SCB: StairCase Broadcast for Media-on-Demand Systems Fulu Li
Ioanis Nikolaidis
OpenIP Environment, Nortel Networks Corp., Canada
Dept. of Computing Science, Univ. of Alberta, Edmonton, Canada
[email protected]
[email protected]
ABSTRACT Periodic broadcast schemes have been proposed to solve the Media-on-Demand (MoD) distribution problem for the set of the most frequently requested media objects. Most of the current proposals for periodic broadcast schemes assume Constant-Bit-Rate (CBR) encoded media objects [1,2,5,9]. The few existing proposals for support of the bandwidth-efficient family of VariableBit-Rate (VBR) encoded media objects are available at the cost of data loss due to overflow of the broadcast link capacity by the aggregate traffic of the simultaneouslytransmitted segments of the media contents [3,8]. In this paper, we investigate a novel broadcast scheme, called StairCase Broadcast (SCB), for VBR encoded media contents, which can guarantee, by its design, zero data loss and predictable service delay with minimal required de-coupled server and client bandwidth.
1 Introduction With the advent of high-speed networks, the popularity of the Internet, the improvement of data compression technology, Media-on-Demand (MoD), and in particular Video-on-Demand (VoD), is becoming a major application of future digital networks. The following discussion focuses on VoD, but the principle is equally applicable for other media objects. Periodic broadcast schemes broadcast the videos periodically, which can substantially reduce the bandwidth requirements for the most frequently requested media objects by serving the multiple users via one single transmission. Efficient periodic broadcast schemes [1,2,3,4,5,8,9] consider that the entire video is partitioned into smaller successive and non-overlapping segments before broadcasting, the operation of which is called fragmentation. Each segment of the video is then continuously and periodically broadcast on a separate stream at a certain bandwidth. The way in which the entire video is fragmented is a central point of any periodic broadcast schemes. In this paper, we present a novel broadcast scheme, called StairCase Broadcast (SCB), for VBR encoded media objects. We explore the targets to achieve both guaranteed zero data loss and the least required
bandwidth. SCB is, to the best of our knowledge, the first proposal that supports, by its design, the lossless periodic broadcast of VBR encoded media contents with de-coupled per-media-object server and client bandwidth. The original results on coupled per-media-object server and client bandwidth were reported in [4]. In this paper we do not consider VCR-like functionality, which is the focus of further research. We note that if the fast forward/backward or pause functionalities are to be implemented, it is always possible to do so once the complete video data are available at the client set-top box. We also consider that the underlying network can provide dedicated broadcast/multicast service without interference from other traffic flows in the network. The remaining of this paper is organized as follows: Section 2 provides a brief review of the related research. Section 3 provides the necessary notation and definitions used in SCB. Section 4 outlines the periodic schedule construction process to minimize the required server and client bandwidth. Section 5 illustrates through experimental results the properties of SCB. A summary discussion and future research directions are given in Section 6.
2 Related Work Most of the current proposals for periodic broadcast schemes assume Constant-Bit-Rate (CBR) encoded media objects [1,2,5,9]. The few existing proposals for support of the bandwidth-efficient family of Variable-Bit-Rate (VBR) encoded media objects are available at the cost of data loss due to overflow of the broadcast link capacity by the aggregate traffic of the simultaneously-transmitted segments of the media contents [3,8]. For the same video and the same image quality, CBR encoding requires twice or more bandwidth than the average bandwidth of the corresponding VBR encoding [8]. Clearly, there are substantial gains by using VBR encoded videos.
3 StairCase Broadcast (SCB) Scheme Following the similar definition in [3,4,8], let M denote the number of VBR videos to be broadcast. The bandwidth of the broadcast link from server to clients is B Mbits/sec. All video streams sent by the server share the B Mbits/sec. The
consumption rate of each video is F frames per second. The trace sequence of each video is fully known a priori. Let
f mi , i = 1 ,..., N m , m = 1,..., M , stand for the i th frame of the m th video, where th denotes the total number of frames of the m
S mK m } is: Km
number of bits in the
Nm
video. th
The m video is divided into K m segments of different sizes prior to broadcasting. The server M
broadcasts
∑K m =1
video streams simultaneously, each
m
S m = { S m1 , …,
media server given a fragmentation
Bm ( S m ) =
∑b i =1
i m
( Sm )
(2)
In SCB, the client downloads the media data from at most U m streams simultaneously and it behaves in a greedy fashion, that is, so long as there are more segments necessarily to be downloaded from subsequent streams of
m th video it will download as many streams as it can. Moreover, the download of the first U m segments starts at
the
the same time point: the tune--in instant. Let
Bc , m ( S m )
stream periodically broadcasts the same segment of the same video. Let U m (1 ≤ U m ≤ K m ) stand for the
denote the required client bandwidth to download the
number of streams that the client can download
video for a given transmission schedule
simultaneously for the
m
th
S
video. Let
set of successive frame indexes of the
i m
denote the
th
i segment of the
m th video, we have:
of the 1
m th video for the client given a fragmentation S m =
{ S m , …,
∑S i =1
i m
S mK m } is:
Bc , m ( S m ) =
(1)
K m segments for the m th video is
In SCB, each of the
transmitted on a separate stream at the bandwidth of
bmi , i = 1 ,..., K m . Let Bm ( S m ) denote the total required server bandwidth to transmit the a given transmission schedule
S m . Thus, the total
bandwidth necessary to download the subsequent segments
Km
Nm =
i +U m −1
max
1≤i ≤ K m −U m +1
∑b j =i
j m
(3)
Essentially, the required per-video server and client bandwidth are de-coupled. Figure 1 illustrates the operation of SCB:
m th video for
S m . Thus, the total
bandwidth necessary to transmit the
m th video for the
Play-out S m1
S m2
S m3
S m4
wm 1 Km
∑b i =1
m th
i m
2 3 Download Figure 1: An Example of the Operation of SCB.
t
4
In the above figure, the x-axis is time, the y-axis is bandwidth. The play-out part describes the consumption of the video at the client. The download part describes the continuous and concurrent periodic broadcast of the four example segments. The maximum number of streams that the client can download simultaneously, i.e., U m , is 2. Each of the four segments is periodically transmitted on a separate stream of bandwidth
bmi . The
shaded area in the download part corresponds to the information that is actually downloaded by the client. Once the download of one segment is completed, the client will start downloading one more segment immediately if there are more segments needed to be downloaded for the selected video. Each segment is completely stored at the client just in time for its playout. We call this scheme StairCase Broadcast due to the fact that the actual download part (the shaded area in the download part of Figure 1) at the client looks like a downwards staircase as time progresses. Following the construction illustrated in Figure 1, and in order to guarantee the service latency
wm for the m th
video, we note that the first segment must be broadcast at a bandwidth: 1 m
b ( Sm
∑ )=
i∈S 1m
f mi (4)
wm
Equation (4) establishes that the surface of the first horizontal rectangle of the step-function for the client download in Figure 1 is the same as the surface of the area denoted by the
S
1 m
in the play-out graph of the
same figure. A similar relation is true for all subsequent segments. That is, in order for the continuous and timely play-out, the next segment,
S mi , is fully downloaded and
available at the client just before the end of the play-out of segment
S mi −1 . Thus, the bandwidth at which the i th
stream of the m determined by:
th
video must broadcast segment
S mi is
∑ j∈S i f m , 1≤ i ≤ Um i −1 j S ∑ m wm + j =1 i F bm ( S m ) = j f i ∑ j∈Sm m , U m < i ≤ Km i −1 j S ∑ m j =i −U m F j m
(5)
Overall, after the service latency of
wm seconds, the
uninterrupted play-out of the video is possible. Each segment is available on local storage at the client just in time for its play-out. The data are played out at their nominal frame rate of
F frames per second in the order of S m1 • S m2 • S m3 …
S mK m . Note that because the frames have different sizes, the play-out curve of Figure 1, which represents the per-frame consumed data, is also variable. The loss-less nature of SCB is evident since the aggregation of the bandwidth required for all the
K m segments of m th
video is constant as described by equation (2) and (5).
4 On Minimizing Server and Client Bandwidth The minimization of the server bandwidth, without any regard for the client bandwidth, was addressed in [4] in the form of a shortest path problem in a DAG. Nevertheless, our objective is to combine the minimization of the server bandwidth along with that of the client bandwidth. An optimal solution for the server bandwidth is not immediately optimal for the client bandwidth. Furthermore, due to the proposed construction of the SCB schedule, even the server bandwidth minimization becomes more complicated, compared to [4]. The target to achieve the minimal required server bandwidth is to find a fragmentation of the frame sequence with K m segments such that the sum of the necessary bandwidth to broadcast each segment according to SCB can be minimized. On the other hand, the target to minimize the client bandwidth is to find a fragmentation of the frame sequence with K m segments such that the maximum of the sum of the necessary bandwidth to broadcast any
U m consecutive
segments can be minimized. We can observe that most likely the closer the necessary bandwidth for each segment, the lower the sum for any U m consecutive segments and the lower for the total necessary bandwidth for all the segments. Therefore, we can approximate the optimal solution by picking the fragmentation with the closest necessary bandwidth to broadcast each segment. The near-optimal solution for minimizing both server and client bandwidth is very simple and intuitively appealing. It operates as follows: (a) initialize N m segment, each consisting of one and only one frame, (b) merge the two neighboring segments resulting in the closest necessary bandwidth among all of current segments, (c) repeat step (b) until there are only K m segments. The running time of the resulting algorithm is
O( N m2 ) and the space requirement is O( N m ) .
14
5 Experimental Results The presented experiments are based on the application of SCB on a set of sample traffic traces coded according to the MPEG-1 standard [6]. All traces used herein are captured at 25 frames per second with a GOP (Group of Picture) of 12 frames. We selected a total of M = 10 videos from the set of available traces. The set contains both low-motion and high-motion VBR-encoded content. We do not present separate per-video results for all video traces examined since the performance results we derived (unless stated otherwise) lead to the same basic conclusions regardless of the video content. The following observations present the results on minimizing both server and client bandwidth for variable U m and K m . Figure 2 presents the results on required server and client bandwidth for variable
K m for a given
U m and service latency wm . Notably, both necessary server and client bandwidth decrease with increasing number of streams K m . In particular, the necessary bandwidth for server and client converge when K m = U m = 3. 9
Bandwidth (Mbits/sec)
8 7 6 5
Server BW
4
Client BW
3 2 1 0 3
4
5
6
7
Km
Figure 2: Server and Client bandwidth by heuristic vs. K m (trace FUSS, wm = 2 sec, N m = 5000,
U m = 3 ). The results on minimizing both server and client bandwidth for variable U m are shown in Figure 3. For the required server bandwidth, it decreases with the increasing of U m . While the required client bandwidth does not change monotonically with variable U m . This is because the fact that the required server bandwidth is reduced with the increasing of U m , thus less necessary bandwidth for each stream, on the other hand, the number of streams that the client can download simultaneously, i.e., U m , is increasing.
Bandwidth (Mbits/sec)
12 10 8
Server BW
6
Client BW
4 2 0 1
2
3
4
6
9
Um
Figure 3: Server and Client bandwidth by heuristic vs. U m (trace FUSS, wm = 2 sec, N m = 5000,
K m = 9). Notably, the seemingly large required server/client bandwidth in Figure 2 and 3 is because of the fact the service latency in the experiments is set as 2 seconds to emulate the near-VoD systems.
6 Discussion and Conclusion We propose a new broadcast scheme, called StairCase Broadcast (SCB), which can guarantee by its design the lossless distribution of VBR encoded media contents with de-coupled per-media-object server and client bandwidth constraint. Because of the particular structure and distribution setup for media content, we relax the assumption that was used to force the start of downloading to coincide with the beginning of a segment [1,2,3,8,9]. We assume the clients can start downloading the media data immediately from the moment when they make the requests for the media objects of their choices, by utilizing which the bandwidth requirement can be substantially reduced. Once the first segment of the selected media object is fully downloaded, the continuous play-out of the media content can be guaranteed according to SCB. Given the continuous decline in prices for secondary storage devices, it is reasonable that we relax the constraints related to the client-side secondary storage size. We assume that the client set-top box can store a large portion of the selected media object data (even near 100%). SCB significantly differs from the smoothing related techniques such as the optimal smoothing scheme by Salehi et al in [7] in the sense that the optimal smoothing approach is to reduce the rate variability for the transmission of stored VBR-encoded video given a limited client buffer capacity, while SCB essentially forces to smooth each periodicallybroadcasted video segment during each segment duration such that the loss-less nature of SCB can be guaranteed. However, no jitter can be observed for the play-out of the
video data at the client side in SCB since according to the broadcast schedule by SCB, once a segment is completely downloaded, the play-out of the segment video data can begin. Further, in SCB the segment duration is not determined by the client buffer capacity but by the timing requirement of the broadcast schedules to guarantee the uninterrupted and continuous play-out of the video data for the client, the given service delay and the minimal required server and client bandwidth. The resulting scheme, SCB, achieves loss-less distribution of VBR encoded media contents while achieving the minimal required server/client bandwidth. Please note that this scheme can also be applied to the CBR encoded media contents with the fame size of
f mi
as a constant to allow SCB to produce periodic broadcast schedules for a mixture of VBR and CBR encoded media contents. We will explore the potential to improve the efficiency of the presented heuristics and the support for VCR-like functionalities as our future directions.
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