Moreover, we will show that the
performance depends on the retry limit R, where R becomes eventually infinite in the
analytical model.
Let us denote with (TX) the event that a station is transmitting a frame into a time slot,
and denote with (s=i) the event that the station is found in backoff stage i.
We are ultimately interested in the unconditional probability ?„ = P{TX} that the station
transmits in a randomly chosen slot. Thanks to Bayes??™ Theorem, for i ??? (0, ??¦, R),
(25)
{ } { }{
}
{ } TX P
i s P i s TX P TX i s P = =
= = | |
which in turn can be rewritten as:
(26) { } { }
{ } {i s P
i s TX P
TX i s P TX P = =
=
=
|
| }
Since this equality holds for all i ??? (0, ??¦, R), it also holds for the summation:
(27) { } { }
{ } { ??‘ ??‘
= =
= =
=
= R
i
R
i
i s P
i s TX P
TX i s P TX P
0 0 |
| }
However, the rightmost term in the equation is a probability distribution (namely, the
probability that a station is in backoff stage i). Hence, the sum over all i ???(0, ??¦, R) equals
1. We can thus derive an expression for ?„:
{ } { }
{ } ??‘=
=
=
= = R
i i s TX P
TX i s P
TX P
0 |
|
1 ?„ (28)
Performance Study of IEEE 802.
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