window algorithm that operates on consecutive overlapping windows of size D r ¹ J in Fig. 2. That is, this algorithm computes the transmission rate, r(j), per Dt by averaging coded-frames in the range [j ¹ (D r ¹ J),j ¹ 1]. By using the notations in Section 3, the
J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
Fig. 6. Characteristics of COV and PAR according to the changes of buffer sizes in D r ¼ 150: (i) a s ¼ 0.9 is fixed and a r is varying; (ii) a r ¼ 0.9 is fixed and a s is varying. (a) PAR (peak-to-average ratio); (b) COV (coefficient of variation).
following form can be written as r(j) ¼
JX ¹1 i¼0
s(j ¹ J þ i Dr ¹ J þ i
(26)
Simply, we do not incorporate the future incoming framesizes with the above equation and we use a s ¼ a r ¼ 1.0 for this scheme [4,5]. 4.3.1. The peak-to-average ratio (PAR) As mentioned before, the proposed algorithm selects the maximally smoothed rate that can be extended as far as possible. Accordingly, the proposed algorithm gives better PAR performances than the sliding window scheme, in the case of a s ¼ a r ¼ 0.8, as shown in Fig. 7(a). But, in the case of small buffer sizes(a s ¼ 0.5, a r ¼ 0.7), the performance of the proposed algorithm is worse than the sliding window scheme. In this case, it is shown that the proposed scheme are somewhat unstable and the peak rate is increased for increasing of delay bound (D r). This is because the buffer sizes which are determined by Eq. (25) are not linearly proportional to the value of D r and the buffer size constraints get to be more dominant than the other constraints in deciding the transmission rate.
651
Fig. 7. Characteristics of COV and PAR for delay bound (D rDt): (a) PAR (peak-to-average ratio); (b) COV (coefficient of variation).
4.3.2. The coefficient of variation (COV) The superiority of the proposed algorithm over the sliding window scheme is less obvious for the COV-metric, as shown in Fig. 7(b). As expected, the temporal variations of the smoothed traffic monotonically decay as the delay bound increases. And in the sufficient buffer sizes, the proposed algorithm has slightly better performance than the sliding window scheme. This performance is mainly owing to the coded-frame size estimates, which are found with extra computation burdens explained in Section 3. 4.3.3. The number of rate changes Rate changes requires the sender and receiver sides to modify the different I/O rates for the stream. As a result, if the number of rate changes is large, we can expect that the overall system complexity is increased. From this point of view, Fig. 8 shows the average number of rate changes of the proposed algorithm based on two different buffer sizes arrangements. As shown in this figure, the average number of rate changes is decaying for the increase of the delay bound, and the average number of rate changes under small sender buffer size is slightly larger, because a bursty region in the unsmoothed stream is directly affected by the small smoothing buffer space as mentioned before.
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J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
(C eff) is computed as log Ceff ¼
Fig. 8. Characteristics of average number of rate changes for two different buffer arrangements.
4.4. The performance evaluation of effective bandwidth Fig. 9(a) shows a discrete-time queue model with constant service rate in ATM networks. In this model, the large deviations in effective bandwidths (simply called ‘effective bandwidth’, or also ‘equivalent bandwidth’) estimate statistically the network throughput required to transmit the video service under a cell loss probabilities (CLP) with switch buffer (B). For more details, one may refer to Refs. [19,20]. By simplifying the results of Ref. [19], for transmission rates with {r(j)} j¼1,…,N, the effective bandwidth
N X
!
exp(vr(j)=N
i¹1
v
(27)
where v ¼ ¹ log(CLP)/B is a switch buffer size and CLP is a tolerable cell loss rate. By using this formal equation, we explore how the effective bandwidth metrics change for each smoothing scheme. We use B ¼ 10 kbytes and CLP ¼ 10 ¹5, and obtain the effective bandwidth estimates of a smoothed video stream, as depicted in Fig. 9(b). This figure shows the significant reduction of bandwidth requirement which is achieved by introducing a long playback delay of several seconds for a live video service. For example, it is observed that with D r ¼ 150, by using the proposed scheme in a s ¼ 0.5, a r ¼ 0.7 and in a s ¼ 0.8, a r ¼ 0.8, the effective bandwidth drops by 31.2% and 22.8%, respectively, compared with unsmoothed original traffic. In these experiments, it is observed that the intervals with a lot of cells have a great influence in the loss probability although they are not frequent. Through the above experiments and evaluations, we conclude that the proposed algorithm is useful for reducing peak rate, temporal variations, and effective bandwidth of a given live VBR video, stream, although, in the cases of small buffer sizes, the rate bounds corresponding to buffer sizes are more domimant than the other bounds and the performance is degraded, more or less, in characterizing the smoothed traffic.
5. Conclusion
Fig. 9. Effective bandwidth estimates: (a) conceptual overview for effective bandwidth allocations; (b) performance evaluation with B ¼ 10 kbytes and CLP ¼ 10 ¹5 in (a).
In this paper, we present a new online traffic smoothing algorithm which is useful for live video services such as visual lectures or television news. In these applications, many receivers may be willing to tolerate a playback delay of several seconds in exchange for a smaller bandwidth requirement. For this aim and practical implementations, we describe the physical constraints imposed not only by the delay bound, but also by the sender and receiver buffer sizes. By using these constraints, an adaptive traffic smoothing algorithm is designed in such a dynamic way as to smooth maximally the transmission rate, while avoiding the buffer overflow and underflow. Through computer experiments, it is shown that by delaying the transmission and playback of a live video service and by smoothing the transmission rate on a large time scale (several seconds), the proposed scheme reduces significantly the bandwidth requirement of a given video traffic. Particularly, compared with the simple sliding window scheme, it is observed that the proposed method is effective in reducing peak rate, temporal variations, and effective bandwidth of a given video stream. Additionally, it is shown that the proposed scheme can be applied to some
J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
applications that the overall buffer sizes are finite or asymmetrically located. However, it is noted that the performance of the proposed algorithm does come at a cost. In a practical situation where computation complexity is extremely limited, it is required for the sender side to balance the trade-off between computational load and the efficiency in the bandwidth requirements by modifying the proposed scheme. Besides, as one of the further works, we consider a modified algorithm that can adapt to network with no QoS guarantees.
[7]
[8]
[9]
[10]
Acknowledgements This work is partially supported by a Korea Telecom Research Grant. We thank Oliver Rose for making the news trace available.
[11]
References
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[1] A.R. Reibman, B.G. Haskell, Constraints on variable bit rate video for ATM networks, IEEE Transactions on Circuits and Systems for Video Technology 2 (4) (1992) 361–371. [2] T. Ott, T. Lakshman, A. Tabatabai, A scheme for smoothing delaysensitive traffic offered to ATM networks, in: Proceedings of IEEE INFOCOM, Florence, Italy, May 1992, pp. 776–785. [3] S.S. Lam, S. Chow, D.K.Y. Yau, An algorithm for lossless smoothing of MPEC video, Proceedings of ACM/SIGCOMM, August 1994, pp. 281–293. [4] W. Ding, Joint editor and channel rate control of VBR video over ATM networks, IEEE Transactions on Circuits and Systems for Video Technology 7 (2) (1997) 266–278. [5] K. Joseph, D. Reininger, Source traffic smoothing and ATM network interfaces for VBR MPEG video encoders, in: IEEE International Conference on Communication, Seatle, WA, June 1995, pp. 1761– 1767. [6] J.S. Kim, J.K. Kim, An adaptive source traffic smoothing method for VBR MPEG video under constraints of delay bound and sender/
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receiver buffer sizes, in: 3rd Asia Pacific Conference on Communications (APCC’97), Sydney, Australia, Dec. 1997, p. 5155. S. Dixt, P. Skelly, Video traffic smoothing and ATM multiplexer performance, in: IEEE GLOBECOM’91, Arizona, USA, Dec. 1991, pp. 239–243. W.C. Feng, S. Sechrest, Critical bandwidth allocation for the delivery of compressed video, Computer Communications 18 (10) (1995) 709–717. J.D. Salehi, S.L. Zhang, J.F. Kurose, D. Towsley, Supporting stored video: reducing rate variability and end-to-end resource requirements through optimal smoothing, in: Proceedings of the ACM SIGMETRICS, May 1996, pp. 222–231. J. Ni, T. Yang, D.H.K. Tsang, CBR transportation of VBR MPEC-2 video traffic for video-on-demand in ATM networks, in: IEEE International Conference on Communication, TX, June 1996, pp. 1391–1395. J.M. McManus, K.W. Ross, Video on demand over ATM: constantrate transmission and transport, in: Proceedings of the IEEE INFOCOM, March 1996, pp. 1357–1362. M. Grossglauser, S. Keshav, D. Tse, RCBR: a simple and efficient service for multiple time-scale traffic, in: Proceedings of the ACM SIGCOMM, Aug./Sept. 1995, pp. 219–230. ITU-T SG15 AVC, Draft Recommendation H.222.0, June 1994. N. Ohta, Packet Video: Modeling and Signal Processing, Aretech House, 1994. Haykin, Adaptive Filter Theory, Prentice Hall, Englewood Cliffs, NJ, 1991. J. Shin, VBR video traffic modeling based on scene change detections using slice-level traffic characterizations, Ph.D. Thesis, KAIST, 1995. I. Hsu, J. Walrand, Quick detection of changes in traffic statistics: application to variable rate compression, in: Proceedings of the 32nd Allerton Conference on Comm.s, Control and Computing, Monticello, IL, 1993. Rose, O., Statistical properties of MPEG video traffic and their impact on traffic modeling in ATM systems, University of Wuerzburg, Institute of Computer Science Research Report Series, Report No. 101, 1995. G. Kesidis, J. Walrand, C.S. Chang, Effective bandwidths for multiclass markov fluids and other ATM sources, IEEE/ACM Transactions on Networking 1 (4) (1993) 424–428. G. Kesiclis, ATM Network Performance, Kluwer Academic, Dordrecht, 1996.
Adaptive traffic smoothing for live VBR MPEG video service Jin-soo Kim*, Jae-kyoon Kim Department of Electrical Engineering, KAIST 373-1 Kusong-dong, Taejon 305-701, South Korea Received 31 October 1997; received in revised form 16 January 1998; accepted 16 January 1998
Abstract In this paper, we propose an online source traffic smoothing algorithm, that can be effectively used in live video applications such as visual lectures or television news. For a practical implementation, firstly, we describe the constraints imposed by the delay bound at the sender side, and by the sender/receiver buffer sizes. Then, by using these constraints, the proposed algorithm is designed in such a dynamic way as to smooth maximally the transmission rate. Through experimental results, it is shown that the proposed scheme is effective in reducing the peak rate, temporal variations, and effective bandwidth of a given video stream. Particularly, it is noted that the proposed algorithm can be used in some applications where overall buffer sizes are finite or asymmetrically located. q 1998 Elsevier Science B.V. Keywords: Online traffic smoothing; Buffer constraints; Live VBR MPEG video
1. Introduction In the near future, it is expected that many emerging multimedia applications will rely on the efficient transmission of VBR-coded MPEG video streams. Recently, as one way to provide VBR-coded services, some works have dealt with source traffic smoothing methods [1–12], which are based on the introduction of delay and rate buffering between the video encoding and decoding processes. In Ref. [2], the problem of online traffic smoothing satisfying a delay bound was analyzed, assuming that all coded-frame sizes are known a priori. Based on Ref. [2], the improved algorithm in Ref. [3] was developed using a lookahead parameter and the number of frames with known codedframe sizes as well as frame delay at the sender, but this algorithm didn not consider buffer sizes at the sender and receiver sides. On the other hand, several transmission techniques of a prerecorded video source such as VoD applications have been addressed in Refs. [8–12]. In these applications, by capitalizing on prior knowledge of the coded-frame sizes for the entire video, these techniques can smooth traffic on a large time scale by prefetching frames into a receiver buffer in advance of bursts of large frames. In contrast to prerecorded video applications, live video services such as visual lectures or television news typically have the limited * Corresponding author. Tel.: 0082 42 869 5418; fax: 0082 42 869 8018; e-mail: [email protected]
0140-3664/98/$19.00 q 1998 Elsevier Science B.V. All rights reserved PII S 01 40 - 36 6 4( 9 8) 0 01 3 5- 2
knowledge of coded-data sizes and finite buffer sizes in the sender and receiver sides. As a result, live video applications require dynamic techniques that can react to changes in coded-frame sizes and the available buffer sizes. For live VBR video services, Reibman and Haskell studied constraints imposed by buffer sizes and transmission rates in Ref. [1]. But, they focused on the encoder rate control to prevent overflow and underflow at the sender and receiver buffers. In this paper, based on the works in Refs. [1,3,6], we develop an online traffic smoothing algorithm that can be effectively applicable for delaytolerant live video services such as visual lectures or television news. In these applications, receivers may be willing to tolerate a playback delay of several seconds in exchange for a smaller bandwidth requirement. First, for practical implementations, we describe constraints imposed by the delay bound, and by the sender/receiver buffer sizes. Then, by using these constraints, we propose an online source traffic smoothing algorithm that makes transmitted data maximally smooth, while dynamically controlling the data so that overflow and underflow may be avoided [13]. This paper is organized as follows. In Section 2, we present the system model and the notations used in this paper, and briefly review relationships between the buffer sizes and the transmitted data sizes. In Section 3, first we describe constraints imposed by the receiver buffer size, the delay bound, and the sender buffer size on the transmitted data sizes. Then, based on these constraints an online traffic smoothing algorithm which control adoptively the outgoing
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645
Fig. 1. An overview figure for adaptive source traffic smoothing.
transmission rate of the sender buffer. In Section 4, the experimental results are presented and it is shown that the proposed algorithm are effective at reducing the peak rate, coefficient of variation, and effective bandwidth of a live VBR coded-MPEG stream. Finally, a conclusion is given in Section 5.
2. Basic assumptions and notations
j X i¼1
1
s(i) ¹
j X
r(i), for j . 0
¼
j X
Xj
i ¼ 1 r(i)for0
r(i) ¹
jX ¹ Dr
. j # Dr
(2)
s(i) for j . Dr
i¼1
i¼1
From Eqs. (1) and (2), two different forms of B r(j) can be written for j . D r as follows j X
Br (j) ¼
In Fig. 1, the situation in an online traffic smoothing system is shown as a simplified block diagram. Let s(j) be the number of generated bits in the interval [(j ¹ 1)Dt, jDt), where Dt is the duration corresponding to one uncoded frame interval. It is assumed that s(i) is uniformly fed to the sender buffer during this time interval. Additionally, the size of decoding data package(receiver buffer readout package) is assumed to be same as the generated-data size by encoding per frame. Similarly, let r(j) be the number of bits that are uniformly transmitted into the network in the interval [(j ¹ 1)Dt, jDt). The value of r(j) depends on the nature of the sender and receiver buffer fullness, as well as the delay bound. Let us define D sDt as the allowable delay bound with which a specific coded-frame data can be stayed in the sender buffer [1]. It means that the sender side must terminate transmitting a specific coded-frame data within D sDt into network, after the first bit of that data is generated. Let us define D rDt as the decoding startup latency at the receiver side1. As expressed in Ref. [1], based on the above definitions and assumptions, the sender and receiver buffer fullness at time jDt; B s(j) and B r(j) can be expressed as Bs (j) ¼
Br (j) ¼
s(i) ¹ Bs (j)
(3)
i ¼ j ¹ Dr þ 1 j X
¼
r(i) ¹ Bs (j ¹ Dr ), for j . Dr
(4)
i ¼ j ¹ Dr þ 1
We note that in order to guarantee lossless online smoothand 0 # Br (j) # Bsize ing, the conditions of 0 # Bs (j) # Bsize s r size must be satisfied for all j, where Bs and Bsize represent the r sizes of sender and receiver buffers, respectively. Hence, from Eqs. (3) and (4), we obtain simple boundaries of partial sums over D rDt intervals. j X
size s(i) # Bsize s þ Br
(5)
size r(i) # Bsize s þ Br , for j $ Dr
(6)
i ¼ j ¹ Dr þ 1 j X i ¼ j ¹ Dr þ 1 size must be large It means that overall buffer size Bsize s þ Br enough to absorb the variability of data generated, or transmitted during the delay bound. In other words, a larger value of D r facilitates a smoothing transmission of the given video, at the expense of a larger buffer requirement at the sender and receiver sides.
(1)
i¼1
In this paper, it is assumed for clarity that D s and D r are integer values(D r $ D s $ 1). In practice, since the largest expected network delay (t) should be considered, we assume that D r ¹ D s . t is satisfied. The network jitter can be considered by introducing additional buffer space at the receiver.
3. Proposed source traffic smoothing algorithm For a live video service, the sender side cannot perform traffic smoothing over the entire video stream. Because the amount of smoothing is limited by the coded-frame data in the given delay bound as well as the sizes of the sender and receiver buffers. From Eq. (4), it is shown that the
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transmission rate, r(j), depends on the past informations of r(j) as well as the sender and receiver buffer occupancies. From these points of view, we describe in detail the constraints imposed by: (i) the receiver buffer size; (ii) the delay bound; and (iii) the sender buffer size. Based on these constraints, a new dynamic r(j) decision algorithm is designed. 3.1. Constraint imposed by the receiver buffer size If the receiver buffer size is sufficiently large, the selection range of r(j) can be wide. But, in the real case that the receiver buffer size is small and fixed, the maximum value of r(j) is restricted by the overflow prevention condition of must be the receiver buffer. From Eq. (4), since Br (j) # Bsize r satisfied for all j, that is, j X
r(i) ¹ Bs (j ¹ Dr ) # Bsize for all j r
(7)
i ¼ j ¹ Dr þ 1
must be maintained. Hence, the maximum value of r(j) is bound as follows, ( ) jX ¹1 max size r(i), 0 r (j) ; max Br þ Bs (j ¹ Dr ) ¹ i ¼ j ¹ Dr þ 1
(8) or by using Eq. (1) in Eq. (8), ( rmax (j) ; max þ
Bsize r Bs (j ¹ 1) ¹
jX ¹1
departure time ¹ buffer entering time # Ds Dt Therefore, (j ¹ 1)Dt þ
s¯(j ¹ J) Dt ¹ bj ¹ J Dt # Ds Dt r(j)
(j ¹ 1)Dt þ
s(j ¹ J þ 1) s¯(j ¹ J) Dt ¹ bj ¹ J þ 1 Dt # Ds Dt Dt þ r(j) r(j) (11)
By extending this procedure to p frame data, a lower inequality for r(j) can be formally defined as s¯(j ¹ J) Ds þ bj ¹ J ¹ j þ 1
(9)
i ¼ j ¹ Dr þ 1
The underflow prevention of the receiver buffer can be replaced by the constraint on the delay bound, as explained in the next subsection. 3.2. Constraint imposed by the delay bound Fig. 2 shows the queueing structure in the sender buffer at time (j ¹ 1)Dt. The coded-frame data that waits for transmission in the sender buffer cannot wait longer than the delay bound (D sDt). In other words, the time interval for each batch of coded-frame data, between the time of the first bit entering the sender buffer and the time of last bit
(10)
where the new symbols are defined as follows: J is a value an integer less than D s and represent the queueing length at time (j ¹ 1)Dt in the sender buffer (see Fig. 2); s¯(j ¹ J) is the first data size which will be transmitted at (j ¹ 1)Dt and the remainder of s(j ¹ J) which was not transmitted before (j ¹ 1)Dt; b j¹j Dt represents the instantaneous time when the first bit of s¯(j ¹ J) has begun entering the sender buffer. The departing time of s¯(j ¹ J) may be the transmission starting time of s(j ¹ J þ 1). As soon as the transmission of s¯(j ¹ J) is terminated, in order to transmit s(j ¹ J þ 1) continuously at the same rate, r(j) the following inequality must be simultaneously satisfied as follows.
rL1 (j, 0) ;
) s(i), 0
departing the buffer must be less than D sDt, as specified in Section 2, i.e.
s¯(j ¹ J) þ r (j, p) ;
iX ¼p
Ds þ bj ¹ J þ p ¹ j þ 1
, 1 #p # J ¹1
iX ¼p
sˆ(j ¼ J þ i) , J#p Ds þ bj ¹ J þ p ¹ j þ 1
Bs (j ¹ 1) þ rL1 (j, p) ;
s(j ¼ J þ i)
i¼1
L1
(12)
i¼J
(13)
where, if p is equal to or greater than J, sˆ(j ¹ J þ p) is a value which is estimated by using the characteristics of pseudoperiodic patterns in the MPEG-coded video sequence. The coded-data size estimation method is proposed in detail in Section 3.4.
Fig. 2. Queueing structure in the sender and receiver buffers.
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3.3. Constraint imposed by the sender buffer In deciding the transmission rate, it is required that the sender buffer overflow and underfiow should be avoided. For these purposes, we describe the constraints imposed by the sender buffer size. Eq. (1) can be recursively written as Bs (j) ¼ Bs (j ¹ 1) þ sˆ(j) ¹ r(j), for j . 0
# r(j) # Bs (j ¹ 1) þ sˆ(j) Bs (j ¹ 1) þ sˆ(j) ¹ Bsize s
(15)
To obtain an identical transmission rate for the incoming hDt intervals, the following inequalities should be simultaneously satisfied. Bs (j ¹ 1) þ
hX ¹1
hX ¹1
$ max;h Bsize s
h¹1 Ds ¹ 1 X s(j þ k) h k¼0
The proof is completed. A Lemma 2. If the following inequality, that is, ( ) j X size sk , ;j Br $ max k ¼ j ¹ Dr þ 1
is satisfied, r ðj; hÞ # r max ðjÞ holds for ;h $ 1: Similarly, this proof is straightforward from Eqs. (9) and (18).
sˆ(j þ k) ¹ Bsize # h·r(j) # Bs (j ¹ 1) s
sˆ(j þ k), h $ 1
ð16Þ
k¼0
For convenience of explanation, from Eq. (16) let us define the upper bounds and the second lower bounds of r(j), which are a function of lookahead interval h, respectively. 9 8 hX ¹1 > > > > > > sˆ(j þ k) ¹ Bsize > > Bs (j ¹ 1) þ s = < k¼0 L2 , 0 , r (j, h) ; max > > h > > > > > > ; : h$1
ð17Þ
Bs (j ¹ 1) þ rU1 (j, h) ;
$ (j ¹ 1) should be satisfied for all j, the above Since Bsize s expression is written by
U1
k¼0
þ
respectively. Accordingly, in order that rL1 (j,p) $ r L2(j,h) is satisfied in all regions of h $ 1, we can obtain ( ) hX ¹1 Ds ¹ 1 size {B (j ¹ 1) þ s(j þ k)} Bs $ max;h Ds ¹ 1 þ h s k¼0
(14)
where sˆ(j) is a estimate value of s(j). Since 0 # Bs (j) # Bsize s must be satisfied for all j, the following inequalities can be written by
647
hX ¹1 k¼0
h
sˆ(j þ k) , h$1
(18)
where {ˆs(j þ k), k ¼ 0, 1, …} are estimated values by using the proposed method described in detail in the next subsection. It is noted that as h increases, the effect of the sender buffer size disappears gradually and r L2(j,h) get closer to the value of r U1(j,h). Additionally, in the case that Bsize is s not sufficiently large, r L2(j,h) tends to be more dominant than r L1(j,p) as h increases. But, in some applications with a sufficiently large sender buffer size, r L1(j,p) is always greater than r L2(j,h) for all p and h. From the above constraints, the following lemmas can be remarked. Lemma 1. If the inequality, that is, L1 L1 $ (D ¹ 1)max {s(j)} is satisfied, r (j,p) $ r (j,h) Bsize s s ;j holds for p $ J and h $ 1. Proof. From Eqs. (13) and (17), it is directly expressed as p ¼ h þ J ¹ 1 and bj ¹ j þ p Dt ¼ (h þ j ¹ 2)Dt for h $ 1,
3.4. The proposed coded-frame size estimation In this paper, it is assumed that {s(j þ k),k $ 0} are not known at time (j ¹ 1)Dt. Accordingly, in order to efficiently estimate the coded-frame sizes for future frames in Eqs. (13), (17) and (18), k-step linear predictor is used [15]. That is, s(j þ k) is estimated by using a linear combination of the previous values of s(j). Let us denote the value as sˆ(j þ k). Thus, Lth order linear predictor has the form: sˆ(j þ k) ¼
LX ¹1
w(l)s(j ¹ l)
(19)
l¼0
where w(l), for l ¼ 0,1,…,L-1, are the linear prediction filtering coefficients. The optimal linear predictor in the mean square sense is one which minimizes the mean square error, E{s(j þ k) ¹ sˆ(j þ k)}. The {w(l)} l¼0,…,L¹1 is found by adoptively solving the Wiener–Hopf equations at time (j ¹ 1)Dt [15]2. Since I, P, and B frame types have different statistical characteristics, we separate them and estimate s(j þ k) based on the each frame type. Besides, in the MPEG compression sense, since P and B frames exploit causal-temporal redundancies and noncausal temporal redundancies as well as spatial ones, respectively, the characteristics of bit rate may be significantly affected by a scene changed frame. Accordingly, in order to obtain the exact rate bounds for new coming P or B frames, it is necessary to detect whether scene change has occurred or not in s(j ¹ 1) at time (j ¹ 1)Dt (Fig. 3). There are many ways to detect a scene-changed frame from the past statistical informations [16,17]. But, in this paper, to facilitate implementation and reduce the computation 2 In this paper, to reduce computation load, we fixed L ¼ 3 for all experiments.
648
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Fig. 3. Typical example for four rate bounds.
complexity, the following simple decision method is used. if 0:85 3 Idata , s(j ¹ 1), else
scene changed not changed
where Idata is the data size generated by the most recently encoded I frame. Once s(j ¹ 1) is detected as a scenechanged frame, this data would not be used in estimating the coded-data sizes of new coming frames. 3.5. The proposed r(j) decision algorithm
else r min(j) ¼ max{r L1(j,p),p ¼ 0,…,J ¹ 1} and go to Step 2. Step 2. Let us define r L(j,h) ; max{r L1(j,J þ h ¹ 1), r L2(j,h),r min(j)} and r U(j,h) ; min{r U1(j,h), r max(j)}, respectively. If r L(j,1) . r U(j,1), then r(j) ¼ r max(j) and stop. else go to Step 3. Step 3. Find the largest integer H( , GOPsize) such that max rL (j, h) # min rU (j, h)
1#h#H
The proposed algorithm consists of two parts. First, the data which await for transmission within the sender buffer have to satisfy the delay constraints as well as the receiver buffer constraints. Second, the data which will arrive at the sender buffer does not have to give rise to overflow and underflow. In a dynamic way, a new r(j) decision rule is designed by using Eqs. (8), (12), (13), (17) and (18) as follows. Step 1. If there exists p satisfying r max(j) , r L1(j,p), as p increases from 0 up to J ¹ 1, let us denote P ¼ p,r P ¹ 1} and go to Step 2.
min
L1
(j) ¼ max{r (j,p),p ¼ 0,…,
1#h#H
If H ¼ GOPsize, then go to Step 4. else if max 1 # h # H r L(j,h) . r U(j,H þ 1), then r(j) ¼ max r L (j, h) 1#h#H
(20)
else r(j) ¼ min r U (j, h) 1#h#H
and stop.
(21)
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Step 4. If r(j ¹ 1) # max 1 # h # GOPsizer L(j,h), then r(j) ¼
max
1#h#GOPsize
rL (j, h)
(22)
else if max 1 # h # GOPsizer L(j,h) # r(j ¹ 1) # min 1 # h # GOPsizer U(j,h), then r(j) ¼ r(j ¹ 1)
(23)
else r(j) ¼
min
1#h#GOPsize
rU (j, h)
(24)
and stop. In Step 1, a maximum value of r(j) is found based on the receiver buffer sizes and the delay bound constraint. In Step 3 and 4, a maximally smoothed value of r(j) is selected as shown in Fig. 4. That is, at every frame starting point, the proposed algorithm determines the longest trajectory for arrived and incoming coded-frames. Cosequently, this method results in a transmission trajectory that has the smallest possible peak rate requirement and the smallest rate change between adjacent different transmission rates.
The proposed algorithm is simple to implement for a practical application. But, as the value of D r increases, the computation burdens are increase linearly. From Eqs. (8), (9), (12), (17) and (18), it is easily found that the required computation burdens in the worst case are (3GOPsize þ 2D r þ 1) additive operations and (3GOPsize þ D r þ 1) multiplicative operations. Additionally, the computation burdens for finding the coded-frame sizes estimates by using Eq. (19) in the worst case are GOPsize·(3 3 3 matrix inversion þ 18 multiplicative þ 8 additive) operations are required. For a practical situation where the computation burden is extremely limited, it is necessary for the sender side to balance the trade-off between the computation loads and the efficiency in the bandwidth requirements. But, in the case that the sender and/or receiver buffer sizes are restricted on the above Lemma 1 and 2, it is noted that the proposed r(j) decision rule can be simplified.
4. Experimental results and performance evaluation 4.1. The experimental conditions The trace used in our experiments is the ‘news’ sequence which is composed of 40 000 frames [18]. The GOP pattern is given by (GOPsize, P-frame period) ¼ (12,3) where GOPsize is the distance between two successive I frames and P-frame period is the distance between I or P frame and the subsequent P frame. For more details about the encoder parameters, one may refer to Ref. [18]. In this paper, we conduct all experiments under the condition of D s ¼ D r ¹ 1, although various experimental situations can be established for performance evaluations. For a given D r, this paper determines the sender buffer size size, Bsize s , and the receiver buffer size, Br , by using the following relations: nXj (25) Bsize s ¼ as · max;j i ¼ j ¹ Dr þ 1 s(i)g, 0 , as # 1 ( Bsize r
¼ ar · max ;j
j X
) s(i) , 0 , ar # 1
i ¼ j ¹ Dr þ 1
where s(i) is the coded-frame data size of the ith frame in the given video trace. a s and a r represent the buffer multiplicative factors, which are introduced to investigate the smoothing effects that arise by changing the sender and receiver buffer sizes. As expressed in Eq. (5), we select a s, a r such that a s þ a r $ 1 should be satisfied. 4.2. The effects of buffer size
Fig. 4. Rate decision methods for Step 3 and 4 in proposed algorithm: (a) Eq. (20) in Step 3; (b) Eq. (21) in Step 3; (c) Step 4.
Fig. 5 demonstrates the benefits of increasing the buffer sizes in smoothing VBR MPEG video streams. As expected, this figure shows that under large buffer sizes a bursty behavior of the original traffic is significantly smoothed, since the smoothing ability can be extended as large as
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Fig. 5. One segment of smoothed traffic.
the additional buffering space. These facts are obvious, especially in the regions that original stream has peaks in the same scene. In order to investigate the effects of the buffer sizes, we establish two different experimental scenarios: (i) the sender buffer size is fixed (a s ¼ 0.9) and the receiver buffer size is varying; (ii) the receiver buffer size is fixed (a r ¼ 0.9) and the sender buffer size is varying. Fig. 6 shows the experimental results obtained by using the proposed algorithm with D r ¼ 150. 4.2.1. The peak-to-average ratio (PAR) The PAR or peak rate is one of the measures that determines the worst-case bandwidth requirement for a piecewise CBR service. As shown in Fig. 6(a), the PAR is decaying for the increase of the sender and receiver buffer sizes and gets closer to a constant value which is independent of the buffer sizes. In extremely small buffer sizes (a s , 0.7, a r , 0.4), it is noted that the dependency of PAR on the sender buffer sizes is larger than the receiver buffer size. This is because the small sender buffer size the PAR is directly affected by the abrupt coded-frame sizes changes such as fast moving frames or scene changed frames. 4.2.2. The coefficient of variation(COV) The coefficient of variation (COV) is introduced as a measure to investigate and evaluate the temporal variations of the transmission rate around mean rate [3,5,14]. Fig. 6(b)
shows the characteristics of COV obtained from the above experiments. The decaying behavior of COV is similar to that of PAR and get to be independent of the buffer size in the large buffer size region, since the delay bound (r L1(j,p) in Section 3) becomes the major limitation on the ability to determine r(j). In the above experiments, it is observed that in the cases of extremely small buffer sizes(a s , 0.7, a r , 0.4), the buffer overflow is incurred mainly owing to the abrupt rate increases and the loss rates are in the range of 10 ¹4,10 ¹6. For more related results, one may refer to Ref. [6]. 4.3. The effects of delay bound In this subsection, the performance characteristics of a smoothed traffic in the proposed algorithm are investigated as a function of the delay bound. As we mentioned in Section 1 that the online smoothing scheme can achieve a smaller bandwidth requirement by introducing a large delay bound (D r), even with D r ¼ 30, a s ¼ a r ¼ 0.8, the proposed scheme reduces the PAR by 23.3% and the COV by 51.4%, respectively, over the original unsmoothed video stream. For performance comparisons of the proposed scheme, we consider the sliding window algorithm that operates on consecutive overlapping windows of size D r ¹ J in Fig. 2. That is, this algorithm computes the transmission rate, r(j), per Dt by averaging coded-frames in the range [j ¹ (D r ¹ J),j ¹ 1]. By using the notations in Section 3, the
J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
Fig. 6. Characteristics of COV and PAR according to the changes of buffer sizes in D r ¼ 150: (i) a s ¼ 0.9 is fixed and a r is varying; (ii) a r ¼ 0.9 is fixed and a s is varying. (a) PAR (peak-to-average ratio); (b) COV (coefficient of variation).
following form can be written as r(j) ¼
JX ¹1 i¼0
s(j ¹ J þ i Dr ¹ J þ i
(26)
Simply, we do not incorporate the future incoming framesizes with the above equation and we use a s ¼ a r ¼ 1.0 for this scheme [4,5]. 4.3.1. The peak-to-average ratio (PAR) As mentioned before, the proposed algorithm selects the maximally smoothed rate that can be extended as far as possible. Accordingly, the proposed algorithm gives better PAR performances than the sliding window scheme, in the case of a s ¼ a r ¼ 0.8, as shown in Fig. 7(a). But, in the case of small buffer sizes(a s ¼ 0.5, a r ¼ 0.7), the performance of the proposed algorithm is worse than the sliding window scheme. In this case, it is shown that the proposed scheme are somewhat unstable and the peak rate is increased for increasing of delay bound (D r). This is because the buffer sizes which are determined by Eq. (25) are not linearly proportional to the value of D r and the buffer size constraints get to be more dominant than the other constraints in deciding the transmission rate.
651
Fig. 7. Characteristics of COV and PAR for delay bound (D rDt): (a) PAR (peak-to-average ratio); (b) COV (coefficient of variation).
4.3.2. The coefficient of variation (COV) The superiority of the proposed algorithm over the sliding window scheme is less obvious for the COV-metric, as shown in Fig. 7(b). As expected, the temporal variations of the smoothed traffic monotonically decay as the delay bound increases. And in the sufficient buffer sizes, the proposed algorithm has slightly better performance than the sliding window scheme. This performance is mainly owing to the coded-frame size estimates, which are found with extra computation burdens explained in Section 3. 4.3.3. The number of rate changes Rate changes requires the sender and receiver sides to modify the different I/O rates for the stream. As a result, if the number of rate changes is large, we can expect that the overall system complexity is increased. From this point of view, Fig. 8 shows the average number of rate changes of the proposed algorithm based on two different buffer sizes arrangements. As shown in this figure, the average number of rate changes is decaying for the increase of the delay bound, and the average number of rate changes under small sender buffer size is slightly larger, because a bursty region in the unsmoothed stream is directly affected by the small smoothing buffer space as mentioned before.
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(C eff) is computed as log Ceff ¼
Fig. 8. Characteristics of average number of rate changes for two different buffer arrangements.
4.4. The performance evaluation of effective bandwidth Fig. 9(a) shows a discrete-time queue model with constant service rate in ATM networks. In this model, the large deviations in effective bandwidths (simply called ‘effective bandwidth’, or also ‘equivalent bandwidth’) estimate statistically the network throughput required to transmit the video service under a cell loss probabilities (CLP) with switch buffer (B). For more details, one may refer to Refs. [19,20]. By simplifying the results of Ref. [19], for transmission rates with {r(j)} j¼1,…,N, the effective bandwidth
N X
!
exp(vr(j)=N
i¹1
v
(27)
where v ¼ ¹ log(CLP)/B is a switch buffer size and CLP is a tolerable cell loss rate. By using this formal equation, we explore how the effective bandwidth metrics change for each smoothing scheme. We use B ¼ 10 kbytes and CLP ¼ 10 ¹5, and obtain the effective bandwidth estimates of a smoothed video stream, as depicted in Fig. 9(b). This figure shows the significant reduction of bandwidth requirement which is achieved by introducing a long playback delay of several seconds for a live video service. For example, it is observed that with D r ¼ 150, by using the proposed scheme in a s ¼ 0.5, a r ¼ 0.7 and in a s ¼ 0.8, a r ¼ 0.8, the effective bandwidth drops by 31.2% and 22.8%, respectively, compared with unsmoothed original traffic. In these experiments, it is observed that the intervals with a lot of cells have a great influence in the loss probability although they are not frequent. Through the above experiments and evaluations, we conclude that the proposed algorithm is useful for reducing peak rate, temporal variations, and effective bandwidth of a given live VBR video, stream, although, in the cases of small buffer sizes, the rate bounds corresponding to buffer sizes are more domimant than the other bounds and the performance is degraded, more or less, in characterizing the smoothed traffic.
5. Conclusion
Fig. 9. Effective bandwidth estimates: (a) conceptual overview for effective bandwidth allocations; (b) performance evaluation with B ¼ 10 kbytes and CLP ¼ 10 ¹5 in (a).
In this paper, we present a new online traffic smoothing algorithm which is useful for live video services such as visual lectures or television news. In these applications, many receivers may be willing to tolerate a playback delay of several seconds in exchange for a smaller bandwidth requirement. For this aim and practical implementations, we describe the physical constraints imposed not only by the delay bound, but also by the sender and receiver buffer sizes. By using these constraints, an adaptive traffic smoothing algorithm is designed in such a dynamic way as to smooth maximally the transmission rate, while avoiding the buffer overflow and underflow. Through computer experiments, it is shown that by delaying the transmission and playback of a live video service and by smoothing the transmission rate on a large time scale (several seconds), the proposed scheme reduces significantly the bandwidth requirement of a given video traffic. Particularly, compared with the simple sliding window scheme, it is observed that the proposed method is effective in reducing peak rate, temporal variations, and effective bandwidth of a given video stream. Additionally, it is shown that the proposed scheme can be applied to some
J.-s. Kim, J.-k. Kim/Computer Communications 21 (1998) 644–653
applications that the overall buffer sizes are finite or asymmetrically located. However, it is noted that the performance of the proposed algorithm does come at a cost. In a practical situation where computation complexity is extremely limited, it is required for the sender side to balance the trade-off between computational load and the efficiency in the bandwidth requirements by modifying the proposed scheme. Besides, as one of the further works, we consider a modified algorithm that can adapt to network with no QoS guarantees.
[7]
[8]
[9]
[10]
Acknowledgements This work is partially supported by a Korea Telecom Research Grant. We thank Oliver Rose for making the news trace available.
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