11 DCF and IEEE 802.11e EDCA 78
The value ?„ is thus known, as long as we find an expression for P{s=i|TX} and
P{TX|s=i}. Let us first focus on the conditional probability P{s=i|TX} that a transmitting
station is found in backoff stage i. Since, for i>0, this probability is given by the probability
that the station, in the previous transmission event, was found in stage i-1 and that the
transmission failed (by assumption, this occurs with constant probability p), it follows that
P{s=i|TX} is a geometric distribution8 (truncated, in the case of finite value R), i.e.:
{ } ) R ,..., ( i
p
p ) p ( TX | i s P R
i
0
1
1
1
???
??’
??’
= = +
(29)
Let us now find an explicit expression for P{TX|s=i}. This represents the transmission
probability of a station in backoff stage i, or, in other words, the frequency of transmission
(the number of transmission slots per channel slot) for a station assumed to always remain
in backoff stage i. Under very general conditions9, this probability can be computed by
dividing the average number of slots spent in the transmission state while in stage i (owing
to the time scale adopted, exactly 1 slot), with the average number of total slots spent by
the station in stage i (i.
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