storage, user waiting time, and bandwidth consumption. This ... harmonic-based protocols require much less server broadcast .... with few dedicated channels.
➠
➡ A HYBRID PAGODA BROADCASTING PROTOCOL: FIXED-DELAY PAGODA BROADCASTING PROTOCOL WITH PARTIAL PRELOADING Hong Kee Sul, Hyunchul Kim, Kilnam Chon Department of Computer Science Korean Advanced Institute of Science and Technology Daejeon, Korea ABSTRACT Broadcasting protocols offer an efficient and scalable method to provide video-on-demand. We present a new broadcasting protocol that assumes that some portions of the video are already preloaded in the set-top-box (STB), and at the same time, requires the user to wait for a fixed-delay before viewing. As a result, there is a trade-off between the size of the consumed local storage, user waiting time, and bandwidth consumption. This trade-off makes this protocol very flexible, in that we can control the consumption of one resource by adjusting the use of the other two. Also, the performance of the proposed protocol is not very far from the theoretical minimum. We also present a heuristic version of the protocol, in which the performance is improved a little.
1. INTRODUCTION Video-on-Demand (VoD) proposes to allow the subscribers to view the video of their choice at the time of their choice [1]. But to fully satisfy such requests, there must be enough bandwidth proportional to the number of concurrent users. This lack of scalability makes VoD expensive, and so broadcasting protocols were introduced. Although the broadcasting protocols force the users to wait, and require broadcasting medium, they have two major advantages. They scale up extremely well, and they have modest bandwidth requirements [2]. Broadcasting protocols divide the video into many segments, and broadcast the segments into different channels. The segments are mapped into channels so that different users can share the same stream regardless of the time of their request. Since the staggered broadcasting [3], many broadcasting protocols have appeared. Recent work in broadcasting protocols has nearly reached the theoretical lower bound in terms of channel usage and waiting time of the user. Among all protocols using segments of equal duration and channels of equal bandwidth, the fixed-delay pagoda broadcasting (FDPB) protocol [2] provides the lowest waiting time, which is very close to the theoretical lower bound [2]. It implies that a new approach must be taken. In this paper we propose the hybrid pagoda broadcasting (HPB) protocol, a new approach combining the FDPB protocol with partial preloading. Partial preloading is a buffering scheme introduced in [4] and [5], utilizing the local storage of the STB to provide zero-delay access. The amount of preloading required to provide zero-delay access is decided from the number channels used. We incorporated the ideas of partial preloading
0-7803-7965-9/03/$17.00 ©2003 IEEE
into the HPB protocol in a different manner. By giving up the zero-delay feature and assuming that the user has to wait a certain amount of time, we can adjust the amount of required preloading. In other words, our HPB protocol generates a tradeoff between the size of the consumed local storage, user waiting time, and bandwidth consumption. We have also derived the theoretical lower bound of the HPB protocol. By comparing it with the theoretical lower bound given in [2] and [5], it is shown that our HPB protocol is a generalized approach of the two. We also present a version of the HPB protocol in which the number of subchannels is chosen heuristically. With the heuristic version, there is a little improvement in the performance.
2. RELATED WORK Broadcasting protocols can be categorized into one of the followings: pyramid-based broadcasting protocols, harmonicbased broadcasting protocols, and pagoda-based broadcasting protocols. Pyramid-based broadcasting protocols include pyramid broadcasting [6], skyscraper broadcasting [7], and fast broadcasting [8]. Pyramid-based protocols divide the video into multiple segments of different sizes, and the segments are broadcasted in channels of equal bandwidth. Harmonic-based protocols include harmonic broadcasting [9] and polyharmonic broadcasting (PHB) [10]. In the PHB protocol, equal sized segments are broadcasted in its own channel of different bandwidth. The segments are broadcasted so that every segment arrives just in time, right before the segment is needed for viewing [1]. Since segments are transmitted just in time, harmonic-based protocols require much less server broadcast bandwidth compared to pyramid-based protocols. But the drawback of harmonic-based protocols is that it requires a large number of streams, making it very expensive [2]. Pagoda-based protocols include pagoda broadcasting [11], pagoda broadcasting protocol with partial preloading [5], and the FDPB protocol. Pagoda-based protocols divide the video into multiple segments of equal sizes, and the segments are broadcasted in channels of equal bandwidth. Pagoda-based protocols are hybrid of pyramid-based protocols and harmonicbased protocols [1]. As in harmonic-based protocols, video is partitioned into fixed size segments. As in pyramid-based protocols, segments are mapped into a small number of streams of equal bandwidth. The FDPB protocol simulates the just in time transmission of the PHB protocol by using time-division multiplexing. While forcing the user to wait for a fixed-delay amount of segments, the FDPB protocol broadcasts each segment in such frequency that it ensures that every segment will be received before it is
I - 801
ICME 2003
➡
➡ Order First Second Third in Subchannel Subchannel Subchannel Subchannel 1 S10 S14 S19 2 S11 S15 S20 3 S12 S16 S21 4 S13 S17 S22 5 S18 S23 6 S24 7 8 Number of slots: 4 = 10+ 9 −1 5 = 14+9 −1 6 = 19+9−1 i SC + m − 1 4 4 4 s
1
Fourth Subchannel S25 S26 S27 S28 S29 S30 S31 S32
8 = 25+9−1 4
Figure 1. The segment-to-subchannel mapping of the first channel. (m = 9, p = 9)
needed [2]. Since the FDPB protocol simulates the just in time transmission of the PHB protocol while using only a few channels, most segments are broadcasted a bit more frequently compared to the PHB protocol. Therefore the FDPB protocol performs slightly worse compared to the PHB protocol. Still, the FDPB protocol provides the lowest waiting times of all protocols using segments of equal duration and channels of equal bandwidth [2]. In most broadcasting protocols, the first few segments are broadcasted more frequently than the latter ones. So, it is important to reduce the bandwidth consumption of the first few segments. The partial preloading protocols in [4] and [5] resolves this issue by preloading the first few segments in the STB. In this way, the bandwidth originally consumed by the first few segments can be saved. In [5], the fast broadcasting protocol and the pagoda broadcasting protocol were modified to provide instant access by utilizing local storage. The partial preloading method used in [4] and [5] is very restricted in that it assumes zero-delay access. The number of preloaded segments required to provide zero-delay access is determined from the number of allocated channels. In other words, viewing is possible only if there is enough local storage to store the amount of segments determined from the number of channels. What if we preload less number of segments than required for zero-delay access? Although zero-delay access would not be possible, bandwidth consumed by the preloaded segments can be saved.
3. THE HYBRID PAGODA BROADCASTING PROTOCOL In this paper we present a hybrid protocol, combining the FDPB protocol with partial preloading. Our partial preloading is a little different from the partial preloading used in [4] and [5] in that we do not preload enough to provide zero-delay access. The Aim of our partial preloading is not to provide zero-delay access, but to reduce bandwidth consumption. The hybrid pagoda broadcasting protocol is a combination of the FDPB protocol and the partial preloading. The HPB protocol combines the two by implementing both partial preloading and fixed-delay waiting. The HPB protocol assumes that some portions of the video have been already preloaded in the STB, and at the same time, demands the user to wait for a fixed-delay. Hence the number of total segments is derived from three variables: the number of preloaded segments, the number of fixed-delay waiting segments, and the number of channels. Thus, there is a trade-off between the size of the consumed local
storage, the user waiting time, and the given bandwidth consumption. This trade-off makes this protocol very flexible, since we can control the use of one resource by adjusting the use of the other two. We will consider a video of duration D to be broadcast over k channels Cj (1 ≤ j ≤ k). The bandwidths of these channels will be equal to the video consumption rate b, and so the total bandwidth consumed by the protocol will be kb. The HPB protocol will partition each video into n equal size segments, S1 to Sn, of duration d = D/n. Like the pagoda broadcasting protocol with partial preloading protocol, the HPB protocol assumes that the first p segments of video have been preloaded into the user’s STB, where p is some integer p ≥ 1 or 0 when m ≠ 0. The k channels will be partitioned into slots, where the duration of a slot is equal to the duration of a segment. The n-p segments will be broadcast at different frequencies over the k channels. Like the FDPB protocol, the HPB protocol requires all users to wait for a fixed time interval w = md, where m is some integer m ≥ 1 or 0 when p ≠ 0. The segments Sp+1~ Sn are distributed by time-division multiplexing, similar as to how the FDPB protocol broadcasts segments S1~ Sn. To guarantee that segment Si (p+1 ≤ i ≤ n) would arrive before it is needed, Si needs to be transmitted at least once every (m+i-1)d seconds. Like the FDPB protocol, the HPB protocol maps segments into subchannels in a strict sequential fashion. First, we shall choose s1, where sj is the number of subchannels for channel Cj As in the FDPB protocol, we shall choose sj to be the closest integer to m + iC − 1 where S iC is the first segment assigned to channel Cj. Then, starting from segment Sp+1, we shall sequentially allocate i + m − 1
SC
s
j
segments to each subchannel where S i is the first segment SC assigned to each subchannel. The process repeats for all k channels. As a result, the whole segment-to-channel mapping can be constructed. As in pagoda broadcasting protocol with partial preloading, the preloaded segments will be distributed with few dedicated channels. By computing the limit of the consumed bandwidth when n goes to infinity, we can derive the theoretical lower bound of the HPB protocol as in [2] and [5]. Using 3 variables x, y, and k, we can create a formula describing the relationship between the proportion of preloading, proportion of fixed-delay waiting, and bandwidth consumption. Let x = p/n represent the proportion of preloaded segments to the total number of segments, and let y = m/n represent the proportion of fixed-delay segments to the total number of segments. Since segment Si must be broadcast at a period of minimum i+m-1, the minimum bandwidth consumption of segment Si is b/(i+m-1). So the lower bound of the total bandwidth used by all segments would be n n + m −1 b
∫
p +1
i+ m −1
di = b × ln
p + m
Since k channels are used, we will assume that the above bandwidth is equal to kb. And since x = p/n and y = m/n, we can deduce the following: e
k
=
1+ y − 1 n + m −1 n = p + m x + y
Since n goes to infinity we have
I - 802
y=
1 − ek x ek − 1
(1)
➡
➡ Table 1. Result of the HPB protocol where k = 4, n ≈ 50000 Number of Number of Number of total x (=p/n) y (=m/n) waiting segments preloaded * 100 * 100 segments (n) (m) segments (p) 0
989
49981
0
1.9788
Table 2. Comparison of the HPB and its lower bound where n ≈ 50000 Relative Error HPB protocol of y-intercept (n = 49750~50250) (%) 1 y = 58.1977%-1.5820x y = 58.6380%-1.5844x 0.7566
139
849
50000
0.2780
1.6980
2
y = 15.6518%-1.1565x
y = 15.9190%-1.1579x
1.7072
220
763
50000
0.4400
1.5260
298
684
50000
0.5960
1.3680
3
y = 5.2396%-1.0524x
y = 5.4128%-1.0534x
3.3056
401
580
50000
0.8020
1.1600
4
y = 1.8657%-1.0187x
y = 1.9784%-1.0201x
6.0460
549
430
50000
1.0980
0.8600
5
y = 0.6784%-1.0068x
y = 0.7508%-1.0066x
10.6722
606
371
50000
1.2120
0.7420
6
y = 0.2485%-1.0025x
y = 0.2923%-1.0039x
17.6258
744
232
50000
1.4880
0.4640
819
153
50000
1.6380
0.3060
929
41
50000
1.8580
0.0820
969
0
50007
1.9377
0
Number of Theoretical lower bound channels (k)
Table 3. Comparison of the heuristic HPB and its lower bound where n ≈ 50000 Relative Error Heuristic HPB protocol Number of of y-intercept Theoretical lower bound (n = 49750~50250) channels (k) (%) 1 y = 58.1977%-1.5820x y = 58.6250%-1.5844x 0.7342
Waiting Time/Video duration(m/n) * 100
2.5 y = 1.9784% - 1.0201x [HPB n = 49750~50250]
2
y = 1.8657% - 1.0187x [Theoretical Lower Bound]
1.5
y = 15.6518%-1.1565x
y = 15.908%-1.1579x
1.6369
3
y = 5.2396%-1.0524x
y = 5.4018%-1.0532x
3.0957
4
y = 1.8657%-1.0187x
y = 1.9658%-1.0198x
5.3653
5
y = 0.6784%-1.0068x
y = 0.7401%-1.0074x
9.0949
6
y = 0.2485%-1.0025x
y = 0.2874%-1.0029x
15.6539
able for the fourth subchannel. So, S10~S32 will be broadcast on channel C1. The detailed segment-to-subchannel mapping is illustrated in Figure 1.
1
0.5
4. ANALYSIS
0 0
0.5 1 1.5 2 Preloaded Segments/Total Segments(p/n) * 100
Figure 2. Theoretical lower bound and results of the HPB protocol (k = 4, n ≈ 50000) k
And the minimum waiting time is given by wmin= 1−e x D k e −1
(2)
We can see that a linear relationship exists between the user waiting time and the size of the consumed local storage. Moreover, the above equations generate the same results as the lower bound of the FDPB protocol and the lower bound of the conventional partial preloading protocols. When y = 0, the equation (1) generates 1 , which is the lower bound given =x ek in [5]. When x = 0, the equation (2) generates D , wmin =
ek −1
which is the lower bound of the FDPB protocol shown in [2]. We can see that the HPB protocol generates the same lower bound as the FDPB protocol and partial preloading. Consider the case when m = 9, p = 9. Since p = 9, segments S1~S9 are preloaded on the STB. First we must decide s1, the number of subchannels for channel C1. Since segment S10 is the first segment to be broadcast on channel C1, ic = 10 and s1 = 4(Q m + i C − 1 = 18 = 4.243 ). So we shall partition channel C1 into 4 subchannels. Next we must decide how many segments can be allocated to each subchannel. Since S10 is the first segment to be broadcast on the first subchannel of C1, isc = 10 and so the number of slots available for the first subchannel of C1 is i SC + m − 1 10 + 9 − 1 . So segments S10~S 13 will be
2
s1
=
4
=4
transmitted in the first subchannel. For the second subchannel of slots are available. Similarly, 6 C1, isc = 14 and so 14 + 9 − 1
4
=5
slots are available for the third subchannel and 8 slots are avail-
For any given pair of p and m, our HPB protocol can create the segment-to-mapping table, and thus generate n. For our analysis, only the pairs in which the corresponding n is close to 50000 will be selected. As in [10] and [2], our HPB protocol performs better when n is larger. But as noted in [2], n should not be so large that it might affect the performance of the disk subsystem. Assuming a 5Mbps video of 120 minutes, the size of a single segment would be about 88 KB when n is 50000. We have decided that it is a reasonable size, and therefore all of our results are created from pairs in which the corresponding n is in between 49750 and 50250. The detailed results of the selected pairs where k = 4 is in Table 1. There are hundreds of pairs of p and m in which n ≈ 50000, and a few are selected in Table 1. Figure 2 shows the same results, depicting the relationship between x and y. The theoretical lower bound from equation (1) is also shown in Figure 2. One can easily notice the linear relation among x and y. The HPB protocol generates a linear formula y = 1.9784% – 1.0201x, where n ≈ 50000. This means that the HPB protocol offers a waiting time of (1.9784% – 1.0201x) of the total duration, where x is the proportion of the preloaded segments to the total number of segments and the total number of segments is around 50000. Table 2 compares the theoretical lower bounds and the results of the HPB protocol for other values of k. Although the results are close to the theoretical lower bound when the number of channels is few, it becomes inefficient as the number of channels grows. Since the total number of segments is fixed, the number of segments allocated to each channel decreases as k grows. It is speculated that as the number of segments for each channel decreases, the segments are broadcast at a less optimal frequency, and thus becomes more inefficient. So, the gap between the HPB protocol and its theoretical lower bound grows as we increase k.
I - 803
➡
➠
Waiting Time/Video duration(m/n) *100
5
of subchannels. The result of the heuristic HPB protocol is displayed in Table 3. As one can see, there is some increase in the performance.
PHB (n=50000) HPB=FDPB, x = 0
4
5. CONCLUSION
HPB, x = 0.5/100 HPB, x = 1.5/100
3
n=50000(±250) for HPB
2
1
0 3
4
5
6
Number of channels
Figure 3. Comparison of the HPB protocol and the PHB protocol
Figure 3 compares the waiting times of the PHB protocol and the HPB protocol. When x = 0, the HPB protocol acts just like the FDPB protocol. A good example of the HPB protocol can be found when k = 4 and x = (1.5)/100. By preloading only 1.5% (x = 1.5/100) of the video, the user can view the video by waiting only 0.4483% of the total duration. That is less that 24% of the waiting time of the PHB protocol, which is 1.873%. And it is less than 22.7% of the waiting time of the FDPB protocol, which is 1.972%. Of course, zero-delay access can be achieved when there is enough storage to preload 1.9394% of the video. But there might not be enough storage, or storing such amount could be prohibited since it is not certain that the users will actually view the content that is preloaded. The HPB protocol resolves both issues, since it is possible to preload any amount between 0% and 1.9394%. The HPB protocol provides trade-off between the size of the consumed local storage, user waiting time, and the given bandwidth consumption. To reduce the user waiting time, we can either allocate more channels or preload more. To use less number of channels, we can either wait longer or preload more. To preload less, we can wait longer or allocate more channels. There appears to be two problems in the HPB protocol. First, the performance of the HPB protocol drops as n decreases. With n decreasing, the size of a single segment becomes larger, and segments tend to be broadcast at a frequency less optimal. The FDPB protocol shows the same weak point. As seen on the above Figure 3, the performance gap between the FDPB protocol and PHB protocol is minimum when n is 50000. But when n is only a few hundred, as seen on Figure 7 of [2], the FDPB protocol performs rather worse. Second, there may be implementation challenge when n is too large. As noted earlier, the size of a single segment might be too small if n were to be too large. And handling such segments would cause many problems. If handling such small-sized segments weren’t of any problem, increasing n might be a good solution to improve the performance of the HPB protocol. Aside from increasing n, another solution is to adjust the number of subchannels. As in [2], we have observed that the close-to-best results were achieved when the number of subchannels was set to the closest integer to m + iC − 1 . But in some cases, it did not turn out to be the optimum. By comparing the results of the 10 closest integers to m + iC − 1 , we have heuristically decided the optimal number
VoD broadcasting protocols aim to resolve the scalability problem in VoD systems. With broadcasting protocols many users can share the same stream, and thus bandwidth is saved. We have presented the hybrid pagoda broadcasting protocol, a new broadcasting protocol that combines the fixed-delay waiting of the FDPB protocol with partial preloading. The HPB protocol assumes that some portions of the video are already preloaded in the STB, and forces the user to wait for a fixeddelay. As a result, there is a trade-off between the given bandwidth consumption, size of the local storage, and user waiting time in the proposed protocol. This trade-off provides much flexibility, in that we can adjust the three factors according to its importance. We have also shown a heuristic version of the protocol, which performs a little better. More work can be done to improve the performance of the protocol. The HPB protocol could be combined with reactive broadcasting protocols to improve the overall performance for less popular videos.
REFERENCES [1] Ailan Hu, "Video-on-Demand Broadcasting Protocols: A Comprehensive Study", Proc. of the IEEE Infocom 2001, pp. 508-517, Apr. 2001. [2] J.-F. Pâris, "A Fixed-Delay Broadcasting Protocol for Video-onDemand", Proc. of the 10th International Conference on Computer Communications and Networks (ICCCN’01), pp. 418-423, Oct. 15-17, 2001. [3] K. C. Almeroth and M. H. Ammar, “The use of multicast delivery to provide a scalable and interactive video-on-demand service”, IEEE Journal on Selected Areas in Communications, 14(5):1110–22, Aug. 1996. [4] J.-F. Pâris, D. D. E. Long, and P.E. Mantey, "Zero-Delay Broadcasting Protocol for Video-on-Demand", Proc. of the 1999 ACM Multimedia Conference, pp. 189-197, Nov. 1999 [5] J.-F. Pâris and D. D. E. Long, "The Case for Aggressive Partial Preloading in Broadcasting Protocols for Video-on-Demand", Proc. of the 2001 IEEE International Conference on Multimedia and Expo (ICME’01), pp. 113-116, Aug. 2001 [6] S. Viswanathan and T. Imielinski, "Pyramid Broadcasting for Video on Demand Service", IEEE Multimedia Computing and Networking Conference, Volume 2417, pp. 66-77, San Jose, California, 1995 [7] Hua, K. A., and S. Sheu, "Skyscraper broadcasting: a new broadcasting scheme for metropolitan video-on-demand systems", In SIGCOMM 97, pp. 89-100, Sep. 1997. [8] L. Juhn and L. Tseng, "Fast Data Broadcasting and Receiving Scheme for Popular Video Service", IEEE Transactions on Broadcasting, 44(1): 100-105, Mar. 1998. [9] L. Juhn and L. Tseng, "Harmonic broadcasting for video-on-demand service", IEEE Trans. on Broadcasting, 43(3): 268-271, Sep. 1997. [10] J.-F. Pâris, S. W. Carter and D. D. E. Long, "A low bandwidth broadcasting protocol for video on demand," Proc. of the 7th International Conference on Computer Communications and Networks (IC3N’98), pp. 690-697, Oct. 1998. [11] J.-F. Pâris, S. W. Carter, and D. D. E. Long, "A Hybrid Broadcasting Protocol for Video on Demand", Proc. of the 1999 Multimedia Computing and Networking Conference (MMCN'99), pp. 317-326, Jan. 1999.
I - 804
