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18.2.3 Fixed-Segment Variable-Bandwidth Schemes
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Alternatively, we can broadcast xed-size media segments over variable-bandwidth channels. Notable examples include the Harmonic Broadcasting scheme proposed by Juhn and Tseng [5] in 1997 and the Poly-harmonic Broadcasting scheme [6] proposed by Paris et al. in 1998. In the Poly-harmonic Broadcasting scheme, the media stream is partitioned into N equalsize media segments. Given the desired start-up latency T and a control parameter m, one can choose N by solving the equation T = (m L)/N . The network bandwidth B is then divided into N channels (i.e., same as the number of media segments), with the bandwidth for channel b i equal to Bi = m+i , i = 0, 1, . . . , N 1. Media segment L i is then repeatedly broadcast over channel i. The client, on the other hand, is required to cache media segments from all channels simultaneously once it enters the system. The Poly-harmonic Broadcasting scheme can achieve near-optimal performance when m is large. There are, however, also a few practical issues. First, as the client must receive all channels simultaneously, the client s access network bandwidth requirement is very large (same as the server bandwidth requirement). This may not be practical in all wired systems as in some cases the access bandwidth is substantially more limited than server bandwidth (e.g., ADSL, cable modem). Second, using a large value of m, while it improves performance, will generate a huge number of media segments, each requiring its own network channel for transmission. For some types of network (e.g., IP multicast), this may become a bottleneck as the number of network channels is limited (e.g., IP multicast addresses). We address these issues in the Consonant Broadcasting scheme described later in this chapter.
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18.2.4 Variable-Segment Variable-Bandwidth Schemes
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The nal type of broadcasting scheme is to have both variable segment size and variable channel bandwidth. Juhn and Tseng proposed the rst variable-segment variable-bandwidth scheme called Staircase Data Broadcasting [4] scheme in 1997. In Staircase Data Broadcasting, a media stream is rst partitioned into N equal-size media segments, based on the number of channels K, derived from the equation N = K 1 2 j = 2 K 1. The network bandwidth j=0 B is then divided equally into K channels, with the same bandwidth b for the ith logical channel. For each media segment L i ,it is further divided into 2i continuous media sub-segments for i = 0, 1, . . . , K 1. Similarly, each logical channel i is further sub-divided into 2i subchannels, each with a bandwidth of b/2i . Finally, each sub-segment is then broadcast repeatedly over a separate sub-channel. The client begins by receiving data from the rst occurrence of the beginning of media segment L 0 at time t0 . The 2i continuous media sub-segments L i, j , j = 0, 1, . . . , 2i 1, within channel i(i = 0, 1, . . . , N 1) are then cached at time t0 + (L j)/N . The client access bandwidth requirement is equal to 2b, the maximum start-up latency T is equal to the broadcast
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duration of the rst media segment, and the client buffer requirement is bounded by 25% of the size of the media object.
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18.3 Performance Bounds
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Common to all periodic broadcasting schemes, the key system parameters are start-up latency, network bandwidth, client access bandwidth, and client buffer requirement. Different schemes can be considered as achieving different trade-offs among these four parameters, and thus the natural question is whether bounds on the system s performance exist. This question has been investigated independently by Hu [12], and Birk and Mondri [13], and others. Although the approaches and the derivations are different, all studies arrive at the same result. Speci cally, given a start-up latency of T , it can be shown that the minimum network bandwidth needed for any periodic broadcasting scheme, is given by B = b ln( L+T ) T (18.1)
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assuming there is no constraint on the client access bandwidth. Additionally, for any optimal periodic broadcasting scheme achieving the performance bound in equation (18.1), it can be shown that the client buffer requirement is equal to t b t b
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