Open-Loop Algorithms - Scalable Continuous Media Streaming Systems - page 316

18.4.2 Type-II Channels
Type-II channels are divided into groups of consecutive channels as shown in Figure 18.1.When
a client completes receiving a media segment, the corresponding channel will be released. With
the increased available client access bandwidth, the client can then begin to receive a group of
Type-II channels. Channels within the same group have their bandwidth allocated according
to equation (18.9) and subject to the same client access bandwidth constraint. For the example
in Figure 18.1, at time ( t 0 + 1) U ), the client completes receiving media segment L 1

(releases channel 1) and then begins receiving data from channels 6 and 7. These two channels
form the group 1 of Type-II channels.
It may appear that it is simpler to reallocate all the available bandwidth to a single channel
instead of a group of channels. However, doing so will unnecessarily increase the bandwidth
requirement because there is more than enough time to transmit the new media segment. To
see why, consider video segment L 4 being broadcast in channel 4 in Figure 18.1. Channel 0 is
released at time t 0 +

( m +

2 U and media segment L 4 will be playback at time t 0 + 6 U , thus we have

4 U seconds to transmit the media segment. However, since the bandwidth released by channel
0 is equal to b

2, media segment L 4 will be transmitted completely in just 2 U seconds if all
the available bandwidth is allocated for this logical channel. The extra 2 U seconds available
are then wasted and the network bandwidth is unnecessarily increased.
We tackle this deficiency by transmitting a media segment in a just-in-time manner. For
the previous example, we can transmit video segment L 4 using the lowest possible bit-
rate, i.e., b

/

4, to meet the playback schedule. Then we allocate the remaining bandwidth
to the next media segment using the same just-in-time scheduling procedure until no more
media segment transmissions can be added. These channels then form a group of Type-II
channels.
Let n 2 , j be the number of channels in group j , where j

/

= 0 , 1 ,..., etc. Then the bandwidth

allocation for channels in group j is given by

b

B i =

j ,

for i ≥ n 1 (18.9)

i −

and the number of channels in group j can be determined from solving for n 2 , j in

n 1 + n 2 , 0 ... + n 2 , j − 1 n 1 + n 2 , 0 ... + n 2 , j

B i ≤ C and B i > C (18.10)

i = j + 1 i = j + 1

which represents the client bandwidth constraints.
To prove playback continuity for media segments broadcast in Type-II channels, we consider
an arbitrary Type-II channel i in group j . As the client begins receiving all channels in group
j at the same time and it takes ( U B i seconds to completely receive media segment L i ,

we can then compute the time s i at which media segment L i is ready for playback from

· b ) /

t 0 + ( m + j ) · U (18.11)

U · b

s i = t 0 + ( m + j ) · U + (18.12)

B i