Open-Loop Algorithms - Scalable Continuous Media Streaming Systems - page 317

Substituting B i from equation (18.9) into equation (18.12) we obtain

s i = t 0 + ( m + j ) · U + ( i − j ) · U (18.13)

=

t 0 +

+ · ≡

( m i ) U c i

which is equal to the playback schedule and thus playback continuity for media segments
broadcast in Type-II channels is also guaranteed.

18.4.3 Client Buffer
As Figure 18.1 illustrates, the amount of media data accumulated in the client buffer can vary
during the media streaming session. Assume a client arrives at the system at time t 0 . Let t i 's
be the time instants at which a change in the reception schedule occurs, e.g., when the client
releases an existing channel (i.e., media segment completely received) and begins to receive data
from a new group of Type-II channels. As media segments are of the same size U and channel
bit-rates are integral fractions of the media bit-rate b , we can compute t i ( i = 1 , 2 ,... ) from

t i = T + ( i − 1) · U (18.14)

In particular, at time t i , the client begins playback of media segment L i − 1 and begins to
receive group i 1 of Type-II channels (see Figure 18.1).

Let H i be the amount of media data accumulated but not yet played back at time t i . Then
H 0 =

−

0, and we can compute H 1 from

n 1 − 1

H 1 = m · U · B i (18.15)

i = 0

where n 1 is the total number of Type-I channels received and the B i 's are their respective
bit-rates. Similarly, we can compute H 2 from

n 1 + n 2 , 0 − 1

H 2 = H 1 − U · b + U · B k (18.16)

k = 1

where the first term is the buffer occupancy at time t 1 , the second term is the amount of media
data consumed, and the last term is the amount of media data received from time t 1 to t 2 (i.e.,
U seconds).
In general, we can compute H i ( i

≥ 2) recursively from

n 1 + n 2 , 0 + ... + n 2 , i − 2 − 1

H i = H i − 1 − U · b + U · B k (18.17)

k = i − 1

As both media data consumption rate and total reception rate are constant within a given
time interval from t i to t i + 1, the maximum client buffer requirement must occur at one of the

time instants given by the t i 's. Hence we can determine the maximum client buffer requirement
H simply by finding the maximum H i :

= { H i |∀ = , ,... }

H max i 0 1 (18.18)