Open-Loop Algorithms - Scalable Continuous Media Streaming Systems - page 313

duration of the first media segment, and the client buffer requirement is bounded by 25% of
the size of the media object.

18.3 Performance Bounds
Common to all periodic broadcasting schemes, the key system parameters are start-up latency,
network bandwidth, client access bandwidth, and client buffer requirement. Different schemes
can be considered as achieving different trade-offs among these four parameters, and thus the
natural question is whether bounds on the system's performance exist.
This question has been investigated independently by Hu [12], and Birk and Mondri [13],
and others. Although the approaches and the derivations are different, all studies arrive at the
same result. Specifically, given a start-up latency of T , it can be shown that the minimum
network bandwidth needed for any periodic broadcasting scheme, is given by

ln( L

+ T

B = b · ) (18.1)

T

assuming there is no constraint on the client access bandwidth.
Additionally, for any optimal periodic broadcasting scheme achieving the performance
bound in equation (18.1), it can be shown that the client buffer requirement is equal to

L

dt

ln( L

+ T

t · t · t <

b ·

T =

b · ) , 0 ≤ T

t + T

H ( t )

0

= (18.2)

L

dt

ln( L

+ T

t · t ·

t ≤

b ·

T =

b · ) , T ≤ T + L

t

t +

t − T

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 sufficient 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.

18.4 A Generalized Consonant Broadcasting Algorithm
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 impor-
tant 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 broadcast-
ing 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 i th logical channel, for i 1. Thus CB belongs

to the category of fixed-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.

= 0 , 1 ,..., N −