# Simon Sheu Computer Science National Tsing Hua Universtity Taiwan, ROC

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7 If we denote by k, k+, k+2, the segments of unequal szes such that the k+2 segment s the frst W-segment. Therefore, usng formulae (2) (Secton 3.), the worst dsplacement s gven by the followng: Worst_dplacement = 2 2 k+- k+/c (3) Consderng the case. n Fgure 6, f we afford the user n the nteractve mode an extra small amount of tme, we can avod ths specfc case. For example, when performng a Fast Forward acton, by forcng the user to render the content of the nteractve buffer, we can move from case. to the.2 case that shows a smaller dsplacement. Pause m pause the sake of expermentaton, we make the followng assumptons to conduct our smulatons. We frst assume that duratons for a play and for nteractve actons are exponentally dstrbuted wth ther respectve mean shown n Fgure 7. Furthermore, we assume that the duraton of all nteractve operatons are of equal mean.e. m ff = m fr = m pause = m jf = m jb, that we refer to as m or the nteractve mean. Fnally, we set the nteractve probabltes to be equal,.e., P pause = P ff = P fb = P jf = P jb. Therefore, P pause = P ff = P fb = P jf = P jb = P /5. We refer to the duraton rato dr as the average amount of nteracton (m ) over the average duraton of a normal playback nterval (m p ), hence dr = m. Ths rato measures the degree of nteracton. mp Fast Reverse m fr P fr P play P jb Jump Backward m jb Play m p P pause P jf P ff Jump Forward m jf Fgure 7: User Interacton Model Fast Forward m ff 5. PERFORMANCE STUDY To evaluate the performance of the BIT technque, we mplemented detaled smulators to compare t wth the Actve Buffer Management (ABM) scheme. We dscuss the smulaton study n ths secton. We frst present the user behavor model, and then dscuss the performance metrcs, and the smulaton results. 5. User Behavor Model Users can ntate an nteracton followng the model gven n Fgure 7. Smlar user nteracton model have been ntroduced n [2] and also used n [0]. Our model gves the probabltes of ssung an nteracton and the duraton of each nteracton. The probabltes defne the frequency of nteractons; and the m s defne the average amount of vdeo story, n tme unt, fast forwarded or fast reversed n a contnuous nteracton. Ths amount of contnuous nteracton s n terms of the orgnal uncompressed verson of the vdeo. For nstance, m fr = 50 seconds ndcatng that the users, on the average, fast reverse 50 seconds of the vdeo story; ths s not the same as pressng the fast-reverse button for 50 seconds. Snce Jump Forward and Jump Backward are nstantaneous, ther duraton refers to the length of vdeo skpped. A user starts playng the vdeo wth duraton m p. After ths duraton, the user may ssue an nteracton wth the probablty P = -P p or returns to play the vdeo wth the probablty P p. Once the VCR acton s fnshed, the user always returns to play a porton of the vdeo. Fndng typcal values for those parameters s out of the scope of ths paper. However, for 5.2 Performance Metrcs An nteracton can be successful or unsuccessful. An nteracton s consdered unsuccessful f the data currently n the buffers fal to accommodate the nteracton. For nstance, a jump to a destnaton pont outsde the buffer s consdered unsuccessful. In the case of contnuous actons, a long-duraton fast forward pushng the play pont off the nteractve buffer s consdered as an unsuccessful nteracton. To measure the percentage of unsuccessful cases, we use Percentage of Unsuccessful Actons as the frst performance metrc n our study. For those unsuccessful cases, we would lke to know the degree of ncompleteness. Therefore, we use Average Percentage of completon as our second performance metrc. As an example, f the user wshes to fast forward the play pont for 20 seconds, but s forced to resume the normal play after only 5 seconds, the percentage of completon s 5/20 or 75%. Fnally, when the user resumes a normal play after a successful or unsuccessful nteractve acton, the begnnng play pont mght be slghtly dfferent from the desred destnaton pont of the nteractve acton. To capture these dsplacements n the performance comparsons, we use Average Dsplacement as the thrd metrc n our study. A good nteracton technque should have a low percentage of unsuccessful nteractve actons, hgh percentage of VCR acton completon, and low average dsplacement. 5.3 Smulaton results Wthout loss of generalty, we set the CCA parameter c to be 3 n ths study. That s, all clents use three loaders to load the regular segments. We use two more loaders to load the compressed segments. We conduct our smulatons on a vdeo of two hours. The smulaton results are presented n the followng subsectons. We show that our technque outperforms the Actve Buffer Management technque for longer nteractons. We examne the effect of the clent buffer sze on performance, and demonstrate that good average dsplacement can be acheved. Fnally, we llustrate the effect of changng the compresson factor on the percentage of unsuccessful actons and the average percentage of completon Effect of the duraton rato We frst set the compresson factor to 4. The regular clent buffer s 5 mnutes; and the total buffer space s 5 mnutes. The server

8 uses 40 channels, from whch 32 are used for the regular vdeo, and 8 for the compressed verson of the same vdeo (.e. K r =32, K =8). Ths confguraton shows 0 segments of unequal sze and 22 segments of equal sze. The sze of the smallest segment s 2.84 seconds. Hence, the average access latency s.42 seconds. The parameters for the user behavor are as follows. We set an equal probablty for a normal play and for all the nteracton types combned (.e., P p = 0.5, P = 0.5, P pause = P ff = P fr = P jf = P jb = 0.). The mean duraton of a play operaton m p s 00 seconds. We vary the duraton rato dr from 0.5 to 3.5. The values selected for ths rato are hgh for two reasons: () Jump actons ncur a bg change n the poston of the play pont causng a larger dr; (2) we want to study the technques durng perods of ntense nteractve actvtes such as searchng for a desred vdeo segment. In other words, we model the user nteracton behavor, not vdeo watchng behavor. Our objectve s to compare BIT and ABM n supportng nteractons. Fgure 8 shows the effect of changng the duraton rato on the percentage of unsuccessful actons and the average percentage of completon. For dr =0.5, 20% of the nteracton actons are dened under ABM, compared to only % under BIT. We notce that BIT s much less senstve to changng the duraton rato. When dr = 3.5, BIT outperforms ABM by a factor of 48% n terms of percentage of unsuccessful actons, and 3% n terms of average percentage of completon. The poorer performance of ABM s partally due to a very fragmented buffer. The prmary reason, however, s due to the fact that cachng a compressed verson s more effectve n supportng longer-duraton nteractve actons. Average Percentage of Completon Actve Buffer Management BIT Duraton rato Fgure 8: Effect of changng the duraton rato regular buffer sze A.B.M, d_rato = BIT, d_rato A.B.M, d_rato =.5 BIT, d_rato =.5 Percentage of Unsuccessful Actons Percentage of Unsuccessful Actons Actve Buffer Management BIT Duraton rato A.B.M, d_rato = BIT, d_rato = A.B.M, d_rato =.5 BIT, d_rato = regular buffer sze Effect of the buffer sze In ths study, we vared the clent buffer sze from 3 mnutes to 2 mnutes. We kept the same parameters for the user behavor as n the last experment except for the duraton rato that we set to.0 and.5 for two dfferent smulaton runs. Snce the sze of the regular playback buffer n our technque s a thrd of the total buffer sze (the other two thrds s used to hold the compressed segments), we had to use at least 20 regular channels to broadcast the entre vdeo f the regular buffer sze s mnute. However, f the regular buffer sze s 7 mnutes only 8 channels are needed. We use 32 regular channels, 4 of them broadcast segments of unequal sze and 8 channels broadcast segments of equal sze. Snce the compresson factor s 4, the total number of nteractve channels s 33 (wth K r =32 and K =33). Fgure 9 shows the effect of changng the buffer sze for a duraton rato of.0 and.5. We can see from the fgure that BIT does not requre nearly as much buffer space as ABM to acheve an average percentage of completon of more than 80%. When the buffer sze s small (.e., mnute), BIT doubles the performance of ABM n terms of number of unsuccessful actons. As the buffer sze ncreases, both technques show better performance; but BIT contnues to perform sgnfcantly better. Agan, the advantage of BIT can be attrbuted to cachng the compressed verson n the nteractve buffer Effect of server bandwdth to the total average dsplacement We recall that a dsplacement occurs when the resumpton from an nteractve acton starts the normal playback at a play pont dfferent from the desred destnaton pont of the nteractve acton. In ths experment, we nvestgate the effect of server bandwdth on the average dsplacement. We fxed the same user behavor parameters as n the prevous experments, wth the duraton rato set at.5. We vared the server bandwdth between 30 channels and 65 channels. The szes of the W-segment correspondng to dfferent server bandwdths are gven n Table 5.. The table also shows the number of regular channel (Kr) and the number of nteractve channels (K). In all of these confguratons, the smallest segment s less than 0 seconds. The plot for the average dsplacement under varous server bandwdth (n terms of number of regular channels) s presented n Fgure 0. We observe that the average dsplacements of BIT and ABM are comparable. Ther dfference decreases wth the ncreases n the server bandwdth. Ths s due to the fact that the sze of the W- segment s smaller for a larger server bandwdth. When the W- segment s very small, the average dsplacement becomes small regardless of the nteracton technque. Table 5. W-segments and ther respectve Kr and K W-segments (mn) K r K Fgure 9: Effect of changng the buffer sze

10 ACM. Multmeda, pages 5-23, San Francsco, Calforna 994. [8] A. Dan, D. Staram, and P. Shahabudn. Dynamc batchng polces for an on-demand vdeo server. Multmeda Systems, 4(3) : June 996. [9] Z. Fe, I. Kamal, S. Mukherjee, M. Ammar: Provdng nteractve functons for staggered multcast near vdeo-on demand systems. In Proc. of the IEEE Internatonal Conference on Multmeda Computng and Systems, June 999. [0] Z. Fe, I. Kamel, S. Mukherjee, and M. Ammar: Provdng nteractve functons through actve clent buffer management n parttoned vdeo broadcast. Proc. of Frst Internatonal Worlshop on Networked Group Communcaton, (NGC 99) Psa, Italy, v [] L.Gao, J. Kurose, and D. Towsley: Effcent schemes for broadcastng popular vdeos. In Proc. of NOSSDAV 98, 998. [2] L. Golubchk, J.Lu, and R. Muntz. Adaptve pggybackng: A novel technque for data sharng n vdeo-on-demand storage servers. ACM Multmeda Systems, 4(3): 40-55, 996. [3] K. A. Hua., JungHuang Oh, and Khan Vu. An Adaptve Vdeo Multcast Scheme for Varyng Workloads Proc. Int l Conf. on Computer Communcatons and Networks, 998, pp [4] K. A. Hua., S. Sheu, and W. Tavanapong. Channg: A generalzed batchng technque for vdeo on demand. In Proc. of the Int l Conf On Multomeda Computng and System. June 997. [5] K. A. Hua and S. Sheu. Skyscraper Broadcastng: A new broadcastng scheme for metropoltan vdeo-on-demand systems. In Proc. of the ACM SIGCOMM 97, Cannes, France, September 997. [6] K. A. Hua, Y. Ca, and S. Sheu: Explotng clent bandwdth for more effcent vdeo broadcast. In Proc. of 998 Int l Conf. on Computer Communcatons and Networks. [7] K. A. Hua, Y. Ca and S. Sheu. Patchng: A multcast technque for true vdeo-on-demand servces. In Proc. of ACM Multmeda, Brstol, Unted Kngdom, September 998. [8] W. Lao and V. O. L. The splt and merge (SAM) protocol for nteractve vdeo-on-demand. IEEE Multmeda, vol.4 pp. 5-62, October-December 997. [9] J.F. Pars, S.W. Carter, and D.D.E. Long. Effcent broadcastng protocols for vdeo on demand. In Proc. of SPIES s Conf. on Multmeda Computng and Networkng (MMCN 99), pages 37,326, San Jose, CA, USA, January 99. [20] [S.Sen, L.Gao, J.Rexford, and D. Towsley. Optmal patchng schemes for effcent multmeda streamng. In Proc. of IEEE NOSSDAV, NJ, USA, June 999. [2] Vswanathan and T. Imelnsk. Metropoltan area vdeo-ondemand servce usng pyramd broadcastng. Multmeda systems, 4(4): , August 996

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