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dt L+T = t b ln( ), t+T T dt L+T = t b ln( ), t+T t
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0 t <T (18.2) T t T +L
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where t is the elapsed time after the client has entered the media streaming system and t is the time relative to the start of media stream. The upper bound of this client buffer requirement is 37% of the size of the media stream. Note that this is only a suf cient condition so it is still possible for a periodic broadcasting scheme to achieve lower client buffer requirement at the expense of increased latency or bandwidth.
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18.4 A Generalized Consonant Broadcasting Algorithm
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Starting from this section, we use an open-loop algorithm called Consonant Broadcasting (CB) to illustrate the design and trade-offs of open-loop multicast streaming algorithms. An important feature of CB is that it can be used in networks with limited client access bandwidth, which is the norm in typical metropolitan broadband networks. Figure 18.1 shows CB s broadcasting schedule and reception schedule. We divide a media stream into N equal-size segments and repeatedly broadcast them in separate variable-bandwidth multicast channels, i.e., media segment L i is multicast in the ith logical channel, for i = 0, 1, . . . , N 1. Thus CB belongs to the category of xed-segment variable-bandwidth schemes. We assume the media stream is constant-bit-rate encoded and thus the playback duration for each media segment is the same, denoted by U seconds.
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Scalable Continuous Media Streaming Systems
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Shaded region represents the reception schedule of a client that enters the system at time t0 Logical channel 0 L0 L0 L0 L0 L0 L0
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Logical channel 1
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Type-I channels
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. . . . . . . .
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Client reception bit-rate Playback
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L2 LL3 3 L4 L5 L6 L7 L8 L4 L5 L6
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L2 L3 L4 L5
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L2 L3 L4 Type-II channels, group 0 L6 Type-II channels, group 1 L8 I Type-II channels, group 2
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T: m: L: Li : N: N Startup latency Configurable parameter Length of video Video segment number (0,1, ,N 1) Total number of segments
m L T= N
b: i: j: t0 :
Client access bandwidth constraint C Video bit-rate Logical channel number (0,1, ,N 1) Group number of type-II channel(s) Time when the client enters the system
Figure 18.1 Bandwidth partition scheme and reception schedule in Consonant Broadcasting with m = 2
To determine the bandwidth for the logical channels, we need to rst set a target latency T in multiples of media segment duration U and the number of segments N in the following equation: T = m L N (18.3)
where m is a con gurable parameter to trade off between performance and system complexity. Given the same target latency T , increasing m will result in larger value of N (i.e., dividing the media stream into more segments of shorter duration) and this in turn will reduce the bandwidth requirement, and vice versa. While larger m is desirable from the bandwidth point of view, some network technologies (e.g., IP multicast) have limited number of logical multicast channels (e.g., multicast IP addresses) and thus m cannot be too large. We will return to this issue in Section 18.6. Next, each media segment is multicast over a separate logical transmission channel (e.g., an IP multicast group address) in the network. There are two types of logical channels, namely
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Type-I, and Type-II channels. We de ne their respective bandwidth partition schemes and reception schedules in the following chapters.
18.4.1 Type-I Channels
The set of Type-I channels begins with the rst channel, with a bandwidth allocation of B0 = b m (18.4)
Subsequent channels are allocated with progressively less bandwidth as given by Bi = b , m +i i = 0, 1, . . . , n 1 1 (18.5)
for the ith channel, where n 1 is the total number of Type-I channels. We can solve for n 1 so that the following two constraints are both satis ed:
n 1 1 i=0 n1
Bi C
Bi > C
(18.6)
The rst constraint represents the requirement that the aggregate bandwidth must be smaller than the client access bandwidth. This allows the client to receive all Type-I channels simultaneously. The second constraint represents the requirement that we should allocate as many channels as the client access bandwidth will allow maximizing utilization of the client access bandwidth. It is worth noting that if we remove the client access bandwidth constraint C, the number of Type-I channels n 1 will simply equal to N , i.e., all channels are of Type-I. In this special case, the bandwidth partition scheme in equation (18.5) will be identical to the Poly-harmonic Broadcasting scheme [6]. Therefore, Poly-harmonic Broadcasting can be considered as a special case of Consonant Broadcasting when there is no client access bandwidth constraint. Figure 18.1 illustrates the operation of Type-I channels (channels 0 to 3). When a client enters the system to start a new media stream, it will immediately start caching data from all Type-I channels simultaneously. The client can start playback after a latency of T seconds as the rst media segment L 0 will be completely received by then. In general, let t0 be the time the client enters the system, and let ci be the playback time for media segment L i , which can be computed from ci = t0 + (m + i) U, i = 0, 1, . . . , n 1 1 (18.7)
As the client caches all Type-I channels immediately at time t0 , it will have completely received media segment L i by the time si given by si = t0 + (L b)/N , b/(m + i) i = 0, 1, . . . , n 1 1 L =U N (18.8)
= t0 + (m + i) U,