Performance Study of IEEE 802.11 DCF and IEEE 802.11e EDCA 79
By substituting Eqs. (29) and (30) into Eq. (28) we can finally derive an explicit
expression for ?„:
, (32)
( ) ??‘ ??‘
=
+
=
+ ??’
??’
+
=
+
??’
??’
= R
i
i
i
R
R
i
i R
i
p
p
) p (
p
p ) p (
0
1
0
1 1
1 1
1
1
1
1
1
?? ??
?„
where we have made use of the fact that P{s=i|TX} is a distribution which, in the
considered range (0,??¦,R), sums to 1.
This expression depends on the values R (retry limit), and the sequence of ??
i values
(the mean per-stage backoff values), which are specified by the employed backoff model.
Moreover, it depends on the conditional collision probability p which is still unknown. To
find the value of p, it is sufficient to note that the probability p that a transmitted frame
encounters a collision, is the probability that, in a time slot, at least one of the N-1
remaining stations transmits. The fundamental independence assumption #1 given at the
beginning of this section implies that each transmission ???sees??? the system in the same state,
i.e., in steady state. At steady state, according to assumption #2, each remaining station
transmits a frame with constant permission probability ?„.
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