Information Technology Reference
In-Depth Information
4.1 Channel Usage Analysis
Before discuss the channel usage, we make the following assumptions and def-
initions. There are C available channels in the network. Each node equips K
network interfaces that work on K different channels. K satisfies the connectiv-
ity invariant condition, which is K
2
+ 1. The transmission probability of
node n on channel c is P ( n,c ). The neighbors of node n is defined as B ( n ).
The node n detects no communication conflicts on channel c only if there is
no nodes transmitting or one node transmitting. The probability that only one
node is transmitting is
P ( i,c ) ×
(1 − P ( j, c ))
i∈B ( n ) {n}
j∈B ( n ) {n}−{i}
=
j∈B ( n ) {n}
P ( i,c )
(1
P ( j, c ))
×
P ( i,c ) .
1
i∈B ( n ) {n}
And the probability that no node is transmitting is
(1
P ( i,c )) .
i∈B ( n ) {n}
Then, the conflicting probability is 1 minus the above two parts. Thus:
P conflict ( n,c )=1
P ( i,c )
×
P ( i,c ) +1
(1
P ( j, c )) . (1)
1
i∈B ( n ) {n}
j∈B ( c ) {n}
Assume that
B ( n )
P ( i,c )= q
and
|
{
n
}|
= m.
i∈B ( n ) {n}
q can be considered as the total channel usage. Usually, if all the nodes access the
channel based on CSMA/CA and there is no hidden terminal, q will be
1. If
there are hidden terminals, q can be > 1. Because the transmission probability
of each node is
1,
P conflict ( n,c ) reaches the maximum when P ( i,c )= m for all i , using Lagrange
multiplier method. The maximum of P conflict ( n,c )is
1, q is always
m , . We can prove that with 0
q
1
m− 1 .
m + q 1
q
m
q
m
1
For a fixed m , we define function
f m ( q )= 1
m + q 1
m− 1
q
m
q
m
.
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