Open-Loop Algorithms - Scalable Continuous Media Streaming Systems - page 315

Type-I, and Type-II channels. We define 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 first channel, with a bandwidth allocation of

b
m

B 0 = (18.4)

Subsequent channels are allocated with progressively less bandwidth as given by

b

B i =

i ,

i = 0 , 1 ,..., n 1 − 1 (18.5)

m +

for the i th 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 satisfied:

n 1 − 1 n 1

B i ≤ C and B i > C (18.6)

i = 0 i = 0

The first 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 simul-
taneously. 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 first media segment L 0 will be completely received by then.
In general, let t 0 be the time the client enters the system, and let c i be the playback time for
media segment L i , which can be computed from

c i = t 0 + ( m + i ) · U , i = 0 , 1 ,..., n 1 − 1 (18.7)

As the client caches all Type-I channels immediately at time t 0 , it will have completely
received media segment L i by the time s i given by

( L · b ) / N

s i = t 0 +

i ) ,

i = 0 , 1 ,..., n 1 − 1 (18.8)

b / ( m +

L
N =

=

t 0 +

+ · , ∵

( m i ) U U

which precisely meets the playback schedule c i 's and thus playback continuity is guaranteed.