Incentives - Peer-to-Peer Computing: Applications, Architecture, Protocols, and Challenges - page 121

where α S (i) is given by:

E R p (i)
E RX
s

α S (i) = (5.52)

From Equations (5.51) and (5.52), the threshold values for master and
slave as α varies between 0 and 1.2, are shown in Figure 5.23. When two
neighboring clients whose types satisfy the two thresholds collaborate, they
form a master-slave relationship for media streaming. We can see that the type
of a slave is much smaller than that of a master. This is because the slave does
not contribute but relies mostly on the master for all media packets. On the
other hand, the energy cost of being a master is higher than that of acting
alone, which leads to the increase in the threshold values. Let us illustrate the
master-slave relationship with the following numerical example.

FIGURE 5.23: Master-slave: number of subscribed stripes versus the type
of a client (n = 10).

Consider two neighboring clients: x and y whose types are 1.2 and 0.25,
respectively. If each of them independently streams the media from the server,
x will subscribe to 10 stripes while y will subscribe to 2 stripes. However, they
may collaborate and form a master-slave relationship for media streaming, as
illustrated in Figure 5.22(a). Specifically, x becomes the master and y is the
slave. Equation (5.51) suggests that x subscribes to 10 stripes and also sends
them to y, which receives the 10 stripes via its peer interface.
The master-slave collaboration arrangement allows the slave to take advan-
tage of the generosity of the master, which provides the media content through
its peer interface. The performance of the slave is improved at the expense of
the master's energy resources. However, it would be more interesting if both
clients contribute their resources to form a peer-to-peer relationship, as de-
picted in Figure 5.22(b). Here, we can assume that client x and y subscribe to
i and j stripes from the server, respectively. They periodically exchange their
stripes with each other using the peer interfaces. Effectively, each client ob-
tains (i + j) stripes of the media content, where (i + j)≤n. This peer-to-peer
collaboration arrangement improves the performance of both clients. However,
the values of i and j depend on the type of the corresponding clients. If client
x subscribes to i stripes from the server, we require: α x ≥α 2 (i), where α 2 (i)