Information Technology Reference
In-Depth Information
individually or as a group. Similar to previous cases, the following conditions
can be obtained:
v(c r )≤V (G n )−V (G n \{c r }) ∀c r
(5.35)
v(c i )≤V (G n )−V (G 1 )−(n−1)e
(5.36)
∀c i ∈P
v(c r )≥e ∀c r (5.37)
The term “V (G n )−V (G n \{c r })” is called the marginal utility of c r . It is
the additional amount of value created by c r to the original coalition. Since
p's effort is increased by e if c r is accepted as its child, the share of value
allocated to c r is:
v(c r ) = V (G n )−V (G n \{c r })−e
(5.38)
A Specific Value Function
A specific value function for the peer selection game is proposed [Yeung
and Kwok, 2009]:
8
<
1
b i
: log(1 +
)
p∈G
V (G) =
(5.39)
∀i=p
0
otherwise
Without loss of generality, the value function is zero when the parent is
the sole coalition member, i.e., V (G 1 ) = 0. This is an increasing function in
coalition size. In other words, a new peer always brings additional value to an
existing coalition. Furthermore, a peer may create different values to different
coalitions. Therefore, the value function satisfies Conditions (5.13), (5.14), and
(5.15).
Besides the above characteristics, the value function can also differentiate
peers according to their outgoing bandwidth values. For the same coalition,
G, peer x would receive a larger share of the value than peer y if b x < b y .
The reason for that arrangement would become evident with the following
numerical example.
Consider two coalitions: G X and G Y where G X ={p x , c 1 , c 2 }and G Y =
{p y , c 3 , c 4 , c 5 }. A peer c 6 would like to join one of the two coalitions. We take
e = 0.01 and the outgoing bandwidths of the peers are listed as follows:
b 1
b 2
b 3
b 4
b 5
b 6
1
2
2
2
3
2
It is easy to see that V (G X ) = 0.92 and V (G Y ) = 0.85. If c 6 joins the
coalition G X , we have V (G X ) = 1.10 and its share of value is: V (G X )−
V (G X )−e = 0.17. On the other hand, c 6 joining coalition G Y would result in
V (G Y ) = 1.04 and its share of value is: V (G Y )−V (G Y )−e = 0.18. Therefore,
c 6 joins G Y and v(c 6 ) = 0.18. The peer's share of value, i.e., v(x), in the
coalition is then used by the parent in determining the amount of bandwidth
allocation [Yeung and Kwok, 2009].
Search WWH ::




Custom Search