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: