To determine the average delay in the finite retry case, we can still start from Little??™s
Result, but we need to replace N in Eq. (43) with the average number of HOL frames that
will be successfully delivered. This value is lower than the number of competing stations,
as some of the competing frames will ultimately be dropped. Thus, Eq. (43) can be
rewritten as follows:
{ } ( )
] P [ E / S
LOSS P N D ??’
= 1 (44)
where P{LOSS} represents the probability that a randomly chosen HOL frame will
ultimately be dropped. Let us now randomly pick an HOL frame among the N contending
ones. Such an HOL frame can be found in any of the i=0,??¦,R possible backoff stages. The
probability that a random frame is found in backoff stage i has been expressed in Eq. (26),
and can be rewritten in terms of known values p, ?„ = P{TX} and ??
i by means of the
equalities in Eqs. (29) and (30):
(45)
{ } { } { }
{ } ) (
p
p ) p (
i s | TX P
TX | i s P TX P i s P i R
i
?? ?„ +
??’
??’
=
=
=
= = + 1
1
1
1
By conditioning on the backoff stage i, P{LOSS} can be now computed as:
) (46)
{ } { } { }
(
( ) ??‘
??‘
??‘
=
+
+
=
+
??’ +
=
+ ??’
??’
=
+
??’
??’
?‹… =
= = ?‹… = =
R
i
i R
R
R
i
i R
i
i R
R
i
) p (
p
p
p
p ) p ( p
i s P i s | LOSS P LOSS P
0
1
1
0
1
1
0
1 1
1
1
1
1
?? ?„
?? ?„
The average access delay expression is now found by substituting Eq.
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