Bandwidth Partitioning and Reception Schedule in .NET

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18.6.1 Bandwidth Partitioning and Reception Schedule
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Type-I channels in GCB are the same as the original CB as de ned in equations (18.5) and (18.6). The difference is in the design of the Type-II channels. In CB, reception of Type-II channels in the same group begins at the same time but ends at different times due to the justin-time scheduling principle. While this technique can reduce the bandwidth requirement, it also requires the use of a separate network transmission channel (e.g., an IP multicast address) for each of the Type-II channels. To reduce the number of channels needed, we modify CB such that reception of Type-II channels in the same group all begins and ends at the same time as shown in Figure 18.6. Consequently, individual Type-II channels in the same group no longer need to be multicast over a separate network channel, but can be transmitted over a single shared channel. Let n 1 be the total number of Type-I channels and n 2, j be the number of Type-II channels in group j ( j = 0, 1, . . .) respectively. Then the bandwidth allocation of each channel in group j,
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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
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Channels in Type-II can be grouped and released at the same time by using one multicast stream L0 L0
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Logical channel 1
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Type-I channels
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b m+i
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Client reception bit-rate Playback
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L2 L3 L4 L5 L6 L7 L8 L4 L5 L6
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L2 L3 L4 L5
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L2 L3 L4 L5 L6 L7 L8 L7 L8
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l Logical channels in group 0 start receiving at h0 and release at g0
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Type-II I channels, group 0 Type-II channels, group 1 Type-II channels, group 2
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b g j hj
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L0 L1 L2 L3 L4 L5 L6 L7
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Time
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T m L Li N b i : : : : : : : Startup latency Configurable parameter Length of video Video segment number (0,1, ,N 1) Total number of segments Video bit-rate Logical channel number (0,1, ,N 1)
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m L T= N
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j : t0 : n2,j : hj :
Client access bandwidth constraint C
Group number of type-II channel(s) Time when the client enters the system Total number of channel in group j Start time of receiving video segment in group j relative to the start of video play back (in the unit of L/N seconds) gj : End time of receiving video segment in group j relative to the start of video play back (in the unit of L/N seconds)
Figure 18.6 Bandwidth partition scheme and reception schedule in Grouped Consonant Broadcasting with m = 2
denoted by W j , is given by Wj = b gj h j (18.19)
where g j and h j represent respectively the completion time and the start time for receiving the video segments in the group relative to the time video playback begins, in unit of U seconds, and are given by gj = n1, n 1 + n 2,0 + . . . + n 2, j 1 , for j = 0 otherwise (18.20)
hj =
j, n 1 + n 2,0 + . . . + n 2, j n 1 1 ,
for j n 1 for j > n 1
(18.21)
Open-Loop Algorithms
We can determine the number of channels in group j from solving for n 2, j in
n 1 +n 2,0 +...+n 2, j 1 n 1 +n 2,0 +...+n 2, j
Bi C
i=h j+1
i=h j+1
Bi > C
(18.22)
where Bi = W j for all i s in the range g j i < g j+1 . To prove playback continuity for media segments broadcast in Type-II channels, we consider an arbitrary Type-II group, say group j, comprising media segments {L i | g j i < g j+1 }. As the client begins receiving all channels in group j at time t0 + (m + h j ) U (18.23)
and it takes (U b)/W j seconds to completely receive the media segments, the time s j at which all media segments in the group is ready for playback can be computed from s j = t0 + (m + h j ) U + U b Wj (18.24)
Substituting W j from equation (18.19) into equation (18.24) we obtain s j = t0 + (m + h j ) U + (g j h j ) U = t0 + (m + g j ) U t0 + (m + i) U, for g j i < g j+1 (18.25)