Information Technology Reference

In-Depth Information

Figure 3. Multi-hop ad hoc network.

The probability of a packet being successfully received at the receiver node is the

probability of success of the packet at forward and reverse channels [7]:

PA

=

(

−

PER

)(

1

−

PER

)

f

r

Thus, the packet error probability for ARQ packets is:

PER

=

1

−

[(

1

−

PER

)(

1

−

PER

)]

f

r

This expression can be rewritten as:

PER

=

PER

+

PER

−

(

PER

)(

PER

)

f

r

f

r

The probability of a packet being successfully received at the sink node for the packets

without ARQ is:

P

=

( −

PER

)

H

narq

f

where
H
is the total number of hops. Let
n
be
the number of retransmissions of ARQ

packets. Assuming perfect error detection of the CRC code and infinite retransmissions, the

probability that a packet arrives correctly at the sink node is:

H

=
∞

=

⎤

[

]

P

p

[

n

]

=

1

⎣

⎦

arq

N

n

1

r

The probability of
n
retransmissions is the product of failure in the
n-1
transmissions and

the probability of success at the
n
th
transmission:

p

[

n

]

=

(

−

PER

)(

PER

)

n

−

1

N

Thus, we evaluate the average number of retransmissions
N
in one hop: