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by interchanging the roles of j and k in Equation (5.56). Let us illustrate the
peer-to-peer relationship with the following numerical example.
Consider three neighboring clients: x, y, and z whose types are 0.65, 0.45,
and 0.45, respectively. If they independently stream the media from the server,
x will subscribe to 6 stripes while both y and z will subscribe to 4 stripes.
However, they may collaborate and form a peer-to-peer relationship for media
streaming, as illustrated in Figure 5.25(b). For y and z, each of them subscribes
to 3 stripes from the server and periodically sends them to the coordinator,
x. On the other hand, x subscribes to another 4 stripes from the server and
periodically broadcasts all media packets to y and z. Effectively, this peer-to-
peer relationship allows the three clients to receive 10 stripes, i.e., the complete
media content.
5.3.4.4
The General Scenario
Now, let us generalize the analysis to the scenario with r neighboring
clients. Because the master-slave relationship does not change with the number
of neighboring clients, we focus our attention on the peer-to-peer relationship.
Without loss of generality, let us assume that x is the coordinator, which is
connected to a set of (r−1) neighboring helpers, denoted by R x . In general,
these (r−1) helpers may not be able to communicate with one another. We
can denote the number of subscribed stripes by y as s y , where y∈R x . On the
other hand, x subscribes to s x stripes from the server, where
s≤n. We
can obtain the threshold value for client x's type, i.e., α r (s x ), which is given
by:
E RX
s
(s x ) + E T X
s) + E RX
p
(
(
s−s x )
p
α r (s x ) =
(5.57)
E RX
s
Similarly, the threshold value for helper y's type is: α r (s y ), which is given
by:
E RX
s
(s y ) + E T X
(s y ) + E RX
(
s−s y )
p
p
α r (s y ) =
(5.58)
E RX
s
This suggests that a number of neighboring clients satisfying the above
thresholds may collaborate to improve the performance of media streaming
by utilizing their peer interfaces. This collaboration arrangement allows clients
to share the higher energy cost involved in receiving media packets from the
server directly. Although the coordinator requires a larger threshold, its energy
cost may not be the highest because it may only subscribe to few stripes from
the server, i.e., s x is small or even zero. Because the number of subscribed
stripes depends on the client types, heterogeneous clients may form either
the master-slave relationship or the peer-to-peer relationship. Motivated by
the above analysis, Yeung and Kwok [Yeung and Kwok, 2008] proposed two
protocols to guide the establishment of the two relationships.
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